Von Smekal, L; Sternbeck, A; Williams, A G
2007-01-01
We propose a modified lattice Landau gauge based on stereographically projecting the link variables on the circle S^1 -> R for compact U(1) or the 3-sphere S^3 -> R^3 for SU(2) before imposing the Landau gauge condition. This can reduce the number of Gribov copies exponentially and solves the Gribov problem in compact U(1) where it is a lattice artifact. Applied to the maximal Abelian subgroup this might be just enough to avoid the perfect cancellation amongst the Gribov copies in a lattice BRST formulation for SU(N), and thus to avoid the Neuberger 0/0 problem. The continuum limit of the Landau gauge remains unchanged.
Digital lattice gauge theories
Zohar, Erez; Reznik, Benni; Cirac, J Ignacio
2016-01-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a $\\mathbb{Z}_{3}$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms...
Investigating jet quenching on the lattice
Panero, Marco; Schäfer, Andreas
2014-01-01
Due to the dynamical, real-time, nature of the phenomenon, the study of jet quenching via lattice QCD simulations is not straightforward. In this contribution, however, we show how one can extract information about the momentum broadening of a hard parton moving in the quark-gluon plasma, from lattice calculations. After discussing the basic idea (originally proposed by Caron-Huot), we present a recent study, in which we estimated the jet quenching parameter non-perturbatively, from the lattice evaluation of a particular set of gauge-invariant operators.
Weisz, Peter; Majumdar, Pushan
2012-03-01
Lattice gauge theory is a formulation of quantum field theory with gauge symmetries on a space-time lattice. This formulation is particularly suitable for describing hadronic phenomena. In this article we review the present status of lattice QCD. We outline some of the computational methods, discuss some phenomenological applications and a variety of non-perturbative topics. The list of references is severely incomplete, the ones we have included are text books or reviews and a few subjectively selected papers. Kronfeld and Quigg (2010) supply a reasonably comprehensive set of QCD references. We apologize for the fact that have not covered many important topics such as QCD at finite density and heavy quark effective theory adequately, and mention some of them only in the last section "In Brief". These topics should be considered in further Scholarpedia articles.
Digital lattice gauge theories
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.
Gauge Fixing on the Lattice without Ambiguity
Vink, Jeroen C; 10.1016/0370-2693(92)91372-G
2009-01-01
A new gauge fixing condition is discussed, which is (lattice) rotation invariant, has the `smoothness' properties of the Landau gauge but can be efficiently computed and is unambiguous for almost all lattice gauge field configurations.
Introduction to lattice gauge theory
Gupta, R.
The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off approx. = 1/alpha, where alpha is the lattice spacing. The continuum (physical) behavior is recovered in the limit alpha yields 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics.
Manifestly Gauge Covariant Treatment of Lattice Chiral Fermion
Suzuki, H
1997-01-01
We propose a lattice formulation of the chiral fermion which maximally respects the gauge symmetry and simultaneously is free of the unwanted species doublers. This is achieved by directly dealing with the lattice fermion propagator and the composite operators, rather than the lattice action and the fermionic determinant. The latter is defined as a functional integral of the expectation value of the gauge current operator with respect to the background gauge field. The gauge anomaly is characterized as a non-integrability of this integration process and, the determinant is defined only for anomaly free cases. Gauge singlet operators on the other hand are always regularized gauge invariantly. Some perturbative check is performed to confirm the gauge covariance and the absence of the doublers. This formulation can be applied rather straightforwardly to numerical simulations in the quenched approximation.
Lattice QCD simulations beyond the quenched approximation
Energy Technology Data Exchange (ETDEWEB)
Ukawa, A. (European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.)
1989-07-01
Present status of lattice QCD simulations incorporating the effects of dynamical quarks is presented. After a brief review of the formalism of lattice QCD, the dynamical fermion algorithms in use today are described. Recent attempts at the hadron mass calculation are discussed in relation to the quenched results, and current understanding on the finite temperature behavior of QCD is summarized. (orig.).
Light hadron spectrum and decay constants in quenched lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Allton, C.R.; Lellouch, L.; Sachrajda, C.T.; Wittig, H. (Physics Department, The University, Southampton SO9 5NH (United Kingdom)); Baxter, R.M.; Booth, S.P.; Bowler, K.C.; Henty, D.S.; Kenway, R.D.; McNeile, C.; Pendleton, B.J.; Richards, D.G.; Simone, J.N.; Simpson, A.D. (Department of Physics, The University of Edinburgh, Edinburgh EH9 3JZ (United Kingdom)); (UKQCD Collaboration)
1994-01-01
We present results for light hadrons composed of both degenerate and nondegenerate quarks in quenched lattice QCD. We calculate masses and decay constants using 60 gauge configurations with an [ital O]([ital a])-improved fermion action at [beta]=6.2. Using the [rho] mass to set the scale we find hadron masses within two to three standard deviations of the experimental values (given in parentheses): [ital m][sub [ital K
Technicolor and Lattice Gauge Theory
Chivukula, R Sekhar
2010-01-01
Technicolor and other theories of dynamical electroweak symmetry breaking invoke chiral symmetry breaking triggered by strong gauge-dynamics, analogous to that found in QCD, to explain the observed W, Z, and fermion masses. In this talk we describe why a realistic theory of dynamical electroweak symmetry breaking must, relative to QCD, produce an enhanced fermion condensate. We quantify the degree to which the technicolor condensate must be enhanced in order to yield the observed quark masses, and still be consistent with phenomenological constraints on flavor-changing neutral-currents. Lattice studies of technicolor and related theories provide the only way to demonstrate that such enhancements are possible and, hopefully, to discover viable candidate models. We comment briefly on the current status of non-perturbative investigations of dynamical electroweak symmetry breaking, and provide a "wish-list" of phenomenologically-relevant properties that are important to calculate in these theories
Lattice gauge theories and Monte Carlo simulations
Rebbi, Claudio
1983-01-01
This volume is the most up-to-date review on Lattice Gauge Theories and Monte Carlo Simulations. It consists of two parts. Part one is an introductory lecture on the lattice gauge theories in general, Monte Carlo techniques and on the results to date. Part two consists of important original papers in this field. These selected reprints involve the following: Lattice Gauge Theories, General Formalism and Expansion Techniques, Monte Carlo Simulations. Phase Structures, Observables in Pure Gauge Theories, Systems with Bosonic Matter Fields, Simulation of Systems with Fermions.
Lattice Gauge Theories and Spin Models
Mathur, Manu
2016-01-01
The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. These $Z_2$ results are directly generalized to SU(N) lattice gauge theory in $(2+1)$ dimensions to obtain a dual SU(N) spin model in terms of the SU(N) magnetic fields and electric scalar potentials. The gauge-spin duality naturally leads to a new gauge invariant disorder operator for SU(N) lattice gauge theory. A variational ground state of the dual SU(2) spin model with only nearest neighbour interactions is constructed to analyze SU(2) lattice gauge theory.
Gauge-fixing approach to lattice chiral gauge theories
Bock, W; Shamir, Y; Bock, Wolfgang; Golterman, Maarten F.L.; Shamir, Yigal
1998-01-01
We review the status of our recent work on the gauge-fixing approach to lattice chiral gauge theories. New numerical results in the reduced version of a model with a U(1) gauge symmetry are presented which strongly indicate that the factorization of the correlation functions of the left-handed neutral and right-handed charged fermion fields, which we established before in perturbation theory, holds also nonperturbatively.
Topological Charge of Lattice Abelian Gauge Theory
Fujiwara, T; Wu, K
2001-01-01
Configuration space of abelian gauge theory on a periodic lattice becomes topologically disconnected by excising exceptional gauge field configurations. It is possible to define a U(1) bundle from the nonexceptional link variables by a smooth interpolation of the transition functions. The lattice analogue of Chern character obtained by a cohomological technique based on the noncommutative differential calculus is shown to give a topological charge related to the topological winding number of the U(1) bundle.
Dynamical Gauge Fields on Optical Lattices: A Lattice Gauge Theorist Point of View
Meurice, Yannick
2011-01-01
Dynamical gauge fields are essential to capture the short and large distance behavior of gauge theories (confinement, mass gap, chiral symmetry breaking, asymptotic freedom). I propose two possible strategies to use optical lattices to mimic simulations performed in lattice gauge theory. I discuss how new developments in optical lattices could be used to generate local invariance and link composite operators with adjoint quantum numbers that could play a role similar to the link variables used in lattice gauge theory. This is a slightly expanded version of a poster presented at the KITP Conference: Frontiers of Ultracold Atoms and Molecules (Oct 11-15, 2010) that I plan to turn into a more comprehensive tutorial that could be used by members of the optical lattice and lattice gauge theory communities. Suggestions are welcome.
Thermal dilepton rates from quenched lattice QCD
Ding, H -T; Kaczmarek, O; Karsch, F; Laermann, E; Mukherjee, S; Müller, M; Soeldner, W
2013-01-01
We present new lattice results on the continuum extrapolation of the vector current correlation function. Lattice calculations have been carried out in the deconfined phase at a temperature of 1.1 Tc, extending our previous results at 1.45 Tc, utilizing quenched non-perturbatively clover-improved Wilson fermions and light quark masses. A systematic analysis on multiple lattice spacings allows to perform the continuum limit of the correlation function and to extract spectral properties in the continuum limit. Our current analysis suggests the results for the electrical conductivity are proportional to the temperature and the thermal dilepton rates in the quark gluon plasma are comparable for both temperatures. Preliminary results of the continuum extrapolated correlation function at finite momenta, which relates to thermal photon rates, are also presented.
Lattice Chiral Fermions Through Gauge Fixing
Bock, W; Shamir, Y; Bock, Wolfgang; Golterman, Maarten; Shamir, Yigal
1998-01-01
We study a concrete lattice regularization of a U(1) chiral gauge theory. We use Wilson fermions, and include a Lorentz gauge-fixing term and a gauge-boson mass counterterm. For a reduced version of the model, in which the gauge fields are constrained to the trivial orbit, we show that there are no species doublers, and that the fermion spectrum contains only the desired states in the continuum limit, namely charged left-handed (LH) fermions and neutral right-handed (RH) fermions.
Global anomalies in Chiral Lattice Gauge Theory
Bär, Oliver; Campos, Isabel
As first realized by Witten an SU(2) gauge theory coupled to a single Weyl fermion suffers from a global anomaly. This problem is addressed here in the context of the recent developments on chiral gauge theories on the lattice. We find Witten's anomaly manifests in the impossibility of defining globally a fermion measure that reproduces the proper continuum limit. Moreover, following Witten's original argument, we check numerically the crossing of the lowest eigenvalues of Neuberger's operator along a path connecting two gauge fields that differ by a topologically non-trivial gauge transformation.
Entanglement of Distillation for Lattice Gauge Theories
Van Acoleyen, Karel; Bultinck, Nick; Haegeman, Jutho; Marien, Michael; Scholz, Volkher B.; Verstraete, Frank
2016-09-01
We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws—including a topological correction—emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.
Light-cone Wilson loop in classical lattice gauge theory
Laine, M
2013-01-01
The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity.
Energy Technology Data Exchange (ETDEWEB)
DeGrand, T. [Univ. of Colorado, Boulder, CO (United States). Dept. of Physics
1997-06-01
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and {alpha}{sub s} (M{sub z}), and B-{anti B} mixing. 67 refs., 36 figs.
Integrable Lattice Models From Gauge Theory
Witten, Edward
2016-01-01
These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge theory in four dimensions. This construction will be compared to the more familiar relationship between quantum knot invariants in three dimensions and Chern-Simons gauge theory. (Based on a Whittaker Colloquium at the University of Edinburgh and a lecture at Strings 2016 in Beijing.)
Gauge-Higgs Unification on the Lattice
Irges, Nikos; Yoneyama, Kyoko
2012-01-01
The simplest Gauge-Higgs Unification model is a five-dimensional SU(2) gauge theory compactified on the S^1/Z_2 orbifold, such that on the four-dimensional boundaries of space-time there is an unbroken U(1) symmetry and a complex scalar, the latter identified with the Higgs boson. Perturbatively the U(1) remains spontaneously unbroken. Earlier lattice Monte Carlo simulations revealed however that the spontaneous breaking of the U(1) does occur at the non-perturbative level. Here, we verify the Monte Carlo result via an analytical lattice Mean-Field expansion.
Matrix product states for Hamiltonian lattice gauge theories
Buyens, Boye; Haegeman, Jutho; Verstraete, Frank
2014-01-01
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems. In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model. We deduced the ground state and lowest lying excitations. Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field. In this proceeding we continue our work on the Schwinger model. We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states. Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.
Lattice Landau Gauge via Stereographic Projection
von Smekal, L.; Mehta, D.; Sternbeck, A.
alexander.jorkowski@student.adelaide.edu.au, dhagash.mehta@adelaide.edu.au, andre.sternbeck@adelaide.edu.au The complete cancellation of Gribov copies and the Neuberger 0/0 problem of lattice BRST can be avoided in modified lattice Landau gauge. In compact U(1), where the problem is a lattice artifact, there remain to be Gribov copies but their number is exponentially reduced. Moreover, there is no cancellation of copies there as the sign of the Faddeev-Popov determinant is posi- tive. Applied to the maximal Abelian subgroup this avoids the perfect cancellation amongst the remaining Gribov copies for SU(N) also. In addition, based on a definition of gauge fields on the lattice as stereographically-projected link variables, it provides a framework for gauge fixed Monte-Carlo simulations. This will include all Gribov copies in the spirit of BRST. Their average is not zero, as demonstrated explicitly in simple models. This might resolve present discrepancies between gauge-fixed lattice and continuum studies of QCD Green’s functions.
Local gauge symmetry on optical lattices?
Liu, Yuzhi; Tsai, Shan-Wen
2012-01-01
The versatile technology of cold atoms confined in optical lattices allows the creation of a vast number of lattice geometries and interactions, providing a promising platform for emulating various lattice models. This opens the possibility of letting nature take care of sign problems and real time evolution in carefully prepared situations. Up to now, experimentalists have succeeded to implement several types of Hubbard models considered by condensed matter theorists. In this proceeding, we discuss the possibility of extending this effort to lattice gauge theory. We report recent efforts to establish the strong coupling equivalence between the Fermi Hubbard model and SU(2) pure gauge theory in 2+1 dimensions by standard determinantal methods developed by Robert Sugar and collaborators. We discuss the possibility of using dipolar molecules and external fields to build models where the equivalence holds beyond the leading order in the strong coupling expansion.
Lattice gauge theories and spin models
Mathur, Manu; Sreeraj, T. P.
2016-10-01
The Wegner Z2 gauge theory-Z2 Ising spin model duality in (2 +1 ) dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner Z2 gauge-spin duality is directly generalized to SU(N) lattice gauge theory in (2 +1 ) dimensions to obtain the SU(N) spin model in terms of the SU(N) magnetic fields and their conjugate SU(N) electric scalar potentials. The exact and complete solutions of the Z2, U(1), SU(N) Gauss law constraints in terms of the corresponding spin or dual potential operators are given. The gauge-spin duality naturally leads to a new gauge invariant magnetic disorder operator for SU(N) lattice gauge theory which produces a magnetic vortex on the plaquette. A variational ground state of the SU(2) spin model with nearest neighbor interactions is constructed to analyze SU(2) gauge theory.
Narayanan, Rajamani
2008-01-01
Wilson loops in large N gauge theory exhibit a weak to strong coupling transition as the loop is dilated. A multiplicative matrix model captures the universal behavior associated with this transition. A universal scaling function is obtained in a double scaling limit. Numerical studies show that both large N QCD in three dimensions and the SU(N) principal chiral model in two dimensions are in the same universality class.
Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging
Energy Technology Data Exchange (ETDEWEB)
Solbrig, Stefan
2008-07-01
In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)
Dynamical gauge symmetry breaking on the lattice
Energy Technology Data Exchange (ETDEWEB)
Farakos, K.; Koutsoumbas, G.; Zoupanos, G. (National Research Centre for the Physical Sciences Democritos, Athens (Greece))
1990-10-11
We study, using lattice techniques, the dynamical symmetry breaking of a three-dimensional theory that mimics the electroweak sector of the standard model. We show that in the strong coupling limit of a QCD-like theory the fermion condensates which are produced induce dynamical symmetry breaking of the sector corresponding to the electroweak gauge group. (orig.).
Recent advances in lattice gauge theories
Indian Academy of Sciences (India)
R V Gavai
2000-04-01
Recent progress in the ﬁeld of lattice gauge theories is brieﬂy reviewed for a nonspecialist audience. While the emphasis is on the latest and more deﬁnitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.
Charmonium properties in hot quenched lattice QCD
Ding, H -T; Kaczmarek, O; Karsch, F; Satz, H; Soeldner, W
2012-01-01
We study the properties of charmonium states at finite temperature in quenched QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above $T_c$. Our analysis suggests that both S wave states ($J/\\psi$ and $\\eta_c$) and P wave states ($\\chi_{c0}$ and $\\chi_{c1}$) disappear already at about $1.5 T_c$. The charm diffusion coefficient is estimated through the Kubo formula and found to be compatible with zero below $T_c$ and approximately $1/\\pi T$ at $1.5 T_c\\lesssim T\\lesssim 3 T_c$.
Charmonium properties in hot quenched lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Ding, H. -T.; Francis, A.; Kaczmarek, O.; Karsch, F.; Satz, H.; Soeldner, W.
2012-07-01
We study the properties of charmonium states at finite temperature in quenched QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above Tc. Our analysis suggests that both S wave states (J/ψ and η_{c}) and P wave states (χ_{c0} and χ_{c1}) disappear already at about 1.5Tc. The charm diffusion coefficient is estimated through the Kubo formula and found to be compatible with zero below T_{c} and approximately 1/πT at 1.5T_{c}≲T≲3T_{c}.
Charm as a domain wall fermion in quenched lattice QCD
Lin, H W; Soni, A; Yamada, N; Lin, Huey-Wen; Ohta, Shigemi; Soni, Amarjit; Yamada, Norikazu
2006-01-01
We report a study describing the charm quark by a domain-wall fermion (DWF) in lattice quantum chromodynamics (QCD). Our study uses a quenched gauge ensemble with the DBW2 rectangle-improved gauge action at a lattice cutoff of $a^{-1} \\sim 3$ GeV. We calculate masses of heavy-light (charmed) and heavy-heavy (charmonium) mesons with spin-parity $J^P = 0^\\mp$ and $1^\\mp$, leptonic decay constants of the charmed pseudoscalar mesons ($D$ and $D_s$), and the $D^0$-$\\bar{D^0}$ mixing parameter. The charm quark mass is found to be $m^{\\bar{\\rm MS}}_{c}(m_{c})=1.24(1)(18)$ GeV. The mass splittings in charmed-meson parity partners $\\Delta_{q,J=0}$ and $\\Delta_{q, J=1}$ are degenerate within statistical errors, in accord with experiment, and they satisfy a relation $\\Delta_{q=ud, J} > \\Delta_{q=s, J}$, also consistent with experiment. A C-odd axial vector charmonium state, $h_c), lies 22(11) MeV above the $\\chi_{c1}$ meson, or $m_{h_{c}} = 3533(11)_{\\rm stat.}$ MeV using the experimental $\\chi_{c1}) mass. However, in t...
National Computational Infrastructure for Lattice Gauge Theory
Energy Technology Data Exchange (ETDEWEB)
Brower, Richard C.
2014-04-15
SciDAC-2 Project The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory, from March 15, 2011 through March 14, 2012. The objective of this project is to construct the software needed to study quantum chromodynamics (QCD), the theory of the strong interactions of sub-atomic physics, and other strongly coupled gauge field theories anticipated to be of importance in the energy regime made accessible by the Large Hadron Collider (LHC). It builds upon the successful efforts of the SciDAC-1 project National Computational Infrastructure for Lattice Gauge Theory, in which a QCD Applications Programming Interface (QCD API) was developed that enables lattice gauge theorists to make effective use of a wide variety of massively parallel computers. This project serves the entire USQCD Collaboration, which consists of nearly all the high energy and nuclear physicists in the United States engaged in the numerical study of QCD and related strongly interacting quantum field theories. All software developed in it is publicly available, and can be downloaded from a link on the USQCD Collaboration web site, or directly from the github repositories with entrance linke http://usqcd-software.github.io
Chiral and continuum extrapolation of partially quenched lattice results
Energy Technology Data Exchange (ETDEWEB)
C.R. Allton; W. Armour; D.B. Leinweber; A.W. Thomas; R.D. Young
2005-04-01
The vector meson mass is extracted from a large sample of partially quenched, two-flavor lattice QCD simulations. For the first time, discretization, finite-volume and partial quenching artifacts are treated in a unified chiral effective field theory analysis of the lattice simulation results.
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-01-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.
Noncompact lattice formulation of gauge theories
Friedberg, R; Pang, Y; Ren, H C
1995-01-01
We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation \\,n\\, and a wave number \\,\\vec K\\, restricted to the Brillouin zone. A noncompact formulation of lattice QCD (or QED) can be derived by restricting the expansion only to the \\,0^{th}-band (\\,n = 0\\,) functions, which are simple continuum interpolations of discrete values associated with sites or links on a lattice. The exact continuum theory can be reached through the inclusion of all \\,n = 0\\, and \\,n \
Chiral symmetry and lattice gauge theory
Creutz, M
1994-01-01
I review the problem of formulating chiral symmetry in lattice gauge theory. I discuss recent approaches involving an infinite tower of additional heavy states to absorb Fermion doublers. For hadronic physics this provides a natural scheme for taking quark masses to zero without requiring a precise tuning of parameters. A mirror Fermion variation provides a possible way of extending the picture to chirally coupled light Fermions. Talk presented at "Quark Confinement and the Hadron Spectrum," Como, Italy, 20-24 June 1994.
Gauge theories and integrable lattice models
Witten, Edward
1989-08-01
Investigations of new knot polynomials discovered in the last few years have shown them to be intimately connected with soluble models of two dimensional lattice statistical mechanics. In this paper, these results, which in time may illuminate the whole question of why integrable lattice models exist, are reconsidered from the point of view of three dimensional gauge theory. Expectation values of Wilson lines in three dimensional Chern-Simons gauge theories can be computed by evaluating the partition functions of certain lattice models on finite graphs obtained by projecting the Wilson lines to the plane. The models in question — previously considered in both the knot theory and statistical mechanics — are IRF models in which the local Boltzmann weights are the matrix elements of braiding matrices in rational conformal field theories. These matrix elements, in turn, can be presented in three dimensional gauge theory in terms of the expectation value of a certain tetrahedral configuration of Wilson lines. This representation makes manifest a surprising symmetry of the braiding matrix elements in conformal field theory.
Lattice gaugefixing and other optics in lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Yee, Ken
1992-06-01
We present results from four projects. In the first, quark and gluon propagators and effective masses and {Delta}I = 1/2 Rule operator matching coefficients are computed numerically in gaugefixed lattice QCD. In the second, the same quantities are evaluated analytically in the strong coupling, N {yields} {infinity} limit. In the third project, the Schwinger model is studied in covariant gauges, where we show that the effective electron mass varies with the gauge parameter and that longitudinal gaugefixing ambiguities affect operator product expansion coefficients (analogous to {Delta}I = 1/2 Rule matching coefficients) determined by matching gauge variant matrix elements. However, we find that matching coefficients even if shifted by the unphysical modes are {xi} invariant. In the fourth project, we show that the strong coupling parallelogram lattice Schwinger model as a different thermodynamic limit than the weak coupling continuum limit. As a function of lattice skewness angle these models span the {Delta} = {minus}1 critical line of 6-vertex models which, in turn, have been identified as c = 1 conformal field theories.
Lattice gaugefixing and other optics in lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Yee, Ken.
1992-06-01
We present results from four projects. In the first, quark and gluon propagators and effective masses and {Delta}I = 1/2 Rule operator matching coefficients are computed numerically in gaugefixed lattice QCD. In the second, the same quantities are evaluated analytically in the strong coupling, N {yields} {infinity} limit. In the third project, the Schwinger model is studied in covariant gauges, where we show that the effective electron mass varies with the gauge parameter and that longitudinal gaugefixing ambiguities affect operator product expansion coefficients (analogous to {Delta}I = 1/2 Rule matching coefficients) determined by matching gauge variant matrix elements. However, we find that matching coefficients even if shifted by the unphysical modes are {xi} invariant. In the fourth project, we show that the strong coupling parallelogram lattice Schwinger model as a different thermodynamic limit than the weak coupling continuum limit. As a function of lattice skewness angle these models span the {Delta} = {minus}1 critical line of 6-vertex models which, in turn, have been identified as c = 1 conformal field theories.
Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions
Fujiwara, T; Wu, K; Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
1999-01-01
Axial anomaly of lattice abelian gauge theory in hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a multiplicative constant for finite lattice spacing and can be interpreted as the Chern character of the abelian lattice gauge theory.
Manifestly Gauge Covariant Formulation of Lattice Chiral Fermions
Okuyama, K; Okuyama, Kiyoshi; Suzuki, Hiroshi
1997-01-01
We propose a new formulation of chiral fermions on a lattice, on the basis of a lattice extension of the covariant regularization scheme in continuum field theory. The species doublers do not emerge. The real part of the effective action is just one half of that of Dirac-Wilson fermion and is always gauge invariant even with a finite lattice spacing. The gauge invariance of the imaginary part, on the other hand, sets a severe constraint which is a lattice analogue of the gauge anomaly free condition. For real gauge representations, the imaginary part identically vanishes and the gauge invariance becomes exact.
Lattice gauge theories and Monte Carlo algorithms
Energy Technology Data Exchange (ETDEWEB)
Creutz, M. (Brookhaven National Lab., Upton, NY (USA). Physics Dept.)
1989-07-01
Lattice gauge theory has become the primary tool for non-perturbative calculations in quantum field theory. These lectures review some of the foundations of this subject. The first lecture reviews the basic definition of the theory in terms of invariant integrals over group elements on lattice bonds. The lattice represents an ultraviolet cutoff, and renormalization group arguments show how the bare coupling must be varied to obtain the continuum limit. Expansions in the inverse of the coupling constant demonstrate quark confinement in the strong coupling limit. The second lecture turns to numerical simulation, which has become an important approach to calculating hadronic properties. Here I discuss the basic algorithms for obtaining appropriately weighted gauge field configurations. The third lecture turns to algorithms for treating fermionic fields, which still require considerably more computer time than needed for purely bosonic simulations. Some particularly promising recent approaches are based on global accept-reject steps and should display a rather favorable dependence of computer time on the system volume. (orig.).
Entanglement in Weakly Coupled Lattice Gauge Theories
Radicevic, Djordje
2015-01-01
We present a direct lattice gauge theory computation that, without using dualities, demonstrates that the entanglement entropy of Yang-Mills theories with arbitrary gauge group $G$ contains a generic logarithmic term at sufficiently weak coupling $e$. In two spatial dimensions, for a region of linear size $r$, this term equals $\\frac{1}{2} \\dim(G) \\log\\left(e^2 r\\right)$ and it dominates the universal part of the entanglement entropy. Such logarithmic terms arise from the entanglement of the softest mode in the entangling region with the environment. For Maxwell theory in two spatial dimensions, our results agree with those obtained by dualizing to a compact scalar with spontaneous symmetry breaking.
Lattice Gauge Field Theory and Prismatic Sets
DEFF Research Database (Denmark)
Akyar, Bedia; Dupont, Johan Louis
as and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying......We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set and the prismatic star of . Both have the same homotopy type...
Parallel supercomputers for lattice gauge theory.
Brown, F R; Christ, N H
1988-03-18
During the past 10 years, particle physicists have increasingly employed numerical simulation to answer fundamental theoretical questions about the properties of quarks and gluons. The enormous computer resources required by quantum chromodynamic calculations have inspired the design and construction of very powerful, highly parallel, dedicated computers optimized for this work. This article gives a brief description of the numerical structure and current status of these large-scale lattice gauge theory calculations, with emphasis on the computational demands they make. The architecture, present state, and potential of these special-purpose supercomputers is described. It is argued that a numerical solution of low energy quantum chromodynamics may well be achieved by these machines.
Quiver gauge theories and integrable lattice models
Yagi, Junya
2015-01-01
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\\mathcal{N} = 1$ theories known as brane box and brane tilling models, 3d $\\mathcal{N} = 2$ and 2d $\\mathcal{N} = (2,2)$ theories obtained from them by compactification, and 2d $\\mathcal{N} = (0,2)$ theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.
Quiver gauge theories and integrable lattice models
Energy Technology Data Exchange (ETDEWEB)
Yagi, Junya [International School for Advanced Studies (SISSA),via Bonomea 265, 34136 Trieste (Italy); INFN - Sezione di Trieste,via Valerio 2, 34149 Trieste (Italy)
2015-10-09
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d N=1 theories known as brane box and brane tilling models, 3d N=2 and 2d N=(2,2) theories obtained from them by compactification, and 2d N=(0,2) theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.
From lattice gauge theories to hydrogen atoms
Directory of Open Access Journals (Sweden)
Manu Mathur
2015-10-01
Full Text Available We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space Hp of pure SU(22+1 lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms. One hydrogen atom is assigned to every plaquette of the lattice. A complete orthonormal description of the Wilson loop basis in Hp is obtained by all possible angular momentum Wigner couplings of hydrogen atom energy eigenstates |n l m〉 describing electric fluxes on the loops. The SU(2 gauge invariance implies that the total angular momenta of all hydrogen atoms vanish. The canonical transformations also enable us to rewrite the Kogut–Susskind Hamiltonian in terms of fundamental Wilson loop operators and their conjugate electric fields. The resulting loop Hamiltonian has a global SU(2 invariance and a simple weak coupling (g2→0 continuum limit. The canonical transformations leading to the loop Hamiltonian are valid for any SU(N. The ideas and techniques can also be extended to higher dimension.
Modified $U(1)$ lattice gauge theory towards realistic lattice QED
Bornyakov, V G; Müller-Preussker, M
1992-01-01
We study properties of the compact $~4D~$ $U(1)$ lattice gauge theory with monopoles {\\it removed}. Employing Monte Carlo simulations we calculate correlators of scalar, vector and tensor operators at zero and nonzero momenta $~\\vec{p}~$. We confirm that the theory without monopoles has no phase transition, at least, in the interval $~0 < \\beta \\leq 2~$. There the photon becomes massless and fits the lattice free field theory dispersion relation very well. The energies of the $~0^{++}~$, $~1^{+-}~$ and $~2^{++}~$ states show a rather weak dependence on the coupling in the interval of $~\\beta~$ investigated, and their ratios are practically constant. We show also a further modification of the theory suppressing the negative plaquettes to improve drastically the overlap with the lowest states (at least, for $~J=1$).
Wilson loop expectations in $SU(N)$ lattice gauge theory
Jafarov, Jafar
2016-01-01
This article gives a rigorous formulation and proof of the $1/N$ expansion for Wilson loop expectations in strongly coupled $SU(N)$ lattice gauge theory in any dimension. The coefficients of the expansion are represented as absolutely convergent sums over trajectories in a string theory on the lattice, establishing a kind of gauge-string duality. Moreover, it is shown that in large $N$ limit, calculations in $SU(N)$ lattice gauge theory with coupling strength $2\\beta$ corresponds to those in $SO(N)$ lattice gauge theory with coupling strength $\\beta$ when $|\\beta|$ is sufficiently small.
Testing chiral effective theory with quenched lattice QCD
Giusti, Leonardo; Necco, S; Peña, C; Wennekers, J; Wittig, H
2008-01-01
We investigate two-point correlation functions of left-handed currents computed in quenched lattice QCD with the Neuberger-Dirac operator. We consider two lattice spacings a~0.09,0.12 fm and two different lattice extents L~ 1.5, 2.0 fm; quark masses span both the p- and the epsilon-regimes. We compare the results with the predictions of quenched chiral perturbation theory, with the purpose of testing to what extent the effective theory reproduces quenched QCD at low energy. In the p-regime we test volume and quark mass dependence of the pseudoscalar decay constant and mass; in the epsilon-regime, we investigate volume and topology dependence of the correlators. While the leading order behaviour predicted by the effective theory is very well reproduced by the lattice data in the range of parameters that we explored, our numerical data are not precise enough to test next-to-leading order effects.
Testing chiral effective theory with quenched lattice QCD
Giusti, L.; Hernández, P.; Necco, S.; Pena, C.; Wennekers, J.; Wittig, H.
2008-05-01
We investigate two-point correlation functions of left-handed currents computed in quenched lattice QCD with the Neuberger-Dirac operator. We consider two lattice spacings a simeq 0.09,0.12 fm and two different lattice extents L simeq 1.5,2.0 fm; quark masses span both the p- and the epsilon-regimes. We compare the results with the predictions of quenched chiral perturbation theory, with the purpose of testing to what extent the effective theory reproduces quenched QCD at low energy. In the p-regime we test volume and quark mass dependence of the pseudoscalar decay constant and mass; in the epsilon-regime, we investigate volume and topology dependence of the correlators. While the leading order behaviour predicted by the effective theory is very well reproduced by the lattice data in the range of parameters that we explored, our numerical data are not precise enough to test next-to-leading order effects.
Hadron spectrum in quenched lattice QCD and distribution of zero modes
Energy Technology Data Exchange (ETDEWEB)
Iwasaki, Yoichi (Tsukuba Univ., Sakura, Ibaraki (Japan). Inst. of Physics)
1989-06-01
I report the results of the calculation of the hadron spectrum with the standard one-plaquette gauge action on a 16{sup 3}x48 lattice at beta=5.85 in the quenched lattice QCD. The result remarkably agrees with that of quark potential models for the case where the quark mass is equal to or is larger than the strange quark mass, even when one uses the standard one-plaquette gauge action. This is contrary to what is stated in the literature. We clarify the reason of the discrepancy, paying close attention to systematic errors in numerical calculations. Further, I show the distribution of zero modes of quark matrix, both in the cases of a RG improved gauge action and the standard action, and discuss the difference between the two cases. (orig.).
Banerjee, D; Dalmonte, M; Müller, M; Rico, E; Stebler, P; Wiese, U-J; Zoller, P
2012-10-26
Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.
Gauge-fixing on the lattice via orbifolding
Mehta, Dhagash; Daleo, Noah S.; Hauenstein, Jonathan D.; Seaton, Christopher
2014-09-01
When fixing a covariant gauge, most popularly the Landau gauge, on the lattice, one encounters the Neuberger 0/0 problem, which prevents one from formulating a Becchi-Rouet-Stora-Tyutin symmetry on the lattice. Following the interpretation of this problem in terms of Witten-type topological field theory and using the recently developed Morse theory for orbifolds, we propose a modification of the lattice Landau gauge via orbifolding of the gauge-fixing group manifold and show that this modification circumvents the orbit-dependence issue and hence can be a viable candidate for evading the Neuberger problem. Using algebraic geometry, we also show that though the previously proposed modification of the lattice Landau gauge via stereographic projection relies on delicate departure from the standard Morse theory due to the noncompactness of the underlying manifold, the corresponding gauge-fixing partition function turns out to be orbit independent for all the orbits except in a region of measure zero.
The quenched SU(2) fundamental scalar propagator in minimal Landau gauge
Maas, Axel
2016-01-01
It is a long-standing question whether the confinement of matter fields in QCD has an imprint in the (gauge-dependent) correlation functions, especially the propagators. As the analytic structure plays an important role in this question, high-precision data is necessary for lattice investigations. Also, it is interesting how this depends on the dimensionality of the theory. To make a study over a wide range of parameters possible this suggests to use scalar particles. This is done here: The propagator of a fundamental scalar is studied in two, three, and four dimensions in quenched SU(2) Yang-Mills theory in minimal Landau gauge, both in momentum space and position space. Particular emphasis is put on the effects of renormalization. The results suggest a quite intricate volume dependence and the presence of an intrinsic mass scale, but no obvious connection to confinement.
The quenched SU(2) fundamental scalar propagator in minimal Landau gauge
Maas, Axel
2016-07-01
It is a long-standing question whether the confinement of matter fields in QCD has an imprint in the (gauge-dependent) correlation functions, especially the propagators. As the analytic structure plays an important role in this question, high-precision data is necessary for lattice investigations. Also, it is interesting how this depends on the dimensionality of the theory. To make a study over a wide range of parameters possible this suggests to use scalar particles. This is done here: The propagator of a fundamental scalar is studied in two, three, and four dimensions in quenched SU(2) Yang-Mills theory in minimal Landau gauge, both in momentum space and position space. Particular emphasis is put on the effects of renormalization. The results suggest a quite intricate volume dependence and the presence of an intrinsic mass scale, but no obvious connection to confinement.
Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
Wiese, U -J
2013-01-01
Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev's toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is non-perturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should al...
Continuum extrapolation of finite temperature meson correlation functions in quenched lattice QCD
Francis, Anthony
2010-01-01
We explore the continuum limit $a\\rightarrow 0$ of meson correlation functions at finite temperature. In detail we analyze finite volume and lattice cut-off effects in view of possible consequences for continuum physics. We perform calculations on quenched gauge configurations using the clover improved Wilson fermion action. We present and discuss simulations on isotropic $N_\\sigma^3\\times 16$ lattices with $N_\\sigma=32,48,64,128$ and $128^3 \\times N_\\tau$ lattices with $N_\\tau=16,24,32,48$ corresponding to lattice spacings in the range of $0.01 fm \\lsim a \\lsim\\ 0.031 fm$ at $T\\simeq1.45T_c$. Continuum limit extrapolations of vector meson and pseudo scalar correlators are performed and their large distance expansion in terms of thermal moments is introduced. We discuss consequences of this analysis for the calculation of the electrical conductivity of the QGP at this temperature.
The Gribov ambiguity for maximal abelian and center gauges in SU(2) lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Stack, John D.; Tucker, William W
2001-03-01
We present results for the fundamental string tension in SU(2) lattice gauge theory after projection to maximal abelian and direct maximal center gauges. We generate 20 Gribov copies/configuration. Abelian and center projected string tensions slowly decrease as higher values of the gauge functionals are reached.
Evidence for hard chiral logarithms in quenched lattice QCD
Kim, S; Kim, Seyong; Sinclair, D K
1995-01-01
We present the first direct evidence that quenched QCD differs from full QCD in the chiral (m_q \\rightarrow 0) limit, as predicted by chiral perturbation theory, from our quenched lattice QCD simulations at \\beta = 6/g^2 = 6.0. We measured the spectrum of light hadrons on 16^3 \\times 64, 24^3 \\times 64 and 32^3 \\times 64, using staggered quarks of masses m_q=0.01, m_q=0.005 and m_q=0.0025. The pion masses showed clear evidence for logarithmic violations of the PCAC relation m_{\\pi}^2 \\propto m_q, as predicted by quenched chiral perturbation theory. The dependence on spatial lattice volume precludes this being a finite size effect. No evidence was seen for such chiral logarithms in the behaviour of the chiral condensate \\langle\\bar{\\psi}\\psi\\rangle.
Topology of four-dimensional lattice gauge fields
Panagiotakopoulos, C.
1985-08-01
An extremely careful implementation of Woit's definition of the topological charge for SU(2) lattice gauge fields reveals a scaling violation by the topological susceptibility in the region 2.1Luscher's charge at weak enough coupling.
Banerjee D.; Dalmonte M.; Muller M; Rico E.; Stebler P.; Wiese U.-J.; Zoller P.
2012-01-01
Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in ...
Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the Lattice
Suzuki, H
1999-01-01
Lüscher's recent formulation of Abelian chiral gauge theories on the lattice, in the vacuum (or perturbative) sector in infinite lattice volume, is re-interpreted in terms of the lattice covariant regularization. The gauge invariance of the effective action and the integrability of the gauge current in anomaly-free cases become transparent then. The real part of the effective action is simply one-half of that of the Dirac fermion and, when the Dirac operator has proper properties in the continuum limit, the imaginary part in the continuum limit reproduces the $\\eta$-invariant.}
Spectral properties of quarks above $\\T_{c}$ in quenched lattice QCD
Karsch, Frithjof
2007-01-01
We analyze the quark spectral function above the critical temperature for deconfinement in quenched lattice QCD using clover improved Wilson fermions in Landau gauge. We show that the temporal quark correlator is well reproduced by a two-pole approximation for the spectral function and analyze the bare quark mass dependence of both poles as well as their residues. In the chiral limit we find that the quark spectral function has two collective modes which correspond to the normal and plasmino excitations. At large values of the bare quark mass the spectral function is dominated by a single pole.
A Formulation of Lattice Gauge Theories for Quantum Simulations
Zohar, Erez
2014-01-01
We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We consider both discrete and continuous gauge groups and adopt a realistic multi-component Fock space for the definition of matter degrees of freedom. In particular, we express the Hamiltonian of the gauge theory and the Gauss law in terms of Fock operators. The gauge fields are described in two different bases, based on either group elements or group representations. This formulation allows for a natural scheme to achieve a consistent truncation of the Hilbert space for continuous groups, and provides helpful tools to study the connections of gauge theories with topological quantum double and string-net models for discrete groups. Several examples, including the case of the discrete $D_3$ gauge group, are presented.
Heavy-quarkonium potential with input from lattice gauge theory
Serenone, Willian Matioli
2014-01-01
In this dissertation we study potential models incorporating a nonperturbative propagator obtained from lattice simulations of a pure gauge theory. Initially we review general aspects of gauge theories, the principles of the lattice formulation of quantum chromodynamics (QCD) and some properties of heavy quarkonia, i.e. bound states of a heavy quark and its antiquark. As an illustration of Monte Carlo simulations of lattice models, we present applications in the case of the harmonic oscillator and SU(2) gauge theory. We then study the effect of using a gluon propagator from lattice simulations of pure SU(2) theory as an input in a potential model for the description of quarkonium, in the case of bottomonium and charmonium. We use, in both cases, a numerical approach to evaluate masses of quarkonium states. The resulting spectra are compared to calculations using the Coulomb plus linear (or Cornell) potential.
Comparison of SO(3) and SU(2) lattice gauge theory
De Forcrand, Philippe; Forcrand, Philippe de; Jahn, Oliver
2003-01-01
The Villain form of SO(3) lattice gauge theory is studied and compared to Wilson's SU(2) theory. The topological invariants in SO(3) which correspond to twisted boundary conditions in SU(2) are discussed and lattice observables are introduced for them. An apparent SO(3) phase with negative adjoint Polyakov loop is explained in terms of these observables. The electric twist free energy, an order parameter for the confinement-deconfinement transition, is measured in both theories to calibrate the temperature. The results indicate that lattices with about 700^4 sites or larger will be needed to study the SO(3) confined phase. Alternative actions are discussed and an analytic path connecting SO(3) and SU(2) lattice gauge theory at weak coupling is exhibited. The relevance for confinement of the centre of the gauge group is discussed.
Bloch Waves in Minimal Landau Gauge and the Infinite-Volume Limit of Lattice Gauge Theory
Cucchieri, Attilio; Mendes, Tereza
2017-05-01
By exploiting the similarity between Bloch's theorem for electrons in crystalline solids and the problem of Landau gauge fixing in Yang-Mills theory on a "replicated" lattice, we show that large-volume results can be reproduced by simulations performed on much smaller lattices. This approach, proposed by Zwanziger [Nucl. Phys. B412, 657 (1994), 10.1016/0550-3213(94)90396-4], corresponds to taking the infinite-volume limit for Landau-gauge field configurations in two steps: first for the gauge transformation alone, while keeping the lattice volume finite, and second for the gauge-field configuration itself. The solutions to the gauge-fixing condition are then given in terms of Bloch waves. Applying the method to data from Monte Carlo simulations of pure SU(2) gauge theory in two and three space-time dimensions, we are able to evaluate the Landau-gauge gluon propagator for lattices of linear extent up to 16 times larger than that of the simulated lattice. This approach is reminiscent of the Fisher-Ruelle construction of the thermodynamic limit in classical statistical mechanics.
On the definition of entanglement entropy in lattice gauge theories
Aoki, Sinya; Iritani, Takumi; Nozaki, Masahiro; Numasawa, Tokiro; Shiba, Noburo; Tasaki, Hal
2015-06-01
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the Z N gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the Z N gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.
On the definition of entanglement entropy in lattice gauge theories
Aoki, Sinya; Nozaki, Masahiro; Numasawa, Tokiro; Shiba, Noburo; Tasaki, Hal
2015-01-01
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contain gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the $Z_N$ gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the $Z_N$ gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.
Landau gauge gluon vertices from Lattice QCD
Duarte, Anthony G; Silva, Paulo J
2016-01-01
In lattice QCD the computation of one-particle irreducible (1PI) Green's functions with a large number (> 2) of legs is a challenging task. Besides tuning the lattice spacing and volume to reduce finite size effects, the problems associated with the estimation of higher order moments via Monte Carlo methods and the extraction of 1PI from complete Green's functions are limitations of the method. Herein, we address these problems revisiting the calculation of the three gluon 1PI Green's function.
Real Representation in Chiral Gauge Theories on the Lattice
Suzuki, H
2000-01-01
The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L\\"uscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion integration measure globally over the gauge-field configuration space in the arbitrary topological sector; there is no global obstruction corresponding to the Witten anomaly. It is shown that this Weyl formulation is equivalent to a lattice formulation based on the Majorana (left--right-symmetric) fermion, in which the fermion partition function is given by the Pfaffian with a definite sign, up to physically irrelevant contact terms. This observation suggests a natural relative normalization of the fermion measure in different topological sectors for the Weyl fermion belonging to the complex representation.
Multigrid methods for propagators in lattice gauge theories
Kalkreuter, T
1994-01-01
Multigrid methods were invented for the solution of discretized partial differential equations in ordered systems. The slowness of traditional algorithms is overcome by updates on various length scales. In this article we discuss generalizations of multigrid methods for disordered systems, in particular for propagators in lattice gauge theories. A discretized nonabelian gauge theory can be formulated as a system of statistical mechanics where the gauge field degrees of freedom are SU(N) matrices on the links of the lattice. These SU(N) matrices appear as random coefficients in Dirac equations. We aim at finding an efficient method by which one can solve Dirac equations without critical slowing down. If this could be achieved, Monte Carlo simulations of Quantum Chromodynamics (the theory of the strong interaction) would be accelerated considerably. In principle, however, the methods discussed can be used in arbitrary space-time dimension and for arbitrary gauge group. Moreover, there are applications in multig...
Variational Calculation in SU(3) Lattice Gauge Theory
Institute of Scientific and Technical Information of China (English)
YANG Chun; ZHANG Qi-Ren; GAO Chun-Yuan
2001-01-01
Using the Hamiltonian lattice gauge theory, we perform some variational calculations to obtain the ground-state energy of SU(3) gauge field and scalar (0++) glueball mass. The agreement of our data with the strong and weak expansion results in the corresponding limits indicates that this method can provide us with reliable information in the most interesting medium region. The trial wavefunction used in our variational method is also proven to be a good first approximation of the ground-state of the SU(3) gauge field. Upgrading this function according to correlations of adjacent plaquettes may mean better results.
Kitaev Lattice Models as a Hopf Algebra Gauge Theory
Meusburger, Catherine
2017-07-01
We prove that Kitaev's lattice model for a finite-dimensional semisimple Hopf algebra H is equivalent to the combinatorial quantisation of Chern-Simons theory for the Drinfeld double D( H). This shows that Kitaev models are a special case of the older and more general combinatorial models. This equivalence is an analogue of the relation between Turaev-Viro and Reshetikhin-Turaev TQFTs and relates them to the quantisation of moduli spaces of flat connections. We show that the topological invariants of the two models, the algebra of operators acting on the protected space of the Kitaev model and the quantum moduli algebra from the combinatorial quantisation formalism, are isomorphic. This is established in a gauge theoretical picture, in which both models appear as Hopf algebra valued lattice gauge theories. We first prove that the triangle operators of a Kitaev model form a module algebra over a Hopf algebra of gauge transformations and that this module algebra is isomorphic to the lattice algebra in the combinatorial formalism. Both algebras can be viewed as the algebra of functions on gauge fields in a Hopf algebra gauge theory. The isomorphism between them induces an algebra isomorphism between their subalgebras of invariants, which are interpreted as gauge invariant functions or observables. It also relates the curvatures in the two models, which are given as holonomies around the faces of the lattice. This yields an isomorphism between the subalgebras obtained by projecting out curvatures, which can be viewed as the algebras of functions on flat gauge fields and are the topological invariants of the two models.
Prepotential formulation of SU(3) lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Anishetty, Ramesh [Institute of Mathematical Sciences, CIT-Campus, Taramani, Chennai 600 113 (India); Mathur, Manu; Raychowdhury, Indrakshi [S N Bose, National Centre for Basic Sciences, JD Block, Sector III, Salt Lake City, Kolkata 700 098 (India)], E-mail: ramesha@imsc.res.in, E-mail: manu@bose.res.in, E-mail: indrakshi@bose.res.in
2010-01-22
The SU(3) lattice gauge theory is reformulated in terms of SU(3) prepotential harmonic oscillators. This reformulation has enlarged SU(3)xU(1)xU(1) gauge invariance under which the prepotential operators transform like matter fields. The Hilbert space of SU(3) lattice gauge theory is shown to be equivalent to the Hilbert space of the prepotential formulation satisfying certain color invariant Sp(2, R) constraints. The SU(3) irreducible prepotential operators which solve these Sp(2, R) constraints are used to construct SU(3) gauge invariant Hilbert spaces at every lattice site in terms of SU(3) gauge invariant vertex operators. The electric fields and the link operators are reconstructed in terms of these SU(3) irreducible prepotential operators. We show that all the SU(3) Mandelstam constraints become local and take a very simple form within this approach. We also discuss the construction of all possible linearly independent SU(3) loop states which solve the Mandelstam constraints. The techniques can be easily generalized to SU(N)
cuLGT: Lattice Gauge Fixing on GPUs
Vogt, Hannes
2014-01-01
We adopt CUDA-capable Graphic Processing Units (GPUs) for Landau, Coulomb and maximally Abelian gauge fixing in 3+1 dimensional SU(3) and SU(2) lattice gauge field theories. A combination of simulated annealing and overrelaxation is used to aim for the global maximum of the gauge functional. We use a fine grained degree of parallelism to achieve the maximum performance: instead of the common 1 thread per site strategy we use 4 or 8 threads per lattice site. Here, we report on an improved version of our publicly available code (www.cuLGT.com and github.com/culgt) which again increases performance and is much easier to include in existing code. On the GeForce GTX 580 we achieve up to 470 GFlops (utilizing 80% of the theoretical peak bandwidth) for the Landau overrelaxation code.
Phase structure of pure SU(3) lattice gauge theory in 5-dimensions
Itou, Etsuko; Nakamoto, Norihiro
2014-01-01
We investigate the nonperturbative phase structure of five-dimensional SU(3) pure Yang-Mills theory on the lattice. We perform numerical simulations using the Wilson plaquette gauge action on an anisotropic lattice with a four-dimensional lattice spacing (a4) and with an independent value in the fifth dimension (a5). We investigate both cases of a4 > a5 and a4 < a5. The Polyakov loops in the fourth and the fifth directions are observed, and we find that there are four possible phases for the anisotropic five-dimensional quenched QCD theory on the lattice. We determine the critical values of the lattice bare coupling and the anisotropic parameter for each phase transition. Furthermore, we find that there is novel meta-stable vacuum, where the global gauge symmetry would be spontaneously broken. It appears only in the phase where the center symmetry in four dimensions is preserved while the symmetry in the fifth dimension is spontaneously broken.
Tadpole-improved SU(2) lattice gauge theory
Shakespeare, N H; Shakespeare, Norman H.; Trottier, Howard D.
1999-01-01
A comprehensive analysis of tadpole-improved SU(2) lattice gauge theory is made. Simulations are done on isotropic and anisotropic lattices, with and without improvement. Two tadpole renormalization schemes are employed, one using average plaquettes, the other using mean links in Landau gauge. Simulations are done with spatial lattice spacings $a_s$ in the range of about 0.1--0.4 fm. Results are presented for the static quark potential, the renormalized lattice anisotropy $a_t/a_s$ (where $a_t$ is the ``temporal'' lattice spacing), and for the scalar and tensor glueball masses. Tadpole improvement significantly reduces discretization errors in the static quark potential and in the scalar glueball mass, and results in very little renormalization of the bare anisotropy that is input to the action. We also find that tadpole improvement using mean links in Landau gauge results in smaller discretization errors in the scalar glueball mass (as well as in the static quark potential), compared to when average plaquett...
Kaon matrix elements and CP violation from quenched lattice QCD
Cristian, Calin-Radu
We report the results of a calculation of the K → pipi matrix elements relevant for the DeltaI = 1/2 rule and epsilon '/epsilon in quenched lattice QCD using domain wall fermions at a fixed lattice spacing of a-1 ˜ 2 GeV. Working in the three-quark effective theory, where only the u, d and s quarks enter and which is known perturbatively to next-to-leading order; we calculate the lattice K → pi and K → |0> matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield K → pipi matrix elements, which we then normalize to continuum values through a non-perturbative renormalization technique. For the Delta I = 1/2 rule we find a value of 25.3 +/- 1.8 (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10--20% below the experimental values. For epsilon '/epsilon; using known central values for standard model parameters, we calculate (-4.0 +/- 2.3) x 10-4 (statistical error only) compared to the current experimental average of (17.2 +/- 1.8) x 10-4. Because we find a large cancellation between the I = 0 and I = 2 contributions to epsilon'/epsilon, the result may be very sensitive to the approximations employed. Among these are the use of: quenched QCD, lowest order chiral perturbation theory and continuum perturbation theory below 1.3 GeV. We have also calculated the kaon B parameter, BK and find BK(2 GeV) = 0.532(11). Although currently unable to give a reliable systematic error; we have control over statistical errors and more simulations will yield information about the effects of the approximations on this first-principles determination of these important quantities.
Fusion basis for lattice gauge theory and loop quantum gravity
Delcamp, Clement; Riello, Aldo
2016-01-01
We introduce a new basis for the gauge--invariant Hilbert space of lattice gauge theory and loop quantum gravity in $(2+1)$ dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin--network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel'd double of the gauge group, and can be readily "fused" together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi--local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse--graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin--network basis, in which it ...
Maezawa, Yu; Hatsuda, Tetsuo; Koide, Tomoi
2010-01-01
Transport coefficients of causal dissipative relativistic fluid dynamics (CDR) are studied in quenched lattice simulations. CDR describes the behavior of relativistic non-Newtonian fluids in which the relaxation time appears as a new transport coefficient besides the shear and bulk viscosities. It was recently shown that these coefficients can be given by the temporal-correlation functions of the energy-momentum tensors as in the case of the Green-Kubo-Nakano formula. By using the new formula in CDR, we study the transport coefficients with lattice simulations in pure SU(3) gauge theory. After defining the energy-momentum tensor on the lattice, we extract a ratio of the shear viscosity to the relaxation time which is given only in terms of the static correlation functions. The simulations are performed on $24^3 \\times 4$--16 lattices with $\\beta_{_{\\rm LAT}} = 6.0$, which corresponds to the temperature range of $0.5 \\simle T/T_c \\simle 1.8$, where $T_c$ is the critical temperature.
Fusion basis for lattice gauge theory and loop quantum gravity
Delcamp, Clement; Dittrich, Bianca; Riello, Aldo
2017-02-01
We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2 + 1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel'd double of the gauge group, and can be readily "fused" together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2 + 1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.
On jet quenching parameters in strongly coupled non-conformal gauge theories
Buchel, A
2006-01-01
Recently Liu, Rajagopal and Wiedemann (LRW) [hep-ph/0605178] proposed a first principle, nonperturbative quantum field theoretic definition of ``jet quenching parameter'' \\hat{q} used in models of medium-induced radiative parton energy loss in nucleus-nucleus collisions at RHIC. Relating \\hat{q} to a short-distance behavior of a certain light-like Wilson loop, they used gauge theory-string theory correspondence to evaluate \\hat{q} for the strongly coupled N=4 SU(N_c) gauge theory plasma. We generalize analysis of LRW to strongly coupled non-conformal gauge theory plasma. We find that a jet quenching parameter is gauge theory specific (not universal). Furthermore, it appears it's value increases as the number of effective adjoint degrees of freedom of a gauge theory plasma increases.
Applications of Jarzynski's relation in lattice gauge theories
Nada, Alessandro; Costagliola, Gianluca; Panero, Marco; Toniato, Arianna
2016-01-01
Jarzynski's equality is a well-known result in statistical mechanics, relating free-energy differences between equilibrium ensembles with fluctuations in the work performed during non-equilibrium transformations from one ensemble to the other. In this work, an extension of this relation to lattice gauge theory will be presented, along with numerical results for the $\\mathbb{Z}_2$ gauge model in three dimensions and for the equation of state in $\\mathrm{SU}(2)$ Yang-Mills theory in four dimensions. Then, further applications will be discussed, in particular for the Schr\\"odinger functional and for the study of QCD in strong magnetic fields.
Phase diagrams of exceptional and supersymmetric lattice gauge theories
Energy Technology Data Exchange (ETDEWEB)
Wellegehausen, Bjoern-Hendrik
2012-07-10
In this work different strongly-coupled gauge theories with and without fundamental matter have been studied on the lattice with an emphasis on the confinement problem and the QCD phase diagram at nonvanishing net baryon density as well as on possible supersymmetric extensions of the standard model of particle physics. In gauge theories with a non-trivial centre symmetry, as for instance SU(3)-Yang-Mills theory, confinement is intimately related to the centre of the gauge group, and the Polyakov loop serves as an order parameter for confinement. In QCD, this centre symmetry is explicitly broken by quarks in the fundamental representation of the gauge group. But still quarks and gluons are confined in mesons, baryons and glueballs at low temperatures and small densities, suggesting that centre symmetry is not responsible for the phenomenon of confinement. Therefore it is interesting to study pure gauge theories without centre symmetry. In this work this has been done by replacing the gauge group SU(3) of the strong interaction with the exceptional Lie group G{sub 2}, that has a trivial centre. To investigate G{sub 2} gauge theory on the lattice, a new and highly efficient update algorithm has been developed, based on a local HMC algorithm. Employing this algorithm, the proposed and already investigated first order phase transition from a confined to a deconfined phase has been confirmed, showing that indeed a first order phase transition without symmetry breaking or an order parameter is possible. In this context, also the deconfinement phase transition of the exceptional Lie groups F4 and E6 in three spacetime dimensions has been studied. It has been shown that both theories also possess a first order phase transition.
Energy Technology Data Exchange (ETDEWEB)
Wissel, S.
2006-10-15
In this thesis we investigate thermal in-medium modifications of various mesonic correlation functions by lattice simulations of Quantum Chromodynamics for light valence quark masses and vanishing chemical potential. Mesonic properties are typically extracted from spatial correlation functions. The results presented are based on quenched gauge field configurations generated with the standard Wilson plaquette gauge action. Concerning the fermionic part of the action, we use the non-perturbative O(a) improved Sheikholeslami-Wohlert as well as the truncated hypercube perfect action. Furthermore we utilize the maximum entropy method in order to determine physically relevant pole masses and to investigate thermal modifications of physical states and possible lattice artefacts in the interacting case. The analyses of pole and screening masses, dispersion relations, wave functions, decay constants and spectral functions essentially yield no significant modifications of the zero-temperature behavior up to 0.55 T{sub c}. Close to the phase transition in-medium effects seem to appear, which lead inter alia to significant differences between pole and screening masses. The decay constants are in good agreement with the experimental values. We have simulated above T{sub c} at nearly zero quark masses. At 1.24 T{sub c}, the occurrence of topological effects, a sign for the presence of a still broken U(1){sub A} symmetry, prevent a more thorough analyses close to the phase transition. A complete continuum and infinite volume extrapolation of screening masses, guided by free lattice effective masses is done. It shows that the presence of collective phenomena at 1.5 and 3 T{sub c} cannot be explained by pure lattice artefacts. Unlike the vector meson the pion is far from being considered an unbound state. (orig.)
Independent Plaquette Trial Action for 4-Dimensional Lattice Gauge Theory
Institute of Scientific and Technical Information of China (English)
LIU Jin-Ming
2001-01-01
Based on the explicit expressions of the plaquette formulations, the independent plaquette trial action for 4-dimensional lattice gauge theory is introduced. As an example, the mean plaquette energy EP for the SU(2) lattice gauge theory is calculated by using action variational approach with the independent trial action. The results are in good agreement with the Monte Carlo results in the strong coupling and the crossover region, and the curve is smooth in the whole region, which show that 4-dimensional SU(2) theory has only a single, confining phase. The unwanted discontinuity of EP given by the single link trial action, which is used in the earlier variational calculations has been avoided.
Thick vortices in SU(2) lattice gauge theory
Cheluvaraja, Srinath
2004-01-01
Three dimensional SU(2) lattice gauge theory is studied after eliminating thin monopoles and the smallest thick monopoles. Kinematically this constraint allows the formation of thick vortex loops which produce Z(2) fluctuations at longer length scales. The thick vortex loops are identified in a three dimensional simulation. A condensate of thick vortices persists even after the thin vortices have all disappeared. The thick vortices decouple at a slightly lower temperature (higher beta) than t...
Towards understanding thermal jet quenching via lattice simulations
Laine, M
2013-01-01
After reviewing how simulations employing classical lattice gauge theory permit to test a conjectured Euclideanization property of a light-cone Wilson loop in a thermal non-Abelian plasma, we show how Euclidean data can in turn be used to estimate the transverse collision kernel, C(k_perp), characterizing the broadening of a high-energy jet. First results, based on data produced recently by Panero et al, suggest that C(k_perp) is enhanced over the known NLO result in a soft regime k_perp < a few T. The shape of k_perp^3 C(k_perp) is consistent with a Gaussian at small k_perp.
Gribov horizon and Gribov copies effect in lattice Coulomb gauge
Burgio, Giuseppe; Reinhardt, Hugo; Vogt, Hannes
2016-01-01
Following a recent proposal by Cooper and Zwanziger we investigate via lattice simulations the effect on the Coulomb gauge propagators and on the Gribov-Zwanziger confinement mechanism of selecting the Gribov copy with the smallest non-trivial eigenvalue of the Faddeev-Popov operator, i.e. the one closest to the Gribov horizon. Although such choice of gauge drives the ghost propagator towards the prediction of continuum calculations, we find that it actually overshoots the goal. With increasing computer time, we observe that Gribov copies with arbitrarily small eigenvalues can be found. For such a method to work one would therefore need further restrictions on the gauge condition to isolate the physically relevant copies, since e.g. the Coulomb potential $V_C$ defined through the Faddeev-Popov operator becomes otherwise physically meaningless. Interestingly, the Coulomb potential alternatively defined through temporal link correlators is only marginally affected by the smallness of the eigenvalues.
On the chiral limit in lattice gauge theories with Wilson fermions
Hoferichter, A; Müller-Preussker, M
1995-01-01
The chiral limit ~\\kappa \\simeq \\kappa_c(\\beta)~ in lattice gauge theories with Wilson fermions and problems related to near--to--zero ('exceptional') eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator ~\\mpr_{\\pi}~ for the calculation of the pseudoscalar mass ~m_{\\pi}~ is proposed which does not suffer from 'divergent' contributions at \\kappa \\simeq \\kappa_c(\\beta). We conclude that the main contribution to the pion mass comes from larger modes, and 'exceptional' eigenvalues play {\\it no} physical role. The behaviour of the subtracted chiral condensate ~\\langle \\psb \\psi \\rangle_{subt}~ near ~\\kappa_c(\\beta)~ is determined. We observe a comparatively large value of ~\\langle \\psb \\psi \\rangle_{subt} \\cdot Z_P^{-1}~, which could be interpreted as a possible effect of the quenched approximation.
Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-11-01
The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U{sub A}(1) symmetry and the {eta}{prime} for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk.
Two-dimensional lattice gauge theories with superconducting quantum circuits
Energy Technology Data Exchange (ETDEWEB)
Marcos, D., E-mail: david.marcos@me.com [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Widmer, P. [Albert Einstein Center, Institute for Theoretical Physics, Bern University, CH-3012, Bern (Switzerland); Rico, E. [IPCMS (UMR 7504) and ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg (France); Hafezi, M. [Joint Quantum Institute, NIST/University of Maryland, College Park 20742 (United States); Department of Electrical Engineering and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742 (United States); Rabl, P. [Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien (Austria); Wiese, U.-J. [Albert Einstein Center, Institute for Theoretical Physics, Bern University, CH-3012, Bern (Switzerland); Zoller, P. [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria)
2014-12-15
A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.
Flux-tubes in three-dimensional lattice gauge theories
Trottier, H D; Trottier, Howard D.
1993-01-01
Flux-tubes in different representations of SU(2) and U(1) lattice gauge theories in three dimensions are measured. Wilson loops generate heavy ``quark-antiquark'' pairs in fundamental ($j=1/2$), adjoint ($j=1$), and quartet ($j=3/2$) representations of SU(2). The first direct lattice measurements of the flux-tube cross-section ${\\cal A}_j$ as a function of representation are made. It is found that ${\\cal A}_j \\approx {\\rm constant}$, to about 10\\%. Results are consistent with a connection between the string tension $\\sigma_j$ and ${\\cal A}_j$ suggested by a simplified flux-tube model, $\\sigma_j = g^2 j(j+1) / (2 {\\cal A}_j)$ [$g$ is the gauge coupling], given that $\\sigma_j$ scales like the Casimir $j(j+1)$, as observed in previous lattice studies in both three and four dimensions. The results can discriminate among phenomenological models of the physics underlying confinement. Flux-tubes for singly- and doubly-charged Wilson loops in compact QED$_3$ are also measured. It is found that the string tension scal...
Thermodynamics and reference scale of SU(3) gauge theory from gradient flow on fine lattices
Kitazawa, Masakiyo; Hatsuda, Tetsuo; Iritani, Takumi; Itou, Etsuko; Suzuki, Hiroshi
2015-01-01
We study the parametrization of lattice spacing and thermodynamics of SU(3) gauge theory on the basis of the Yang-Mills gradient flow on fine lattices. The lattice spacing of the Wilson gauge action is determined over a wide range $6.3\\le\\beta\\le7.5$ with high accuracy. The measurements of the flow time and lattice spacing dependences of the expectation values of the energy-momentum tensor are performed on fine lattices.
The QCD Abacus A New Formulation for Lattice Gauge Theories
Brower, R C
1998-01-01
A quantum Hamiltonian is constructed for SU(3) lattice QCD entirely from color triplet Fermions --- the standard quarks and a new Fermionic ``constituent'' of the gluon we call ``rishons''. The quarks are represented by Dirac spinors on each site and the gauge fields by rishon-antirishon bilinears on each link which together with the local gauge transforms are the generators of an SU(6) algebra. The effective Lagrangian for the path integral lives in $R^4 \\times S^1$ Euclidean space with a compact ``fifth time'' of circumference ($\\beta$) and non-Abelian charge ($e^2$) both of which carry dimensions of length. For large $\\beta$, it is conjectured that continuum QCD is reached and that the dimensionless ratio $g^2 = e^2/\\beta$ becomes the QCD gauge coupling. The quarks are introduced as Kaplan chiral Fermions at either end of the finite slab in fifth time. This talk will emphasize the gauge and algebraic structure of the rishon or link Fermions and the special properties that may lead to fast discrete dynamics...
Lattice regularization of gauge theories without loss of chiral symmetry
't Hooft, Gerardus
1994-01-01
Abstract: A lattice regularization procedure for gauge theories is proposed in which fermions are given a special treatment such that all chiral flavor symmetries that are free of Adler-Bell-Jackiw anomalies are kept intact. There is no doubling of fermionic degrees of freedom. A price paid for this feature is that the number of fermionic degrees of freedom per unit cell is still infinite, although finiteness of the complete functional integrals can be proven (details are outlined in an Appendix). Therefore, although perhaps of limited usefulness for numerical simulations, our scheme can be applied for studying aspects such as analytic convergence questions, spontaneous symmetry breakdown and baryon number violation in non-Abelian gauge theories.
Symanzik improvement of the gradient flow in lattice gauge theories
Energy Technology Data Exchange (ETDEWEB)
Ramos, Alberto [PH-TH, CERN, Geneva (Switzerland); Sint, Stefan [Trinity College Dublin, School of Mathematics, Dublin (Ireland)
2016-01-15
We apply the Symanzik improvement programme to the 4 + 1-dimensional local re-formulation of the gradient flow in pure SU(N) lattice gauge theories. We show that the classical nature of the flow equation allows one to eliminate all cutoff effects at O(a{sup 2}), which originate either from the discretised gradient flow equation or from the gradient flow observable. All the remaining O(a{sup 2}) effects can be understood in terms of local counterterms at the zero flow-time boundary. We classify these counterterms and provide a complete set as required for on-shell improvement. Compared to the 4-dimensional pure gauge theory only a single additional counterterm is required, which corresponds to a modified initial condition for the flow equation. A consistency test in perturbation theory is passed and allows one to determine all counterterm coefficients to lowest non-trivial order in the coupling. (orig.)
Fracton topological order, generalized lattice gauge theory, and duality
Vijay, Sagar; Haah, Jeongwan; Fu, Liang
2016-12-01
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, pointlike topological excitations, and subextensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary algebraic geometry provide an effective mathematical tool set for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.
A floating point engine for lattice gauge calculations
Energy Technology Data Exchange (ETDEWEB)
Husby, D.; Atac, R.; Cook, A.; Deppe, J.; Fischler, M.; Gaines, I.; Wash, T.; Pham, T.; Zmuda, T.
1989-02-01
The latest in low cost computing solutions from the Fermilab Advanced Computer Program is targeted at Lattice Gauge theory calculations and delivers supercomputer performance at a fraction of the cost. A typical system with 256 processors, 2.5 Gigabytes of memory, and 64 Gigabytes of on-line tape storage, delivers a peak performance of 5 billion floating point operations per second. The programming environment, Canopy, provides a comprehensive, hardware independent, distributed processing platform from within the more familiar environments of FORTRAN, C, and UNIX. This paper describes the individual processing elements of the system and gives a brief description of the Canopy software.
A floating point engine for lattice gauge calculations
Energy Technology Data Exchange (ETDEWEB)
Husby, D.; Atac, R.; Cook, A.; Deppe, J.; Fischler, M.; Gaines, I.; Nash, T.; Pham, T.; Zmuda, T.; Eichten, E.
1988-11-01
The latest in low cost computing solutions from the Fermilab Advanced Computer Program is targeted at Lattice Gauge theory calculations and delivers supercomputer performance at a fraction of the cost. A typical system with 256 processors, 2.5 Gigabytes of memory, and 64 Gigabytes of on-line tape storage, delivers a peak performance of 5 billion floating point operations per second. The programming environment, Canopy, provides a comprehensive, hardware independent, distributed processing platform from within the more familiar environments of FORTRAN, C, and UNIX. This paper describes the individual processing elements of the system and gives a brief description of the Canopy software. 8 refs., 3 figs.
Lattice Gauge Theory and the Origin of Mass
Energy Technology Data Exchange (ETDEWEB)
Kronfeld, Andreas S.
2013-08-01
Most of the mass of everyday objects resides in atomic nuclei/ the total of the electrons' mass adds up to less than one part in a thousand. The nuclei are composed of nucleons---protons and neutrons---whose nuclear binding energy, though tremendous on a human scale, is small compared to their rest energy. The nucleons are, in turn, composites of massless gluons and nearly massless quarks. It is the energy of these confined objects, via $M=E/c^2$, that is responsible for everyday mass. This article discusses the physics of this mechanism and the role of lattice gauge theory in establishing its connection to quantum chromodynamics.
Lattice Gauge Theory and the Origin of Mass
Kronfeld, Andreas S
2012-01-01
Most of the mass of everyday objects resides in atomic nuclei; the total of the electrons' mass adds up to less than one part in a thousand. The nuclei are composed of nucleons---protons and neutrons---whose nuclear binding energy, though tremendous on a human scale, is small compared to their rest energy. The nucleons are, in turn, composites of massless gluons and nearly massless quarks. It is the energy of these confined objects, via $M=E/c^2$, that is responsible for everyday mass. This article discusses the physics of this mechanism and the role of lattice gauge theory in establishing its connection to quantum chromodynamics.
CERN Theory Institute: Future directions in lattice gauge theory
2010-01-01
The main goal of the Institute is to bring together researchers in lattice gauge theory and in its applications to phenomenology to discuss interesting future directions of research. The focus will be on new ideas rather than on the latest computation of the usual quantities. The aim is to identify calculations in QCD, flavour physics, other strongly-interacting theories, etc. which are of high physics interest, and to clarify the theoretical and technical difficulties which, at present, prevent us from carrying them out.
Lattice gauge theory on the Intel parallel scientific computer
Energy Technology Data Exchange (ETDEWEB)
Gottlieb, S. (Department of Physics, Indiana University, Bloomington, IN (USA))
1990-08-01
Intel Scientific Computers (ISC) has just started producing its third general of parallel computer, the iPSC/860. Based on the i860 chip that has a peak performance of 80 Mflops and with a current maximum of 128 nodes, this computer should achieve speeds in excess of those obtainable on conventional vector supercomputers. The hardware, software and computing techniques appropriate for lattice gauge theory calculations are described. The differences between a staggered fermion conjugate gradient program written under CANOPY and for the iPSC are detailed.
Rigorous mean-field dynamics of lattice bosons: quenches from the Mott insulator
M. Snoek
2011-01-01
We provide a rigorous derivation of Gutzwiller mean-field dynamics for lattice bosons, showing that it is exact on fully connected lattices. We apply this formalism to quenches in the interaction parameter from the Mott insulator to the superfluid state. Although within mean-field the Mott insulator
Loops and Strings in a Superconducting Lattice Gauge Simulator
Brennen, G. K.; Pupillo, G.; Rico, E.; Stace, T. M.; Vodola, D.
2016-12-01
We propose an architecture for an analog quantum simulator of electromagnetism in 2 +1 dimensions, based on an array of superconducting fluxonium devices. The encoding is in the integer (spin-1) representation of the quantum link model formulation of compact U (1 ) lattice gauge theory. We show how to engineer Gauss' law via an ancilla mediated gadget construction, and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by nonlocal order parameters from Wilson loops and disorder parameters from 't Hooft strings. We show how to construct such operators in this model and how to measure them nondestructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Numerical evidence is found for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.
Loops and strings in a superconducting lattice gauge simulator
Brennen, G K; Rico, E; Stace, T M; Vodola, D
2015-01-01
We propose a quantum simulation of electromagnetism in (2+1) dimensions using an array of superconducting fluxonium devices. The encoding is in the integer (S=1) representation of the quantum link model formulation of compact U(1) lattice gauge theory. We show how to engineer the Gauss constraint via an ancilla mediated gadget construction and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by non-local order parameters from Wilson loops and disorder parameters from 't Hooft strings and we show how to measure these operators non-destructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Evidence for existence of the confined phase in the ground state of the simulation Hamiltonian is found by DMRG calculations on a ladder geometry.
Lattice gauge theory of three dimensional Thirring model
Kim, S; Kim, Seyong; Kim, Yoonbai
1999-01-01
Three dimensional Thirring model with N four-component Dirac fermions, reformulated as a lattice gauge theory, is studied by computer simulation. According to an 8^{3} data and preliminary 16^3 data, chiral symmetry is found to be spontaneously broken for N=2,\\;4 and 6. N=2 data exhibits long tail of the non-vanishing chiral condensate into weak coupling region, and N=6 case shows phase separation between the strong coupling region and the weak coupling region. Although the comparison between 8^3 data and 16^3 data shows large finite volume effects, an existence of the critical fermion flavor number N_{{\\rm cr}} (2
Van Enter, A C D
2003-01-01
We consider various sufficiently nonlinear sigma models for nematic ordering of RP^{N-1} type and of lattice gauge type with continous symmetries. We rigorously show that they exhibit a first-order transition in the temperature. The result holds in dimension 2 or more for the RP{N-1} models and in dimension 3 or more for the lattice gauge models. In the two-dimensional case our results clarify and solve a recent controversy about the possibilty of such transitions. For lattice gauge models our methods provide the first prof of a first-order transition in a model with a continous gauge symmetry.
The Light Hadron Spectrum and Decay Constants in Quenched Lattice QCD
Allton, C R; Sachrajda, Christopher T C; Wittig, H; Baxter, R M; Booth, S P; Bowler, K C; Henty, D S; Kenway, R D; McNeile, C; Pendleton, B J; Richards, D G; Simone, J N; Simpson, A D
1994-01-01
We present results for light hadrons composed of both degenerate and non-degenerate quarks in quenched lattice QCD. We calculate masses and decay constants using 60 gauge configurations with an $O(a)$--improved fermion action at $\\beta = 6.2$. Using the $\\rho$ mass to set the scale, we find hadron masses within two to three standard deviations of the experimental values (given in parentheses): $m_{K^*}=868\\er{9}{8}$~MeV (892~MeV), $m_{\\phi}=970\\err{20}{10}$~MeV (1020~MeV), $m_N=820\\err{90}{60}$~MeV (938~MeV), $m_\\Delta=1300\\errr{100}{100}$~MeV (1232~MeV) and $m_\\Omega=1650\\err{70}{50}$~MeV (1672~MeV). Direct comparison with experiment for decay constants is obscured by uncertainty in current renormalisations. However, for ratios of decay constants we obtain $f_K/f_\\pi=1.20\\er{3}{2}$ (1.22) and $f_\\phi/f_\\rho=1.13\\er{2}{3}$ (1.22).
Quark propagator at finite temperature and finite momentum in quenched lattice QCD
Karsch, Frithjof
2009-01-01
We present an analysis of the quark spectral function above and below the critical temperature for deconfinement performed at zero and non-zero momentum in quenched lattice QCD using clover improved Wilson fermions in Landau gauge. It is found that the temporal quark correlation function in the deconfined phase near the critical temperature is well reproduced by a two-pole ansatz for the spectral function. This indicates that excitation modes of the quark field have small decay rates. The bare quark mass and momentum dependence of the spectral function is analyzed with this ansatz. In the chiral limit we find that the quark spectral function has two collective modes corresponding to the normal and plasmino excitations in the high temperature limit. Over a rather wide temperature range in the deconfined phase the pole mass of these modes at zero momentum, which corresponds to the thermal mass of the quark, is approximately proportional to temperature. With increasing bare quark masses the plasmino mode gradual...
Recent progress in lattice supersymmetry: from lattice gauge theory to black holes
Kadoh, Daisuke
2016-01-01
Supersymmetry (SUSY) is a fascinating topic in theoretical physics, because of its unique and counterintuitive properties. It is expected to emerge as new physics beyond the standard model, and it is also a building block for supergravity and superstring theory. A number of exact results obtained via SUSY theories provide insights into field theory. However, the dynamics of many SUSY theories are not yet fully understood, and numerical study of SUSY theories through lattice simulations is promising as regards furthering this understanding. In this paper, I overview the current status of lattice SUSY by discussing its development in chronological order, and by reviewing some simple models. In addition, I discuss the numerical verification of gauge/gravity duality, which is one of the recent significant developments in this field.
Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
Fujiwara, T; Wu, K; Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
2000-01-01
The axial anomaly in lattice gauge theories has topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological techniques. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which validates the Leibniz rule of exterior derivatives on the lattice. The topological nature of the ``Chern character'' on the lattice becomes manifest with NCDC. Our result provides an algebraic proof of Lüscher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions.
An analysis of the nucleon spectrum from lattice partially-quenched QCD
Energy Technology Data Exchange (ETDEWEB)
Armour, W. [Swansea University, Swansea, SA2 8PP, Wales, U.K.; Allton, C. R. [Swansea University, Swansea, SA2 8PP, Wales, U.K.; Leinweber, Derek B. [Univ. of Adelaide, SA (Australia); Thomas, Anthony W. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States); Young, Ross D. [Argonne National Lab. (ANL), Argonne, IL (United States)
2010-09-01
The chiral extrapolation of the nucleon mass, Mn, is investigated using data coming from 2-flavour partially-quenched lattice simulations. The leading one-loop corrections to the nucleon mass are derived for partially-quenched QCD. A large sample of lattice results from the CP-PACS Collaboration is analysed, with explicit corrections for finite lattice spacing artifacts. The extrapolation is studied using finite range regularised chiral perturbation theory. The analysis also provides a quantitative estimate of the leading finite volume corrections. It is found that the discretisation, finite-volume and partial quenching effects can all be very well described in this framework, producing an extrapolated value of Mn in agreement with experiment. This procedure is also compared with extrapolations based on polynomial forms, where the results are less encouraging.
Supersymmetric gauge theories on the lattice: Pfaffian phases and the Neuberger 0/0 problem
Mehta, Dhagash; Galvez, Richard; Joseph, Anosh
2011-01-01
Recently a class of supersymmetric gauge theories have been successfully implemented on the lattice. However, there has been an ongoing debate on whether lattice versions of some of these theories suffer from a sign problem, with independent simulations for the ${\\cal N} = (2, 2)$ supersymmetric Yang-Mills theories in two dimensions yielding seemingly contradictory results. Here, we address this issue from an interesting theoretical point of view. We conjecture that the sign problem observed in some of the simulations is related to the so called Neuberger 0/0 problem, which arises in ordinary non-supersymmetric lattice gauge theories, and prevents the realization of Becchi-Rouet-Stora-Tyutin symmetry on the lattice. After discussing why we expect a sign problem in certain classes of supersymmetric lattice gauge theories far from the continuum limit, we argue that these problems can be evaded by use of a non-compact parametrization of the gauge link fields.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Nielsen, H.B. [Niels Bohr Inst., Kobenhavn (Denmark); Rugh, H.H. [Univ. of Warwick, Coventry (United Kingdom); Rugh, S.E. [Los Alamos National Lab., NM (United States)
1996-12-31
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a {open_quote}no go{close_quotes} for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a {open_quotes}continuum limit{close_quotes} in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined.
Monopoles and Confinement in U(1) Lattice Gauge Theory
Copeland, Timothy John
Available from UMI in association with The British Library. Requires signed TDF. Confinement in U(1) gauge theory is investigated, with particular emphasis on the role of monopoles. Starting from the work of Polyakov, the theoretical aspects are considered first, in some detail. This leads to the conclusion that the conventional techniques for analysing Monte Carlo data may not be adequate, and motivates the development of an alternative interpretation based on the theoretical insight gained. This takes more account of the expected physical properties of the theory, and does not assume beforehand that one type of behaviour (perturbative, or monopole driven) dominates. It is found that better fits to the Monte Carlo data can be achieved this way than by using the conventional methods, although different string tensions are found. The small distance behaviour is found to be best explained in terms of Coulomb effects, rather than the Luscher vibrating string picture sometimes used before. Perturbative calculations are made of Wilson loops on lattices of different shapes, and some comparisons with Monte Carlo data are made. Comments are made on the significance of these results for four dimensions, and for SU(2) and SU(3).
Dualization of non-abelian lattice gauge theory with Abelian Color Cycles (ACC)
Marchis, Carlotta
2016-01-01
We discuss a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theories. The Wilson gauge action is decomposed into a sum over "abelian color cycles" (ACC), which are loops around plaquettes visiting different colors at the corners. ACCs are complex numbers and thus commute such that a dual representation of a non-abelian theory can be obtained as in the abelian case. We apply the ACC approach to SU(2) and SU(3) lattice gauge theory and exactly rewrite the two partition sums in a strong coupling series where all gauge integrals are known in closed form.
Dynamical fermion masses and constraints of gauge invariance in quenched QED3
Energy Technology Data Exchange (ETDEWEB)
Bashir, A. [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Apartado Postal 2-82, Morelia, Michoacan 58040 (Mexico)]. E-mail: adnan@itzel.ifm.umich.mx; Raya, A. [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo no. 340, Col. Villa San Sebastian, Colima, Colima 28045 (Mexico)
2005-03-07
Numerical study of the Schwinger-Dyson equation (SDE) for the fermion propagator (FP) to obtain dynamically generated chirally asymmetric solution in an arbitrary covariant gauge {xi} is a complicated exercise specially if one employs a sophisticated form of the fermion-boson interaction complying with the key features of a gauge field theory. However, constraints of gauge invariance can help construct such a solution without having the need to solve the Schwinger-Dyson equation for every value of {xi}. In this article, we propose and implement a method to carry out this task in quenched quantum electrodynamics in a plane (QED3). We start from an approximate analytical form of the solution of the SDE for the FP in the Landau gauge. We consider the cases in which the interaction vertex (i) is bare and (ii) is full. We then apply the Landau-Khalatnikov-Fradkin transformations (LKFT) on the dynamically generated solution and find analytical results for arbitrary value of {xi}. We also compare our results with exact numerical solutions available for a small number of values of {xi} obtained through a direct analysis of the corresponding SDE.
Charmonium dissociation and heavy quark transport in hot quenched lattice QCD
Ding, H -T; Kaczmarek, O; Karsch, F; Satz, H; Söldner, W
2012-01-01
We study the properties of charmonium states at finite temperature in quenched lattice QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above Tc. Our analysis suggests that the S wave states disappear at about 1.5 Tc. The charm diffusion coefficient is estimated and found to be approximately 1/{\\pi}T at 1.5Tc {\\leq} T {\\leq} 3Tc.
Charmonium dissociation and heavy quark transport in hot quenched lattice QCD
Directory of Open Access Journals (Sweden)
Ding H.-T.
2014-04-01
Full Text Available We study the properties of charmonium states at finite temperature in quenched lattice QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above Tc. Our analysis suggests that the S wave states disappear at about 1.5 Tc. The charm diffusion coeffcient is estimated and found to be approximately 1/πT at 1.5Tc ≲ T ≲ 3Tc.
Bogolubsky, I; Müller-Preussker, M; Sternbeck, A
2013-01-01
We continue the systematic computation of Landau gauge gluon and ghost propagators of SU(2) gluodynamics using a sequence of increasing lattice sizes L^4 up to L=112 with corresponding \\beta-values chosen to keep the linear physical size a(\\beta)L ~ 9.6 fm fixed. To extremize the Landau gauge functional we employ simulated annealing combined with subsequent overrelaxation. Renormalizing the propagators at momentum \\mu= 2.2 GeV we observe quite strong lattice artifacts for the gluon propagator as well as for the ghost dressing function within the momentum region q < 1.0 GeV. The dependence on the lattice spacing for the gluon propagator at lowest accessible physical momentum values does not yet allow a simple extrapolation to the continuum limit. On the contrary, the running coupling derived from the bare dressing functions seems less affected by lattice artifacts.
Kasamatsu, Kenichi; Ichinose, Ikuo; Matsui, Tetsuo
2013-09-13
Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator.
Review of lattice supersymmetry and gauge-gravity duality
Energy Technology Data Exchange (ETDEWEB)
Joseph, Anosh [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Cambridge Univ. (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics (DAMTP)
2015-12-15
We review the status of recent investigations on validating the gauge-gravity duality conjecture through numerical simulations of strongly coupled maximally supersymmetric thermal gauge theories. In the simplest setting, the gauge-gravity duality connects systems of D0-branes and black hole geometries at finite temperature to maximally supersymmetric gauged quantum mechanics at the same temperature. Recent simulations show that non-perturbative gauge theory results give excellent agreement with the quantum gravity predictions, thus proving strong evidence for the validity of the duality conjecture and more insight into quantum black holes and gravity.
Lattice Landau gauge quark propagator and the quark-gluon vertex
Oliveira, Orlando; Silva, Paulo J; Skullerud, Jon-Ivar; Sternbeck, Andre; Williams, Anthony G
2016-01-01
We report preliminary results of our ongoing lattice computation of the Landau gauge quark propagator and the soft gluon limit of the quark-gluon vertex with 2 flavors of dynamical O(a) improved Wilson fermions.
Vortex free energies in SO(3) and SU(2) lattice gauge theory
De Forcrand, Philippe; Forcrand, Philippe de; Jahn, Oliver
2003-01-01
Lattice gauge theories with gauge groups SO(3) and SU(2) are compared. The free energy of electric twist, an order parameter for the confinement-deconfinement transition which does not rely on centre-symmetry breaking, is measured in both theories. The results are used to calibrate the scale in SO(3).
An analysis of the nucleon spectrum from lattice partially-quenched QCD
Energy Technology Data Exchange (ETDEWEB)
Armour, W. [Department of Physics, Swansea University, Swansea SA2 8PP, Wales (United Kingdom); Allton, C.R., E-mail: c.allton@swan.ac.u [Department of Physics, Swansea University, Swansea SA2 8PP, Wales (United Kingdom); Leinweber, D.B. [Special Research Centre for the Subatomic Structure of Matter (CSSM), School of Chemistry and Physics, University of Adelaide, 5005 (Australia); Thomas, A.W. [Jefferson Lab, 12000 Jefferson Ave., Newport News, VA 23606 (United States); College of William and Mary, Williamsburg, VA 23187 (United States); Young, R.D. [Physics Division, Argonne National Laboratory, Argonne, IL 60439 (United States)
2010-09-01
The chiral extrapolation of the nucleon mass, M{sub n}, is investigated using data coming from 2-flavour partially-quenched lattice simulations. A large sample of lattice results from the CP-PACS Collaboration is analysed using the leading one-loop corrections, with explicit corrections for finite lattice spacing artifacts. The extrapolation is studied using finite-range regularised chiral perturbation theory. The analysis also provides a quantitative estimate of the leading finite volume corrections. It is found that the discretisation, finite volume and partial quenching effects can all be very well described in this framework, producing an extrapolated value of M{sub n} in agreement with experiment. Furthermore, determinations of the low energy constants of the nucleon mass's chiral expansion are in agreement with previous methods, but with significantly reduced errors. This procedure is also compared with extrapolations based on polynomial forms, where the results are less encouraging.
SU(2) lattice gauge theory at non-zero temperature with fixed holonomy boundary condition
Ilgenfritz, E M; Müller-Preussker, M; Veselov, A I
2001-01-01
We study SU(2) lattice gauge theory at $T>0$ in a finite box with fixed holonomy value at the spatial boundary. We search for (approximate) classical solutions of the lattice field equations and find in particular the dissociated calorons recently discussed by van Baal and collaborators.
Time evolution of linearized gauge field fluctuations on a real-time lattice
Kurkela, Aleksi; Peuron, Jarkko
2016-01-01
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss's law.
Topological Objects And Confinement In Non-abelian Lattice Gauge Theory
Tucker, W W
2005-01-01
We use lattice methods to study the connection between topological objects and the confining potential in SU(2) and SU(3) Yang-Mills theories. We use Monte Carlo techniques, generating and performing measurements on sample configurations of SU(2) and SU(3) gauge fields. We isolate topological objects, specifically Abelian monopoles and center vortices, in these configurations. We then measure the contribution to the string tension from these objects, and compare the results to “full” measurements made on the original configurations. In addition we investigate the effects of gauge ambiguities (Gribov effects) and cooling on these sets of measurements. For the case of SU(2) lattice gauge theory, our results from monopoles agree with full values but are somewhat lower when gauge ambiguities are taken into account. The situation is not stable under cooling. When we carry out analogous procedures on sample SU(3) lattice configurations, we find disagreement between full SU(3) values and those fr...
Coulomb, Landau and Maximally Abelian Gauge Fixing in Lattice QCD with Multi-GPUs
Schröck, Mario
2013-01-01
A lattice gauge theory framework for simulations on graphic processing units (GPUs) using NVIDIA's CUDA is presented. The code comprises template classes that take care of an optimal data pattern to ensure coalesced reading from device memory to achieve maximum performance. In this work we concentrate on applications for lattice gauge fixing in 3+1 dimensional SU(3) lattice gauge field theories. We employ the overrelaxation, stochastic relaxation and simulated annealing algorithms which are perfectly suited to be accelerated by highly parallel architectures like GPUs. The applications support the Coulomb, Landau and maximally Abelian gauges. Moreover, we explore the evolution of the numerical accuracy of the SU(3) valued degrees of freedom over the runtime of the algorithms in single (SP) and double precision (DP). Therefrom we draw conclusions on the reliability of SP and DP simulations and suggest a mixed precision scheme that performs the critical parts of the algorithm in full DP while retaining 80-90% of...
Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices
Nuske, Marlon; Mathey, L.; Tiesinga, Eite
2016-08-01
We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultracold atoms in a deep hexagonal optical lattice. The dynamical evolution is triggered by a quench of the lattice potential such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency | Uf|/2 π in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the BCS order parameter Δ . The oscillation frequency of Δ is not reproduced by treating the time evolution in mean-field theory. In our theory, the momentum noise (i.e., density-density) correlation functions oscillate at frequency | Uf|/2 π as well as at its second harmonic. For a very deep lattice, with zero tunneling energy, the oscillations of momentum occupation numbers are undamped. Nonzero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. The damping occurs even for a finite-temperature initial BCS state, but not for a noninteracting Fermi gas. Furthermore, damping is stronger for larger order parameter and may therefore be used as a signature of the BCS state. Finally, our theory shows that the noise correlation functions in a honeycomb lattice will develop strong anticorrelations near the Dirac point.
Non-Abelian Lattice Gauge Theories in Superconducting Circuits
Mezzacapo, A; Sabín, C; Egusquiza, I L; Lamata, L; Solano, E
2015-01-01
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure $SU(2)$ gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms.
Landau gauge fixing on the lattice using GPU's
Cardoso, Nuno; Oliveira, Orlando; Bicudo, Pedro
2013-01-01
In this work, we consider the GPU implementation of the steepest descent method with Fourier acceleration for Laudau gauge fixing, using CUDA. The performance of the code in a Tesla C2070 GPU is compared with a parallel CPU implementation.
Vortex liquid in magnetic-field-induced superconducting vacuum of quenched lattice QCD
Braguta, V V; Chernodub, M N; Kotov, A Yu; Polikarpov, M I
2013-01-01
In the background of the strong magnetic field the vacuum is suggested to possess an electromagnetically superconducting phase characterised by the emergence of inhomogeneous quark-antiquark vector condensates which carry quantum numbers of the charged rho mesons. The rho-meson condensates are inhomogeneous due to the presence of the stringlike defects ("the rho vortices") which are parallel to the magnetic field (the superconducting vacuum phase is similar to the mixed Abrikosov phase of a type-II superconductor). In agreement with these expectations, we have observed the presence of the rho vortices in numerical simulations of the vacuum of the quenched two-color lattice QCD in strong magnetic field background. We have found that in the quenched QCD the rho vortices form a liquid. The transition between the usual (insulator) phase at low B and the superconducting vortex liquid phase at high B turns out to be very smooth, at least in the quenched QCD.
Szeless, Balázs; Calvone, F
1996-01-01
The quench heaters are vital elements for the protection of the LHC superconducting lattice magnets in the case of resistive transitions of the conductor. The basic concept of magnet protection and technical solutions are briefly presented. The quench heater consists of partially copper clad stainless steel strips sandwiched in between electric insulating carrier foils with electrical and mechanical properties such as to withstand high voltages, low temperatures, pressures and ionizing radiation. Testing of some commercial available electric insulation foils, polyimide (PI), polyetheretherketon (PEEK) and polyarylate (PA) and combinations of adhesive systems which are suitable for industrial processing are described. Possible industrial methods for series production for some 80 km of these composite quench heaters are indicated.
Polyakov line actions from SU(3) lattice gauge theory with dynamical fermions via relative weights
Höllwieser, Roman
2016-01-01
We extract an effective Polyakov line action from an underlying SU(3) lattice gauge theory with dynamical fermions via the relative weights method. The center-symmetry breaking terms in the effective theory are fit to a form suggested by effective action of heavy-dense quarks, and the effective action is solved at finite chemical potential by a mean field approach. We show results for a small sample of lattice couplings, lattice actions, and lattice extensions in the time direction. We find in some instances that the long-range couplings in the effective action are very important to the phase structure, and that these couplings are responsible for long-lived metastable states in the effective theory. Only one of these states corresponds to the underlying lattice gauge theory.
Strong-coupling study of the Gribov ambiguity in lattice Landau gauge
Energy Technology Data Exchange (ETDEWEB)
Maas, Axel [Karl-Franzens Universitaet Graz, Institut fuer Physik, Graz (Austria); Pawlowski, Jan M.; Spielmann, Daniel [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung, ExtreMe Matter Institute EMMI, Darmstadt (Germany); Sternbeck, Andre [University of Adelaide, Centre for the Subatomic Structure of Matter, SA, Adelaide (Australia); Universitaet Regensburg, Institut fuer Theoretische Physik, Regensburg (Germany); Smekal, Lorenz von [Technische Universitaet Darmstadt, Institut fuer Kernphysik, Darmstadt (Germany)
2010-07-15
We study the strong-coupling limit {beta}=0 of lattice SU(2) Landau gauge Yang-Mills theory. In this limit the lattice spacing is infinite, and thus all momenta in physical units are infinitesimally small. Hence, the infrared behavior can be assessed at sufficiently large lattice momenta. Our results show that at the lattice volumes used here, the Gribov ambiguity has an enormous effect on the ghost propagator in all dimensions. This underlines the severity of the Gribov problem and calls for refined studies also at finite {beta}. In turn, the gluon propagator only mildly depends on the Gribov ambiguity. (orig.)
Quenched Charmed Meson Spectra Using Tadpole Improved Quark Action on Anisotropic Lattices
Institute of Scientific and Technical Information of China (English)
LIU Liu-Ming; SU Shi-Quan; LI Xin; LIU Chuan
2005-01-01
@@ Charmed meson charmonium spectra are studied with improved quark actions on anisotropic lattices. We measured the pseudo-scalar and vector meson dispersion relations for four lowest lattice momentum modes with quark mass values ranging from the strange quark to charm quark with three different values of gauge coupling β and four different values of bare speed of light v. With the bare speed of light parameter v tuned in a mass-dependent way, we study the mass spectra of D, Ds, ηc, D*, Ds* and J/ψ mesons. The results extrapolated to the continuum limit are compared with the experiment, and a qualitative agreement is found.
Decorated tensor network renormalization for lattice gauge theories and spin foam models
Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian
2016-05-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.
The potential of the effective Polyakov line action from the underlying lattice gauge theory
Greensite, Jeff
2012-01-01
I adapt a numerical method, previously applied to investigate the Yang-Mills vacuum wavefunctional, to the problem of extracting the effective Polyakov line action from SU(N) lattice gauge theories, with or without matter fields. The method can be used to find the variation of the effective Polyakov line action along any trajectory in field configuration space; this information is sufficient to determine the potential term in the action, and strongly constrains the possible form of the kinetic term. The technique is illustrated for both pure and gauge-Higgs SU(2) lattice gauge theory at finite temperature. A surprise, in the pure gauge theory, is that the potential of the corresponding Polyakov line action contains a non-analytic (yet center-symmetric) term proportional to |P|^3, where P is the trace of the Polyakov line at a given point, in addition to the expected analytic terms proportional to even powers of P.
Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Grady, Michael, E-mail: grady@fredonia.edu
2013-11-21
Further evidence is presented for the existence of a non-confining phase at weak coupling in SU(2) lattice gauge theory. Using Monte Carlo simulations with the standard Wilson action, gauge-invariant SO(3)–Z2 monopoles, which are strong-coupling lattice artifacts, have been seen to undergo a percolation transition exactly at the phase transition previously seen using Coulomb gauge methods, with an infinite lattice critical point near β=3.2. The theory with both Z2 vortices and monopoles and SO(3)–Z2 monopoles eliminated is simulated in the strong-coupling (β=0) limit on lattices up to 60{sup 4}. Here, as in the high-β phase of the Wilson-action theory, finite size scaling shows it spontaneously breaks the remnant symmetry left over after Coulomb gauge fixing. Such a symmetry breaking precludes the potential from having a linear term. The monopole restriction appears to prevent the transition to a confining phase at any β. Direct measurement of the instantaneous Coulomb potential shows a Coulombic form with moderately running coupling possibly approaching an infrared fixed point of α∼1.4. The Coulomb potential is measured to 50 lattice spacings and 2 fm. A short-distance fit to the 2-loop perturbative potential is used to set the scale. High precision at such long distances is made possible through the use of open boundary conditions, which was previously found to cut random and systematic errors of the Coulomb gauge fixing procedure dramatically. The Coulomb potential agrees with the gauge-invariant interquark potential measured with smeared Wilson loops on periodic lattices as far as the latter can be practically measured with similar statistics data.
Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory
Grady, Michael
2013-11-01
Further evidence is presented for the existence of a non-confining phase at weak coupling in SU(2) lattice gauge theory. Using Monte Carlo simulations with the standard Wilson action, gauge-invariant SO(3)-Z2 monopoles, which are strong-coupling lattice artifacts, have been seen to undergo a percolation transition exactly at the phase transition previously seen using Coulomb gauge methods, with an infinite lattice critical point near β=3.2. The theory with both Z2 vortices and monopoles and SO(3)-Z2 monopoles eliminated is simulated in the strong-coupling (β=0) limit on lattices up to 604. Here, as in the high-β phase of the Wilson-action theory, finite size scaling shows it spontaneously breaks the remnant symmetry left over after Coulomb gauge fixing. Such a symmetry breaking precludes the potential from having a linear term. The monopole restriction appears to prevent the transition to a confining phase at any β. Direct measurement of the instantaneous Coulomb potential shows a Coulombic form with moderately running coupling possibly approaching an infrared fixed point of α˜1.4. The Coulomb potential is measured to 50 lattice spacings and 2 fm. A short-distance fit to the 2-loop perturbative potential is used to set the scale. High precision at such long distances is made possible through the use of open boundary conditions, which was previously found to cut random and systematic errors of the Coulomb gauge fixing procedure dramatically. The Coulomb potential agrees with the gauge-invariant interquark potential measured with smeared Wilson loops on periodic lattices as far as the latter can be practically measured with similar statistics data.
Structure of flux tube in SU(2) lattice gauge theory
Shiba, H
1994-01-01
The structure of the flux tube is studied in SU(2) QCD from the standpoint of the abelian projection theory. It is shown that the flux distributions of the orthogonal electric field and the magnetic field are produced by the effect that the abelian monopoles in the maximally abelian (MA) gauge are expelled from the string region.
Lattice gauge theory simulations in the quantum information era
Dalmonte, M.; Montangero, S.
2016-07-01
The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behaviour of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analysing the symmetric properties of Hamiltonian and states: the most striking examples are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realisation of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review, we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.
Definition of Magnetic Monopole Numbers for SU(N) Lattice Gauge-Higgs Models
Hollands, S
2001-01-01
A geometric definition for a magnetic charge of Abelian monopoles in SU(N) lattice gauge theories with Higgs fields is presented. The corresponding local monopole number defined for almost all field configurations does not require gauge fixing and is stable against small perturbations. Its topological content is that of a 3-cochain. A detailed prescription for calculating the local monopole number is worked out. Our method generalizes a magnetic charge definition previously invented by Phillips and Stone for SU(2).
Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Papinutto, M.; Pena, C. [CERN, Geneva (Switzerland). Physics Dept., Theory Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik
2007-06-15
We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of {delta}B=2 parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by nonperturbatively O(a) improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered. (orig.)
Dual of 3-dimensional pure SU(2) Lattice Gauge Theory and the Ponzano-Regge Model
Anishetty, R; Sharatchandra, H S; Mathur, M; Anishetty, Ramesh; Cheluvaraja, Srinath; Mathur, Manu
1993-01-01
By carrying out character expansion and integration over all link variables, the partition function of 3-dimensional pure SU(2) lattice gauge theory is rewritten in terms of 6j symbols. The result is Ponzano-Regge model of 3-dimensional gravity with a term that explicitly breaks general coordinate invariance. Conversely, we show that dual of Ponzano-Regge model is an SU(2) lattice gauge theory where all plaquette variables are constrained to the identity matrix and therefore the model needs no further regularization. Our techniques are applicable to other models with non-abelian symmetries in any dimension and provide duality transform for the partition function.
Decorated tensor network renormalization for lattice gauge theories and spin foam models
Dittrich, Bianca; Steinhaus, Sebastian
2014-01-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. Using this novel information encoded in the decoration might eventually lead to new methods incorporating both analytical and numerical techniques.
Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions
Chernodub, M N; Molochkov, A V
2016-01-01
We propose a general numerical method to study the Casimir effect in lattice gauge theories. We illustrate the method by calculating the energy density of zero-point fluctuations around two parallel wires of finite static permittivity in Abelian gauge theory in two spatial dimensions. We discuss various subtle issues related to the lattice formulation of the problem and show how they can successfully be resolved. Finally, we calculate the Casimir potential between the wires of a fixed permittivity, extrapolate our results to the limit of ideally conducting wires and demonstrate excellent agreement with a known theoretical result.
Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions
Chernodub, M. N.; Goy, V. A.; Molochkov, A. V.
2016-11-01
We propose a general numerical method to study the Casimir effect in lattice gauge theories. We illustrate the method by calculating the energy density of zero-point fluctuations around two parallel wires of finite static permittivity in Abelian gauge theory in two spatial dimensions. We discuss various subtle issues related to the lattice formulation of the problem and show how they can successfully be resolved. Finally, we calculate the Casimir potential between the wires of a fixed permittivity, extrapolate our results to the limit of ideally conducting wires and demonstrate excellent agreement with a known theoretical result.
The B-meson mass splitting from non-perturbative quenched lattice QCD
Grozin, A G; Marquard, P; Meyer, H B; Piclum, J H; Sommer, R; Steinhauser, M
2007-01-01
We perform the non-perturbative (quenched) renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory and its three-loop matching to QCD. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B-mesons. These new computed factors are affected by an uncertainty negligible in comparison to the known bare matrix element of the operator between B-states. Furthermore, they push the quenched determination of the spin splitting for the Bs-meson much closer to its experimental value than the previous perturbatively renormalized computations. The renormalization factor for three commonly used heavy quark actions and the Wilson gauge action and useful parametrizations of the matching coefficient are provided.
What are the Confining Field Configurations of Strong-Coupling Lattice Gauge Theory?
Faber, M; Olejník, S
2000-01-01
Starting from the strong-coupling SU(2) Wilson action in D=3 dimensions, we derive an effective, semi-local action on a lattice of spacing L times the spacing of the original lattice. It is shown that beyond the adjoint color-screening distance, i.e. for $L \\ge 5$, thin center vortices are stable saddlepoints of the corresponding effective action. Since the entropy of these stable objects exceeds their energy, center vortices percolate throughout the lattice, and confine color charge in half-integer representations of the SU(2) gauge group. This result contradicts the folklore that confinement in strong-coupling lattice gauge theory, for D>2 dimensions, is simply due to plaquette disorder, as is the case in D=2 dimensions. It also demonstrates explicitly how the emergence and stability of center vortices is related to the existence of color screening by gluon fields.
The exact decomposition of gauge variables in lattice Yang-Mills theory
Shibata, Akihiro; Kondo, Kei-Ichi; Shinohara, Toru
2010-07-01
In this Letter, we consider lattice versions of the decomposition of the Yang-Mills field a la Cho-Faddeev-Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU (N) gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU (2) and SU (3). As a result, we obtain the general form of the decomposition for SU (N) gauge link variables and confirm the previous results obtained for SU (2) and SU (3).
Parallel implementation of a lattice-gauge-theory code: studying quark confinement on PC clusters
Cucchieri, A; Travieso, G; Taurines, A R; Cucchieri, Attilio; Mendes, Tereza; Travieso, Gonzalo; Taurines, Andre R.
2003-01-01
We consider the implementation of a parallel Monte Carlo code for high-performance simulations on PC clusters with MPI. We carry out tests of speedup and efficiency. The code is used for numerical simulations of pure SU(2) lattice gauge theory at very large lattice volumes, in order to study the infrared behavior of gluon and ghost propagators. This problem is directly related to the confinement of quarks and gluons in the physics of strong interactions.
apeNEXT: A multi-TFlops Computer for Simulations in Lattice Gauge Theory
Bodin, F; Cabibbo, Nicola; Carlo, F D; De Pietri, R; Renzo, F D; Kaldass, H; Lonardo, A; Lukyanov, M; De Luca, S; Micheli, J; Morénas, V; Pène, O; Pleiter, D; Paschedag, N; Rapuano, F; Sartori, L; Schifano, F; Simma, H; Tripiccione, R; Vicini, P; Boucaud, Ph.
2003-01-01
We present the APE (Array Processor Experiment) project for the development of dedicated parallel computers for numerical simulations in lattice gauge theories. While APEmille is a production machine in today's physics simulations at various sites in Europe, a new machine, apeNEXT, is currently being developed to provide multi-Tflops computing performance. Like previous APE machines, the new supercomputer is largely custom designed and specifically optimized for simulations of Lattice QCD.
Digital Quantum Simulation of Z2 Lattice Gauge Theories with Dynamical Fermionic Matter
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with (2 +1 ) and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a Z2 model in (2 +1 ) dimensions.
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
Martinez, E A; Schindler, P; Nigg, D; Erhard, A; Heyl, M; Hauke, P; Dalmonte, M; Monz, T; Zoller, P; Blatt, R
2016-01-01
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-posi...
Strongly coupled gauge theories: What can lattice calculations teach us?
Hasenfratz, A; Rebbi, C; Weinberg, E; Witzel, O
2015-01-01
The dynamical origin of electroweak symmetry breaking is an open question with many possible theoretical explanations. Strongly coupled systems predicting the Higgs boson as a bound state of a new gauge-fermion interaction form one class of candidate models. Due to increased statistics, LHC run II will further constrain the phenomenologically viable models in the near future. In the meanwhile it is important to understand the general properties and specific features of the different competing models. In this work we discuss many-flavor gauge-fermion systems that contain both massless (light) and massive fermions. The former provide Goldstone bosons and trigger electroweak symmetry breaking, while the latter indirectly influence the infrared dynamics. Numerical results reveal that such systems can exhibit a light $0^{++}$ isosinglet scalar, well separated from the rest of the spectrum. Further, when we set the scale via the $vev$ of electroweak symmetry breaking, we predict a 2 TeV vector resonance which could...
Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED.
Fodor, Z; Hoelbling, C; Krieg, S; Lellouch, L; Lippert, Th; Portelli, A; Sastre, A; Szabo, K K; Varnhorst, L
2016-08-19
In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on N_{f}=2+1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. For the parameter which quantifies violations to Dashen's theorem, we obtain ϵ=0.73(2)(5)(17), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, m_{u}=2.27(6)(5)(4) and m_{d}=4.67(6)(5)(4) MeV in the modified minimal subtraction scheme at 2 GeV and the isospin breaking ratios m_{u}/m_{d}=0.485(11)(8)(14), R=38.2(1.1)(0.8)(1.4), and Q=23.4(0.4)(0.3)(0.4). Our results exclude the m_{u}=0 solution to the strong CP problem by more than 24 standard deviations.
Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED
Fodor, Z.; Hoelbling, C.; Krieg, S.; Lellouch, L.; Lippert, Th.; Portelli, A.; Sastre, A.; Szabo, K. K.; Varnhorst, L.; Budapest-Marseille-Wuppertal Collaboration
2016-08-01
In a previous Letter [Borsanyi et al., Phys. Rev. Lett. 111, 252001 (2013)] we determined the isospin mass splittings of the baryon octet from a lattice calculation based on Nf=2 +1 QCD simulations to which QED effects have been added in a partially quenched setup. Using the same data we determine here the corrections to Dashen's theorem and the individual up and down quark masses. Our ensembles include 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and average up-down quark masses all the way down to their physical value. For the parameter which quantifies violations to Dashen's theorem, we obtain ɛ =0.73 (2 )(5 )(17 ), where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, mu=2.27 (6 )(5 )(4 ) and md=4.67 (6 )(5 )(4 ) MeV in the modified minimal subtraction scheme at 2 G e V and the isospin breaking ratios mu/md=0.485 (11 )(8 )(14 ), R =38.2 (1.1 )(0.8 )(1.4 ), and Q =23.4 (0.4 )(0.3 )(0.4 ). Our results exclude the mu=0 solution to the strong C P problem by more than 24 standard deviations.
Koutentakis, G M; Schmelcher, P
2016-01-01
The non-equilibrium dynamics of small boson ensembles in a one-dimensional optical lattice is explored upon a sudden quench of an additional harmonic trap from strong to weak confinement. We find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system for intermediate quench amplitudes, corresponding to avoided crossings in the many-body eigenspectrum with varying final trap frequency. In particular, we show that these avoided crossings can be utilized to prepare the system in a desired state. The dynamical response is shown to depend on both the interaction strength as well as the number of atoms manifesting the many-body nature of the tunneling dynamics.
Koutentakis, G. M.; Mistakidis, S. I.; Schmelcher, P.
2017-01-01
The nonequilibrium dynamics of small boson ensembles in a one-dimensional optical lattice is explored upon a sudden quench of an additional harmonic trap from strong to weak confinement. We find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system for intermediate quench amplitudes, corresponding to avoided crossings in the many-body eigenspectrum with varying final trap frequency. In particular, we show that these avoided crossings can be utilized to prepare the system in a desired state. The dynamical response is shown to depend on both the interaction strength as well as the number of atoms manifesting the many-body nature of the tunneling dynamics.
Renormalization of Anisotropy and Glueball Masses on Tadpole Improved Lattice Gauge Action
Loan, M; Hamer, C; Loan, Mushtaq; Byrnes, Tim; Hamer, Chris
2003-01-01
The Numerical calculations for tadpole-improved U(1) lattice gauge theory in three-dimensions on anisotropic lattices have been performed using standard path integral Monte Carlo techniques. Using average plaquette tadpole renormalization scheme, simulations were done with temporal lattice spacings much smaller than the spatial ones and results were obtained for the string tension, the renormalized anisotropy and scalar glueball masses. We find, by comparing the `regular' and `sideways' potentials, that tadpole improvement results in very little renormalization of the bare anisotropy and reduces the discretization errors in the static quark potential and in the glueball masses.
Universality and the approach to the continuum limit in lattice gauge theory
De Divitiis, G M; Guagnelli, M; Lüscher, Martin; Petronzio, Roberto; Sommer, Rainer; Weisz, P; Wolff, U; de Divitiis, G; Frezzotti, R; Guagnelli, M; Luescher, M; Petronzio, R; Sommer, R; Weisz, P; Wolff, U
1995-01-01
The universality of the continuum limit and the applicability of renormalized perturbation theory are tested in the SU(2) lattice gauge theory by computing two different non-perturbatively defined running couplings over a large range of energies. The lattice data (which were generated on the powerful APE computers at Rome II and DESY) are extrapolated to the continuum limit by simulating sequences of lattices with decreasing spacings. Our results confirm the expected universality at all energies to a precision of a few percent. We find, however, that perturbation theory must be used with care when matching different renormalized couplings at high energies.
Maximum-Likelihood Approach to Topological Charge Fluctuations in Lattice Gauge Theory
Brower, R C; Fleming, G T; Lin, M F; Neil, E T; Osborn, J C; Rebbi, C; Rinaldi, E; Schaich, D; Schroeder, C; Voronov, G; Vranas, P; Weinberg, E; Witzel, O
2014-01-01
We present a novel technique for the determination of the topological susceptibility (related to the variance of the distribution of global topological charge) from lattice gauge theory simulations, based on maximum-likelihood analysis of the Markov-chain Monte Carlo time series. This technique is expected to be particularly useful in situations where relatively few tunneling events are observed. Restriction to a lattice subvolume on which topological charge is not quantized is explored, and may lead to further improvement when the global topology is poorly sampled. We test our proposed method on a set of lattice data, and compare it to traditional methods.
Geometric approach to chaos in the classical dynamics of Abelian lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Casetti, Lapo [Istituto Nazionale per la Fisica della Materia (INFM), Unita di Ricerca del Politecnico di Torino, Dipartimento di Fisica, Politecnico di Torino, Turin (Italy); Gatto, Raoul [Departement de Physique Theorique, Universite de Geneve, Geneva (Switzerland); Pettini, Marco [Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, Florence (Italy)
1999-04-23
A Riemannian geometrization of dynamics is used to study chaoticity in the classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach allows one to obtain analytical estimates of the largest Lyapunov exponent in terms of time averages of geometric quantities. These estimates are compared with the results of numerical simulations, and turn out to be very close to the values extrapolated for very large lattice sizes even when the geometric quantities are computed using small lattices. The scaling of the Lyapunov exponent {lambda} with the energy density {epsilon} is found to be well described by the law {lambda}{proportional_to}{epsilon}{sup 2}. (author)
Geometric approach to chaos in the classical dynamics of abelian lattice gauge theory
Casetti, L; Pettini, M; Casetti, Lapo; Gatto, Raoul; Pettini, Marco
1998-01-01
A Riemannian geometrization of dynamics is used to study chaoticity in the classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach allows one to obtain analytical estimates of the largest Lyapunov exponent in terms of time averages of geometric quantities. These estimates are compared with the results of numerical simulations, and turn out to be very close to the values extrapolated for very large lattice sizes even when the geometric quantities are computed using small lattices. The scaling of the Lyapunov exponent with the energy density is found to be well described by a quadratic power law.
Direct evidence for a Coulombic phase in monopole-suppressed SU(2) lattice gauge theory
Grady, Michael
2013-01-01
Further evidence is presented for the existence of a non-confining phase at weak coupling in SU(2) lattice gauge theory. Using Monte Carlo simulations with the standard Wilson action, gauge-invariant SO(3)-Z2 monopoles, which are strong-coupling lattice artifacts, have been seen to undergo a percolation transition exactly at the phase transition previously seen using Coulomb-gauge methods, with an infinite lattice critical point near $\\beta = 3.2$. The theory with both Z2 vortices and monopoles and SO(3)-Z2 monopoles eliminated is simulated in the strong coupling ($\\beta = 0$) limit on lattices up to $60^4$. Here, as in the high-$\\beta$ phase of the Wilson action theory, finite size scaling shows it spontaneously breaks the remnant symmetry left over after Coulomb gauge fixing. Such a symmetry breaking precludes the potential from having a linear term. The monopole restriction appears to prevent the transition to a confining phase at any $\\beta$. Direct measurement of the instantaneous Coulomb potential shows...
Mathematical Derivation of Chiral Anomaly in Lattice Gauge Theory with Wilson's Action
Hattori, T G; Hattori, Tetsuya; Watanabe, Hiroshi
1998-01-01
Chiral U(1) anomaly is derived with mathematical rigor for a Euclidean fermion coupled to a smooth external U(1) gauge field on an even dimensional torus as a continuum limit of lattice regularized fermion field theory with the Wilson term in the action. The present work rigorously proves for the first time that the Wilson term correctly reproduces the chiral anomaly.
Energy Technology Data Exchange (ETDEWEB)
Gottlieb, Steven Arthur [Indiana University; DeTar, Carleton [University of Utah; Tousaint, Doug [University of Arizona
2014-07-24
This is the closeout report for the Indiana University portion of the National Computational Infrastructure for Lattice Gauge Theory project supported by the United States Department of Energy under the SciDAC program. It includes information about activities at Indian University, the University of Arizona, and the University of Utah, as those three universities coordinated their activities.
Cold-atom quantum simulation of U(1) lattice gauge-Higgs model
Kasamatsu, Kenichi; Kuno, Yoshihito; Takahashi, Yoshiro; Ichinose, Ikuo; Matsui, Tetsuo
2015-03-01
We discuss the possible methods to construct a quantum simulator of the U(1) lattice gauge-Higgs model using cold atoms in an optical lattice. These methods require no severe fine tunings of parameters of atomic-interactions in contrast with the other previous literature. We propose some realistic experimental setups to realize the atomic quantum simulator of the U(1) lattice gauge-Higgs model in a two-dimensional optical lattice. Our target gauge-Higgs model has a nontrivial phase structure, i.e., existence of the phase boundary between confinement and Higgs phases, and this phase boundary is to be observed by cold-atom experiments. As a reference to such experiments, we make numerical simulations of the time-dependent Gross-Pitaevskii equation and observe the real-time dynamics of the atomic simulators. Clarification of the dynamics of this gauge-Higgs model sheds some lights upon various unsolved problems including the inflation process of the early universe.
Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization
Aoki, Sinya; Nagata, Keitaro
2016-01-01
We study the entanglement entropy (EE) for pure gauge theories in 1+1 dimensions with the lattice regularization. Using the definition of the EE for lattice gauge theories proposed in a previous paper [1] (S. Aoki, T. Iritani, M. Nozaki, T. Numasawa, N. Shiba and H. Tasaki, JHEP 1506 (2015) 187), we calculate the EE for arbitrary pure as well as mixed states in terms of eigenstates of the transfer matrix in 1+1 dimensional lattice gauge theory. We find that the EE of an arbitrary pure state does not depend on the lattice spacing, thus giving the EE in the continuum limit, and show that the EE for an arbitrary pure state is independent of the real (Minkowski) time evolution. We also explicitly demonstrate the dependence of EE on the gauge fixing at the boundaries between two subspaces, which was pointed out for general cases in the paper [1]. In addition, we calculate the EE at zero as well as finite temperature by the replica method, and show that our result in the continuum limit corresponds to the result ob...
Decker, K. M.; Jayewardena, C.; Rehmann, R.
We describe the library lgtlib, and lgttool, the corresponding development environment for Monte Carlo simulations of lattice gauge theory on multiprocessor vector computers with shared memory. We explain why distributed memory parallel processor (DMPP) architectures are particularly appealing for compute-intensive scientific applications, and introduce the design of a general application and program development environment system for scientific applications on DMPP architectures.
Gauge-invariant nonlocal quark condensates in QCD a new interpretation of the lattice results
Meggiolaro, E
2000-01-01
We study the asymptotic short-distance behaviour as well as the asymptotic large-distance behaviour of the gauge-invariant quark-antiquark nonlocal condensates in QCD. A comparison of some analytical results with the available lattice data is performed.
Phase structure of (2+1)d strongly coupled lattice gauge theories
Strouthos, C G
2003-01-01
We study the chiral phase transition in (2+1)d strongly coupled U(N) lattice gauge theories with staggered fermions. We show with high precision simulations performed directly in the chiral limit that these models undergo a Berezinski-Kosterlitz-Thouless (BKT) transition. We also show that this universality class is unaffected even in the large N limit.
From Doubled Chern-Simons-Maxwell Lattice Gauge Theory to Extensions of the Toric Code
Olesen, T Z; Wiese, U -J
2015-01-01
We regularize compact and non-compact Abelian Chern-Simons-Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group $\\mathbb{R}$, each local Hilbert space is analogous to the one of a charged "particle" moving in the link-pair group space $\\mathbb{R}^2$ in a constant "magnetic" background field. In the compact case, the link-pair group space is a torus $U(1)^2$ threaded by $k$ units of quantized "magnetic" flux, with $k$ being the level of the Chern-Simons theory. The holonomies of the torus $U(1)^2$ give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry...
Compact U(1) lattice gauge-Higgs theory with monopole suppression
Krishnan, B; Mitrjushkin, V K; Müller-Preussker, M; Krishnan, Balasubramanian
1996-01-01
We investigate a model of a U(1)-Higgs theory on the lattice with compact gauge fields but completely suppressed (elementary) monopoles. We study the model at two values of the quartic Higgs self-coupling, a strong coupling, \\lambda = 3.0, and a weak coupling, \\lambda=0.01. We map out the phase diagrams and find that the monopole suppression eliminated the confined phase of the standard lattice model at strong gauge coupling. We perform a detailed analysis of the static potential and study the mass spectrum in the Coulomb and Higgs phases for three values of the gauge coupling. We also probe the existence of a scalar bosonium to the extent that our data allow and conclude that further investigations are required in the Coulomb phase.
Tricritical points in a compact $U(1)$ lattice gauge theory at strong coupling
De, Asit K
2016-01-01
Pure compact $U(1)$ lattice gauge theory exhibits a phase transition at gauge coupling $g \\sim {\\cal{O}}(1)$ separating a familiar weak coupling Coulomb phase, having free massless photons, from a strong coupling phase. However, the phase transition was found to be of first order, ruling out any non-trivial theory resulting from a continuum limit from the strong coupling side. In this work, a compact $U(1)$ lattice gauge theory is studied with addition of a dimension-two mass counter-term and a higher derivative (HD) term that ensures a unique vacuum and produces a covariant gauge-fixing term in the naive continuum limit. For a reasonably large coefficient of the HD term, now there exists a continuous transition from a regular ordered phase to a spatially modulated ordered phase which breaks Euclidean rotational symmetry. For weak gauge couplings, a continuum limit from the regular ordered phase results in a familiar theory consisting of free massless photons. For strong gauge couplings with $g\\ge {\\cal{O}}(1...
Chiral Symmetry Breaking for Domain Wall Fermions in Quenched Lattice QCD
Wu, L
2001-01-01
The domain wall fermion formulation exhibits full chiral symmetry for finite lattice spacing except for the effects of mixing between the domain walls. Close to the continuum limit these symmetry breaking effects should be described by a single residual mass. We determine this mass from the conservation law obeyed by the conserved axial current in quenched simulations with beta=5.7 and 6.0 and domain wall separations varying between 12 and 48 on 8^3x32 and 16^3x32 lattices. Using the resulting values for the residual mass we perform two complete and independent calculations of the pion decay constant. Good agreement is found between these two methods and with experiment.
Lattice Gauge Quantum Simulation via State-Dependent Hopping
DEFF Research Database (Denmark)
Salami Dehkharghani, Amin
2017-01-01
We develop a quantum simulator architecture that is suitable for the simulation of U(1) Abelian gauge theories such as quantum electrodynamics. Our approach relies on the ability to control the hopping of a particle through a barrier by means of the internal quantum states of a neutral or charged...... impurity-particle sitting at the barrier. This scheme is highly experimentally feasible, as the correlated hopping does not require fine-tuning of the intra- and inter-species interactions. We investigate the applicability of the scheme in a double well potential, which is the basic building block...... of the simulator, both at the single-particle and the many-body mean-field level. Moreover, we evaluate its performance for different particle interactions and trapping, and, specifically for atom-ion systems, in the presence of micro-motion....
Dense baryonic matter in strong coupling lattice gauge theory
Bringoltz, B
2004-01-01
We investigate the strong coupling limit of lattice QCD in the Hamiltonian formulation for systems with non-zero baryon density. In leading order the Hamiltonian looks like an antiferromagnet that is invariant under global U(N_f)xU(N_f) and local SU(N_c). Physically it describes meson dynamics with a fixed background of baryon density. We study this Hamiltonian with several baryon number distributions, and concentrate on the global symmetries of the ground state and on the properties of low lying excitations. In particular, for uniform non-zero baryon density we write the partition function as a path integral that is tractable in the limit of large N_c. We find that the ground state spontaneously breaks chiral symmetry as well as discrete lattice rotations in a way that depends on N_f and the density. The low energy excitations include type I and type II Goldstone bosons. The energies of the latter are of order 1/N_c, and are quadratic in momentum. Bosons of either type can develop anisotropic dispersion rela...
Precision lattice test of the gauge/gravity duality at large N
Berkowitz, Evan; Rinaldi, Enrico; Hanada, Masanori; Ishiki, Goro; Shimasaki, Shinji; Vranas, Pavlos; Monte Carlo String/M-Theory Collaboration McSmc
2016-11-01
We perform a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-N and continuum limits of the gauge theory are taken for the first time at various temperatures 0.4 ≤T ≤1.0 . As a way to test the gauge/gravity duality conjecture we compute the internal energy of the black hole as a function of the temperature directly from the gauge theory. We obtain a leading behavior that is compatible with the supergravity result E /N2=7.41 T14 /5 : the coefficient is estimated to be 7.4 ±0.5 when the exponent is fixed and stringy corrections are included. This is the first confirmation of the supergravity prediction for the internal energy of a black hole at finite temperature coming directly from the dual gauge theory. We also constrain stringy corrections to the internal energy.
Buyens, Boye; Montangero, Simone; Haegeman, Jutho; Verstraete, Frank; Van Acoleyen, Karel
2017-05-01
It has been established that matrix product states can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavor QED2 , with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field.
Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
Caspar, Stephan; Olesen, Therkel Z; Vlasii, Nadiia D; Wiese, Uwe-Jens
2016-01-01
We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group $G$ in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm pha...
Z2 gauge theory for valence bond solids on the kagome lattice
Hwang, Kyusung; Huh, Yejin; Kim, Yong Baek
We present an effective Z2 gauge theory that captures various competing phases in spin-1/2 kagome lattice antiferromagnets: the topological Z2 spin liquid (SL) phase, and the 12-site and 36- site valence bond solid (VBS) phases. Our effective theory is a generalization of the recent Z2 gauge theory proposed for SL phases by Wan and Tchernyshyov. In particular, we investigate possible VBS phases that arise from vison condensations in the SL. In addition to the 12-site and 36-site VBS phases, there exists 6-site VBS that is closely related to the symmetry-breaking valence bond modulation patterns observed in the recent density matrix renormalization group simulations. We find that our results have remarkable consistency with a previous study using a different Z2 gauge theory. Motivated by the lattice geometry in the recently reported vanadium oxyfluoride kagome antiferromagnet, our gauge theory is extended to incorporate lowered symmetry by inequivalent up- and down-triangles. We investigate effects of this anisotropy on the 12-site, 36-site, and 6-site VBS phases. Particularly, interesting dimer melting effects are found in the 36-site VBS. We discuss the implications of our findings and also compare the results with a different type of Z2 gauge theory used in previous studies.
Kuno, Yoshihito; Kasamatsu, Kenichi; Takahashi, Yoshiro; Ichinose, Ikuo; Matsui, Tetsuo
2015-06-01
Lattice gauge theory has provided a crucial non-perturbative method in studying canonical models in high-energy physics such as quantum chromodynamics. Among other models of lattice gauge theory, the lattice gauge-Higgs model is a quite important one because it describes a wide variety of phenomena/models related to the Anderson-Higgs mechanism, such as superconductivity, the standard model of particle physics, and the inflation process of the early Universe. In this paper, we first show that atomic description of the lattice gauge model allows us to explore real-time dynamics of the gauge variables by using the Gross-Pitaevskii equations. Numerical simulations of the time development of an electric flux reveal some interesting characteristics of the dynamic aspect of the model and determine its phase diagram. Next, to realize a quantum simulator of the U(1) lattice gauge-Higgs model on an optical lattice filled by cold atoms, we propose two feasible methods: (i) Wannier states in the excited bands and (ii) dipolar atoms in a multilayer optical lattice. We pay attention to the constraint of Gauss's law and avoid nonlocal gauge interactions.
Mehta, Dhagash; Kastner, Michael
2011-06-01
We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics. An analytic solution of all stationary points is derived for lattices with an odd number of lattice sites and periodic boundary conditions. In the context of lattice gauge theory, these stationary points and their indices are used to compute the gauge fixing partition function, making reference in particular to the Neuberger problem. Interpreted as stationary points of the one-dimensional XY Hamiltonian, the solutions and their Hessian determinants allow us to evaluate a criterion which makes predictions on the existence of phase transitions and the corresponding critical energies in the thermodynamic limit.
Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, W. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Bigarini, A. [Univ. degli Studi di Perugia (Italy). Dipt. di Fisica]|[INFN, Sezione di Perugia (Italy)]|[Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Torrielli, A. [Massachusetts Institute of Technology, Cambridge, MA (United States). Center for Theoretical Physics, Lab. for Nuclear Sciences
2007-06-15
We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer
2016-06-01
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer.
Martinez, Esteban A; Muschik, Christine A; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer
2016-06-23
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman's idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments-the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.
Lattice gauge theory and gluon color-confinement in curved spacetime
Villegas, Kristian Hauser
2014-01-01
The lattice gauge theory for curved spacetime is formulated. A discretized action is derived for both gluon and quark fields which reduces to the generally covariant form in the continuum limit. Using the Wilson action, it is shown analytically that for a general curved spacetime background, two propagating gluons are always color-confined. The fermion-doubling problem is discussed in the specific case of Friedman-Robertson-Walker metric. Lastly, we discussed possible future numerical implementation of lattice QCD in curved spacetime.
Digital quantum simulation of $\\mathbb{Z}_2$ lattice gauge theories with dynamical fermionic matter
Zohar, Erez; Reznik, Benni; Cirac, J Ignacio
2016-01-01
We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with $2+1$ and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a $\\mathbb{Z}_2$ model in $2+1$ dimensions.
Volume scaling of Dirac eigenvalues in SU(3) lattice gauge theory with color sextet fermions
DeGrand, Thomas
2009-01-01
I observe a rough volume-dependent scaling of the low eigenvalues of a chiral Dirac operator in lattice studies of SU(3) lattice gauge theory with two flavors of color sextet fermions, in its weak-coupling phase. The mean value of the ith eigenvalue scales with the simulation volume V=L^4 as L^p ~zeta_i, where zeta_i is a volume-independent constant. The exponent p is about 1.4. A possible explanation for this phenomenon is that p is the leading relevant exponent associated with the fermion mass dependence of correlation functions in a theory whose zero-mass limit is conformal.
London relation and fluxoid quantization for monopole currents in U(1) lattice gauge theory
Singh, Vandana; Browne, Dana A; 10.1103/PhysRevD.47.1715
2009-01-01
We explore the analogy between quark confinement and the Meissner effect in superconductors. We measure the response of color-magnetic "supercurrents" from Dirac magnetic monopoles to the presence of a static quark-antiquark pair in four dimensional U(1) lattice gauge theory. Our results indicate that in the confined phase these currents screen the color-electric flux due to the quarks in an electric analogy of the Meisner effect. We show that U(1) lattice guage theory obeys both a dual London equation and an electric fluxoid quantization condition.
Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group
Caspar, S.; Mesterházy, D.; Olesen, T. Z.; Vlasii, N. D.; Wiese, U.-J.
2016-11-01
We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k) ⊂ U(1) , the symmetric group S3 ⊂ O(2) , the binary dihedral (or quaternion) group D¯2 ⊂ SU(2) , and the finite group Δ(27) ⊂ SU(3) . In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication.
Thermodynamics of Gauge-Invariant U(1) Vortices from Lattice Monte Carlo Simulations
Kajantie, Keijo; Laine, Mikko; Peisa, J; Rajantie, A
1998-01-01
We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We discretize the system and introduce a gauge-invariant definition of a vortex passing through a loop on the lattice. We then study with Monte Carlo simulations the total vortex density, extract the physically meaningful part thereof, and demonstrate that it has a well-defined continuum limit. The total vortex density behaves as a pseudo order parameter, having a discontinuity in the regime of first order transitions and behaving continuously in the regime of second order transitions. Finally, we discuss further gauge-invariant observables to be measured.
On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
Delcamp, Clement; Riello, Aldo
2016-01-01
Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non--Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non--Abelian analogue of the `magnetic centre choice', as obtained through an extended--Hilbert--space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. W...
DeGrand, Thomas; Golterman, Maarten; Jay, William I.; Neil, Ethan T.; Shamir, Yigal; Svetitsky, Benjamin
2016-09-01
We develop methods to calculate the electroweak gauge boson contribution to the effective Higgs potential in the context of composite Higgs models, using lattice gauge theory. The calculation is analogous to that of the electromagnetic mass splitting of the pion multiplet in QCD. We discuss technical details of carrying out this calculation, including modeling of the momentum and fermion-mass dependence of the underlying current-current correlation function, direct integration of the correlation function over momentum, and fits based on the minimal-hadron approximation. We show results of a numerical study using valence overlap fermions, carried out in an SU(4) gauge theory with two flavors of Dirac fermions in the two-index antisymmetric representation.
Canonical transformations and loop formulation of SU(N) lattice gauge theories
Mathur, Manu; Sreeraj, T. P.
2015-12-01
We construct canonical transformations to reformulate SU(N) Kogut-Susskind lattice gauge theory in terms of a set of fundamental loop and string flux operators along with their canonically conjugate loop and string electric fields. The canonical relations between the initial SU(N) link operators and the final SU(N) loop and string operators, consistent with SU(N) gauge transformations, are explicitly constructed over the entire lattice. We show that as a consequence of SU(N) Gauss laws all SU(N) string degrees of freedom become cyclic and decouple from the physical Hilbert space Hp. The Kogut-Susskind Hamiltonian rewritten in terms of the fundamental physical loop operators has global SU(N) invariance. There are no gauge fields. We further show that the (1 /g2 ) magnetic field terms on plaquettes create and annihilate the fundamental plaquette loop fluxes while the (g2 ) electric field terms describe all their interactions. In the weak coupling (g2→0 ) continuum limit the SU(N) loop dynamics is described by SU(N) spin Hamiltonian with nearest neighbor interactions. In the simplest SU(2) case, where the canonical transformations map the SU(2) loop Hilbert space into the Hilbert spaces of hydrogen atoms, we analyze the special role of the hydrogen atom dynamical symmetry group S O (4 ,2 ) in the loop dynamics and the spectrum. A simple tensor network ansatz in the SU(2) gauge invariant hydrogen atom loop basis is discussed.
Energy Technology Data Exchange (ETDEWEB)
Moriarty, K.J.M. (Royal Holloway Coll., Englefield Green (UK). Dept. of Mathematics); Blackshaw, J.E. (Floating Point Systems UK Ltd., Bracknell)
1983-04-01
The computer program calculates the average action per plaquette for SU(6)/Z/sub 6/ lattice gauge theory. By considering quantum field theory on a space-time lattice, the ultraviolet divergences of the theory are regulated through the finite lattice spacing. The continuum theory results can be obtained by a renormalization group procedure. Making use of the FPS Mathematics Library (MATHLIB), we are able to generate an efficient code for the Monte Carlo algorithm for lattice gauge theory calculations which compares favourably with the performance of the CDC 7600.
Slow relaxation and sensitivity to disorder in trapped lattice fermions after a quench
Schulz, M.; Hooley, C. A.; Moessner, R.
2016-12-01
We consider a system of noninteracting fermions in one dimension subject to a single-particle potential consisting of (a) a strong optical lattice, (b) a harmonic trap, and (c) uncorrelated on-site disorder. After a quench, in which the center of the harmonic trap is displaced, we study the occupation function of the fermions and the time evolution of experimental observables. Specifically, we present numerical and analytical results for the postquench occupation function of the fermions, and analyze the time evolution of the real-space density profile. Unsurprisingly for a noninteracting (and therefore integrable) system, the infinite-time limit of the density profile is nonthermal. However, due to Bragg localization of the higher-energy single-particle states, the approach to even this nonthermal state is extremely slow. We quantify this statement, and show that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localization.
Energy Technology Data Exchange (ETDEWEB)
Braguta, V.V. [IHEP, Protvino, Moscow region, 142284 (Russian Federation); ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218 (Russian Federation); Buividovich, P.V. [ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218 (Russian Federation); JINR, Joliot-Curie str. 6, Dubna, Moscow region, 141980 (Russian Federation); Institute of Theoretical Physics, University of Regensburg, Universitaetsstrasse 31, D-93053 Regensburg (Germany); Chernodub, M.N., E-mail: maxim.chernodub@lmpt.univ-tours.fr [CNRS, Laboratoire de Mathematiques et Physique Theorique, Universite Francois-Rabelais Tours, Parc de Grandmont, 37200 Tours (France); Department of Physics and Astronomy, University of Gent, Krijgslaan 281, S9, B-9000 Gent (Belgium); Kotov, A.Yu.; Polikarpov, M.I. [ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218 (Russian Federation); MIPT, Institutskii per. 9, Dolgoprudny, Moscow region, 141700 (Russian Federation)
2012-12-05
Using numerical simulations of quenched SU(2) gauge theory we demonstrate that an external magnetic field leads to spontaneous generation of quark condensates with quantum numbers of electrically charged {rho} mesons if the strength of the magnetic field exceeds the critical value eB{sub c}=0.927(77) GeV{sup 2} or B{sub c}=(1.56{+-}0.13) Dot-Operator 10{sup 16} Tesla. The condensation of the charged {rho} mesons in strong magnetic field is a key feature of the magnetic-field-induced electromagnetic superconductivity of the vacuum.
Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
Nakagawa, Y.; Voigt, A.; Ilgenfritz, E.-M.; Müller-Preussker, M.; Nakamura, A.; Saito, T.; Sternbeck, A.; Toki, H.
2009-06-01
We study the momentum dependence of the ghost propagator and of the space and time components of the gluon propagator at equal time in pure SU(3) lattice Coulomb-gauge theory carrying out a joint analysis of data collected independently at the Research Center for Nuclear Physics, Osaka and Humboldt University, Berlin. We focus on the scaling behavior of these propagators at β=5.8,…,6.2 and apply a matching technique to relate the data for the different lattice cutoffs. Thereby, lattice artifacts are found to be rather strong for both instantaneous gluon propagators at a large momentum. As a byproduct we obtain the respective lattice scale dependences a(β) for the transversal gluon and the ghost propagator which indeed run faster with β than two-loop running, but slightly slower than what is known from the Necco-Sommer analysis of the heavy quark potential. The abnormal a(β) dependence as determined from the instantaneous time-time gluon propagator, D44, remains a problem, though. The role of residual gauge-fixing influencing D44 is discussed.
Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
Nakagawa, Y; Ilgenfritz, E -M; Müller-Preussker, M; Nakamura, A; Saitô, T; Sternbeck, A; Toki, H
2009-01-01
We study the momentum dependence of the ghost propagator and of the space and time components of the gluon propagator at equal time in pure SU(3) lattice Coulomb gauge theory carrying out a joint analysis of data collected independently at RCNP Osaka and Humboldt University Berlin. We focus on the scaling behavior of these propagators at beta=5.8,...,6.2 and apply a matching technique to relate the data for the different lattice cutoffs. Thereby, lattice artifacts are found to be rather strong for both instantaneous gluon propagators at large momentum. As a byproduct we obtain the respective lattice scale dependences a(beta) for the transversal gluon and the ghost propagator which indeed run faster with beta than two-loop running, but slightly slower than what is known from the Necco-Sommer analysis of the heavy quark potential. The abnormal a(beta) dependence as determined from the instantaneous time-time gluon propagator, D_{44}, remains a problem, though. The role of residual gauge-fixing influencing D_{44...
Numerical Evaluation of the Bose-Ghost Propagator in Minimal Landau Gauge on the Lattice
Cucchieri, Attilio
2016-01-01
We present numerical details of the evaluation of the so-called Bose-ghost propagator in lattice minimal Landau gauge, for the SU(2) case in four Euclidean dimensions. This quantity has been proposed as a carrier of the confining force in the Gribov-Zwanziger approach and, as such, its infrared behavior could be relevant for the understanding of color confinement in Yang-Mills theories. Also, its nonzero value can be interpreted as direct evidence of BRST-symmetry breaking, which is induced when restricting the functional measure to the first Gribov region Omega. Our simulations are done for lattice volumes up to 120^4 and for physical lattice extents up to 13.5 fm. We investigate the infinite-volume and continuum limits.
Landau gauge gluon and ghost propagators from two-flavor lattice QCD at T > 0
Aouane, R; Muller-Preussker, M; Ilgenfritz, E -M; Sternbeck, A
2013-01-01
In this contribution we extend our unquenched computation of the Landau gauge gluon and ghost propagators in lattice QCD at non-zero temperature. The study was aimed at providing input for investigations employing continuum functional methods. We show data which correspond to pion mass values between 300 and 500 MeV and are obtained for a lattice size 32**3 x 12. The longitudinal and transversal components of the gluon propagator turn out to change smoothly through the crossover region, while the ghost propagator exhibits only a very weak temperature dependence. For a pion mass of around 400 MeV and the intermediate temperature value of approx. 240 MeV we compare our results with additional data obtained on a lattice with smaller Euclidean time extent N_t = 8, 10 and find a reasonable scaling behavior.
Numerical evaluation of the Bose-ghost propagator in minimal Landau gauge on the lattice
Cucchieri, Attilio; Mendes, Tereza
2016-07-01
We present numerical details of the evaluation of the so-called Bose-ghost propagator in lattice minimal Landau gauge, for the SU(2) case in four Euclidean dimensions. This quantity has been proposed as a carrier of the confining force in the Gribov-Zwanziger approach and, as such, its infrared behavior could be relevant for the understanding of color confinement in Yang-Mills theories. Also, its nonzero value can be interpreted as direct evidence of Becchi-Rouet-Stora-Tyutin-symmetry breaking, which is induced when restricting the functional measure to the first Gribov region Ω . Our simulations are done for lattice volumes up to 1204 and for physical lattice extents up to 13.5 fm. We investigate the infinite-volume and continuum limits.
Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field arXiv
Figueroa, Daniel G.
Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present a lattice formulation of the interaction between a $shift$-symmetric field and some $U(1)$ gauge sector, $a(x)\\tilde{F}_{\\mu\
Charmonium-Nucleon Interaction from Quenched Lattice QCD with Relativistic Heavy Quark Action
Kawanai, Taichi; Sasaki, Shoichi; Hatsuda, Tetsuo
2009-10-01
Low energy charmonium-nucleon interaction is of particular interest in this talk. A heavy quarkonium state like the charmonium does not share the same quark flavor with the nucleon so that cc-nucleon interaction might be described by the gluonic van der Waals interaction, which is weak but attractive. Therefore, the information of the strength of cc-nucleon interaction is vital for considering the possibility of the formation of charmonium bound to nuclei. We will present the preliminary results for the scattering length and the interaction range of charmonium-nucleon s-wave scattering from quenched lattice QCD. These low-energy quantities can provide useful constraints on the phenomenological cc-nucleon potential, which is required for precise prediction of the binding energy of nuclear-bound charmonium in exact few body calculations. Our simulations are performed at a lattice cutoff of 1/a=2.0 GeV with the nonperturbatively O(a) improved Wilson action for the light quark and a relativistic heavy quark action for the charm quark. A new attempt of calculating the cc-nucleon potential through the Bethe-Salpeter wave function will be also discussed.
Energy Technology Data Exchange (ETDEWEB)
Sternbeck, A.
2006-07-18
Within the framework of lattice QCD we investigate different aspects of QCD in Landau gauge using Monte Carlo simulations. In particular, we focus on the low momentum behavior of gluon and ghost propagators. The gauge group is SU(3). Different systematic effects on the gluon and ghost propagators are studied. We demonstrate the ghost dressing function to systematically depend on the choice of Gribov copies at low momentum, while the influence on the gluon dressing function is not resolvable. Also the eigenvalue distribution of the Faddeev-Popov operator is sensitive to Gribov copies. We show that the influence of dynamical Wilson fermions on the ghost propagator is negligible at the momenta available to us. On the contrary, fermions affect the gluon propagator at large and intermediate momenta. In addition, we analyze data for both propagators obtained on asymmetric lattices and compare these results with data obtained on symmetric lattices. We compare our data with results from studies of Dyson-Schwinger equations for the gluon and ghost propagators. We demonstrate that the infrared behavior of both propagators, as found in this thesis, is consistent with different criteria for confinement. However, the running coupling constant, given as a renormalization-group-invariant combination of the gluon and ghost dressing functions, does not expose a finite infrared fixed point. Rather the data are in favor of an infrared vanishing coupling constant. We also report on a first nonperturbative computation of the SU(3) ghost-gluon-vertex renormalization constant. We present results of an investigation of the spectral properties of the Faddeev-Popov operator. For this we have calculated the low-lying eigenvalues and eigenmodes of the Faddeev-Popov operator. (orig.)
SU(3) gauge theory with four degenerate fundamental fermions on the lattice
Aoki, Yasumichi; Bennett, Ed; Kurachi, Masafumi; Maskawa, Toshihide; Miura, Kohtaroh; Nagai, Kei-ichi; Ohki, Hiroshi; Rinaldi, Enrico; Shibata, Akihiro; Yamawaki, Koichi; Yamazaki, Takeshi
2015-01-01
As a part of the project studying large $N_f$ QCD, the LatKMI Collaboration has been investigating the SU(3) gauge theory with four fundamental fermions (four-flavor QCD). The main purpose of studying four-flavor QCD is to provide a qualitative comparison to $N_f= 8$, $12$, $16$ QCD; however, a quantitative comparison to real-world QCD is also interesting. To make such comparisons more meaningful, it is desirable to use the same kind of lattice action consistently, so that qualitative difference of different theories are less affected by artifacts of lattice discretization. Here, we adopt the highly-improved staggered quark action with the tree-level Symanzik gauge action (HISQ/tree), which is exactly the same as the setup for our simulations for $SU(3)$ gauge theories with $N_f=8$, $12$ and $16$ fundamental fermions~\\cite{Aoki:2013xza, Aoki:2012eq, Aoki:2014oma}. In the next section, we show the fermion mass dependence of $F_\\pi$, $\\langle\\bar{\\psi}\\psi\\rangle$, $M_\\pi$, $M_\\rho$, $M_N$ and their chiral extr...
Infrared fixed point of the 12-fermion SU(3) gauge model based on 2-lattice MCRG matching
Hasenfratz, Anna
2011-01-01
I investigate an SU(3) gauge model with 12 fundamental fermions. The physically interesting region of this strongly coupled system can be influenced by an ultraviolet fixed point due to lattice artifacts. I suggest to use a gauge action with an additional negative adjoint plaquette term that lessens this problem. I also introduce a new analysis method for the 2-lattice matching Monte Carlo renormalization group technique that significantly reduces finite volume effects. The combination of these two improvements allows me to measure the bare step scaling function in a region of the gauge coupling where it is clearly negative, indicating a positive renormalization group $\\beta$ function and infrared conformality.
A Candidate for Solvable Large N Lattice Gauge Theory in D>2
Dubin, A Yu
1999-01-01
I propose a class of D\\geq{2} lattice SU(N) gauge theories dual to certain vector models endowed with the local [U(N)]^{D} conjugation-invariance and Z_{N} gauge symmetry. In the latter models, both the partitition function and Wilson loop observables depend nontrivially only on the eigenvalues of the link-variables. Therefore, the vector-model facilitates a master-field representation of the large N loop-averages in the corresponding induced gauge system. As for the partitition function, in the limit N->{infinity} it is reduced to the 2Dth power of an effective one-matrix eigenvalue-model which makes the associated phase structure accessible. In particular a simple scaling-condition, that ensures the proper continuum limit of the induced gauge theory, is proposed. We also derive a closed expression for the large N average of a generic nonself-intersecting Wilson loop in the D=2 theory defined on an arbitrary 2d surface.
Geometric asymptotics for spin foam lattice gauge gravity on arbitrary triangulations
Hellmann, Frank
2012-01-01
We study the behavior of holonomy spin foam partition functions, a form of lattice gauge gravity, on generic 4d-triangulations using micro local analysis. To do so we adapt tools from the renormalization theory of quantum field theory on curved space times. This allows us, for the first time, to study the partition function without taking any limits on the interior of the triangulation. We establish that for many of the most widely used models the geometricity constraints, which reduce the gauge theory to a geometric one, introduce strong accidental curvature constraints. These limit the curvature around each triangle of the triangulation to a finite set of values. We demonstrate how to modify the partition function to avoid this problem. Finally the new methods introduced provide a starting point for studying the regularization ambiguities and renormalization of the partition function.
Laine, M; Tassler, M
2007-01-01
Recently, a finite-temperature real-time static potential has been introduced via a Schr\\"odinger-type equation satisfied by a certain heavy quarkonium Green's function. Furthermore, it has been pointed out that it possesses an imaginary part, which induces a finite width for the tip of the quarkonium peak in the thermal dilepton production rate. The imaginary part originates from Landau-damping of low-frequency gauge fields, which are essentially classical due to their high occupation number. Here we show how the imaginary part can be measured with classical lattice gauge theory simulations, accounting non-perturbatively for the infrared sector of finite-temperature field theory. We demonstrate that a non-vanishing imaginary part indeed exists non-perturbatively; and that its value agrees semi-quantitatively with that predicted by Hard Loop resummed perturbation theory.
Lattice study for conformal windows of SU(2) and SU(3) gauge theories with fundamental fermions
Huang, Cynthia Y -H; Lin, C.-J. David; Ogawa, Kenji; Ohki, Hiroshi; Ramos, Alberto; Rinaldi, Enrico
2016-01-01
We present our investigation of SU(2) gauge theory with 8 flavours, and SU(3) gauge theory with 12 flavours. For the SU(2) case, at strong bare coupling, $\\beta \\lesssim 1.45$, the distribution of the lowest eigenvalue of the Dirac operator can be described by chiral random matrix theory for the Gaussian symplectic ensemble. Our preliminary result indicates that the chiral phase transition in this theory is of bulk nature. For the SU(3) theory, we use high-precision lattice data to perform the step-scaling study of the coupling, $g_{{\\rm GF}}$, in the Gradient Flow scheme. We carefully examine the reliability of the continuum extrapolation in the analysis, and conclude that the scaling behaviour of this SU(3) theory is not governed by possible infrared conformality at $g_{{\\rm GF}}^{2} \\lesssim 6$.
Lattice study for conformal windows of SU(2) and SU(3) gauge theories with fundamental fermions
Huang, Cynthia Y.-H.; Lin, C.-J. David; Ogawa, Kenji; Ohki, Hiroshi; Ramos, Alberto; Rinaldi, Enrico
2015-10-30
We present our investigation of SU(2) gauge theory with 8 flavours, and SU(3) gauge theory with 12 flavours. For the SU(2) case, at strong bare coupling, $\\beta \\lesssim 1.45$, the distribution of the lowest eigenvalue of the Dirac operator can be described by chiral random matrix theory for the Gaussian symplectic ensemble. Our preliminary result indicates that the chiral phase transition in this theory is of bulk nature. For the SU(3) theory, we use high-precision lattice data to perform the step-scaling study of the coupling, $g_{{\\rm GF}}$, in the Gradient Flow scheme. We carefully examine the reliability of the continuum extrapolation in the analysis, and conclude that the scaling behaviour of this SU(3) theory is not governed by possible infrared conformality at $g_{{\\rm GF}}^{2} \\lesssim 6$.
Status of the Lambda Lattice Scale for the SU(3) Wilson gauge action
Berg, Bernd A
2014-01-01
With the emergence of the Yang-Mills gradient flow technique there is renewed interest in the issue of scale setting in lattice gauge theory. Here I compare for the SU(3) Wilson gauge action the non-perturbative lambda scales of Edwards, Heller and Klassen (EHK), Necco and Sommer (NS), both relying on Sommer's method using the quark potential, with the lambda scale derived by Bazavov, Berg and Velytsky (BBV) from deconfining phase transition data of the Bielefeld group. It turns out that these scales are based on mutually inconsistent data. Nevertheless their over-all agreement is still at a better than +/- 2% in the coupling constant range for which one expects them to apply. Somewhat surprisingly the scale based on the deconfining transition is consistent with the relevant part of the EHK data (baring one data point, which is closest to the strong coupling region), while the NS scale is not.
Twenty-first Century Lattice Gauge Theory: Results from the QCD Lagrangian
Energy Technology Data Exchange (ETDEWEB)
Kronfeld, Andreas S.; /Fermilab
2012-03-01
Quantum chromodynamics (QCD) reduces the strong interactions, in all their variety, to an elegant nonabelian gauge theory. It clearly and elegantly explains hadrons at short distances, which has led to its universal acceptance. Since its advent, however, many of its long-distance, emergent properties have been believed to be true, without having been demonstrated to be true. This paper reviews a variety of results in this regime that have been established with lattice gauge theory, directly from the QCD Lagrangian. This body of work sheds light on the origin of hadron masses, its interplay with dynamical symmetry breaking, as well as on other intriguing features such as the phase structure of QCD. In addition, nonperturbative QCD is quantitatively important to many aspects of particle physics (especially the quark flavor sector), nuclear physics, and astrophysics. This review also surveys some of the most interesting connections to those subjects.
Locality and Efficient Evaluation of Lattice Composite Fields: Overlap-Based Gauge Operators
Alexandru, Andrei
2016-01-01
We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix elements, showing for the first time their local nature on realistic path-integral backgrounds. The framework entails a method for efficient evaluation of such non-ultralocal operators, whose computational cost is volume-indepenent at fixed accuracy, and only grows logarithmically as this accuracy approaches zero. This makes computation of useful operators, such as overlap-based topological density, practical. The key notion underlying these features is that of exponential insensitivity to distant fields, made rigorous by introducing the procedure of statistical regularization. The scales associated with insensitivity property are useful characteristics of non-local continuum operators.
Shear viscosity to relaxation time ratio in SU(3) lattice gauge theory
Kohno, Yasuhiro; Kitazawa, Masakiyo
2011-01-01
We evaluate the ratio of the shear viscosity to the relaxation time of the shear flux above but near the critical temperature $T_c$ in SU(3) gauge theory on the lattice. The ratio is related to Kubo's canonical correlation of the energy-momentum tensor in Euclidean space with the relaxation time approximation and an appropriate regularization. Using this relation, the ratio is evaluated by direct measurements of the Euclidean observables on the lattice. We obtained the ratio with reasonable statistics for the range of temperature $1.3T_c \\lesssim T \\lesssim 4T_c$. We also found that the characteristic speed of the transverse plane wave in gluon media is almost constant, $v \\simeq 0.5$, for $T \\gtrsim 1.5T_c$, which is compatible with the causality in the second order dissipative hydrodynamics.
Vector meson masses in two-dimensional SU(NC) lattice gauge theory with massive quarks
Institute of Scientific and Technical Information of China (English)
JIANG Jun-Qin
2008-01-01
Using an improved lattice Hamiltonian with massive Wilson quarks a variational method is applied to study the dependence of the vector meson mass Mv on the quark mass m and the Wilson parameter r in in the scaling window 1 ≤ 1/g2 ≤ 2, Mv/g is approximately linear in m, but Mv/g obviously does not depend on r (this differs from the quark condensate). Particularly for m → 0 our numerical results agree very well with Bhattacharya's analytical strong coupling result in the continuum, and the value of ((e)Mv/(e)m) |mm=0 in two-dimensional SU(NC) lattice gauge theory is very close to that in Schwinger model.
Flux tubes and their interaction in U(1) lattice gauge theory
Zach, M P; Skála, P; Zach, Martin; Faber, Manfried; Skala, Peter
1997-01-01
We investigate singly and doubly charged flux tubes in U(1) lattice gauge theory. By simulating the dually transformed path integral we are able to consider large flux tube lengths, low temperatures, and multiply charged systems without loss of numerical precision. We simulate flux tubes between static sources as well as periodically closed flux tubes, calculating flux tube profiles, the total field energy and the free energy. Our main results are that the string tension in both three and four dimensions scales proportionally to the charge -- which is in contrast to previous lattice results -- and that in four-dimensional U(1) there is an attractive interaction between flux tubes for beta approaching the phase transition.
Akemann, G; Bloch, J; Shifrin, L; Wettig, T
2008-01-25
We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.
Realization of the Harper Hamiltonian with Artificial Gauge Fields in Optical Lattices
Miyake, Hirokazu; Siviloglou, Georgios; Kennedy, Colin; Burton, William Cody; Ketterle, Wolfgang
2014-03-01
Systems of charged particles in magnetic fields have led to many discoveries in science-such as the integer and fractional quantum Hall effects-and have become important paradigms of quantum many-body physics. We have proposed and implemented a scheme which realizes the Harper Hamiltonian, a lattice model for charged particles in magnetic fields, whose energy spectrum is the fractal Hofstadter butterfly. We experimentally realize this Hamiltonian for ultracold, charge neutral bosonic particles of 87Rb in a two-dimensional optical lattice by creating an artificial gauge field using laser-assisted tunneling and a potential energy gradient provided by gravity. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. Furthermore, this scheme can be extended to realize spin-orbit coupling and the spin Hall effect for neutral atoms in optical lattices by modifying the motion of atoms in a spin-dependent way by laser recoil and Zeeman shifts created with a magnetic field gradient. Major advantages of our scheme are that it does not rely on near-resonant laser light to couple different spin states and should work even for fermionic particles. Our work is a step towards studying novel topological phenomena with ultracold atoms. Currently at the RAND Corporation.
Generating SU(Nc) pure gauge lattice QCD configurations on GPUs with CUDA and OpenMP
Cardoso, Nuno
2011-01-01
The starting point of any lattice QCD computation is the generation of a Markov chain of gauge field configurations. Due to the large number of lattice links and due to the matrix multiplications, generating SU(Nc) lattice QCD configurations is a highly demanding computational task, requiring advanced computer parallel architectures such as clusters of several Central Processing Units (CPUs) or Graphics Processing Units (GPUs). In this paper we present and explore the performance of CUDA codes for NVIDIA GPUs to generate SU(Nc) lattice QCD pure gauge configurations. Our implementation in one GPU uses CUDA and in multiple GPUs uses OpenMP and CUDA. We present optimized CUDA codes SU(2), SU(3) and SU(4). We also show a generic SU(Nc) code for Nc$\\,\\geq 4$ and compare it with the optimized version of SU(4). Our codes are publicly available for free use by the lattice QCD community.
Correlation and specific heat of U(1) and SU(2) lattice gauge models
Nauenberg, M
1981-01-01
Describes some recent work on Monte Carlo simulations of U(1) and SU (2) lattice gauge models. The authors have primarily been interested in the correlations between Wilson plaquettes in order to study the nature of the transition between the strong and weak coupling regimes. Since lattice gauge models confine static charges in the strong coupling limit, it is expected that U(1) models in four dimensions exhibit a phase transition to a weak coupling Coulomb phase, corresponding to QED. For SU(2) models the lore is that there does not exist any phase transition. In this case confinement is also a property of the continuum limit which corresponds to QCD. While the existence of a phase transition in the U(1) model can be demonstrated rigorously, virtually nothing is known theoretically about the order of this transition. For the SU(2) model there is some evidence in support of a single confining phase based on strong coupling expansions, and on Monte Carlo calculations. (8 refs).
Canonical Transformations and Loop Formulation of SU(N) Lattice Gauge Theories
Mathur, Manu
2015-01-01
We construct canonical transformations to reformulate SU(N) Kogut-Susskind lattice gauge theory in terms of a set of fundamental loop & string flux operators along with their canonically conjugate loop & string electric fields. We show that as a consequence of SU(N) Gauss laws all SU(N) string degrees of freedom become cyclic and decouple from the physical Hilbert space ${\\cal H}^p$. The canonical relations between the initial SU(N) link operators and the final SU(N) loop & string operators over the entire lattice are worked out in a self consistent manner. The Kogut-Susskind Hamiltonian rewritten in terms of the fundamental physical loop operators has global SU(N) invariance. There are no gauge fields. We further show that the $(1/g^2)$ magnetic field terms on plaquettes create and annihilate the fundamental plaquette loop fluxes while the $(g^2)$ electric field terms describe all their interactions. In the weak coupling ($g^2 \\rightarrow 0$) continuum limit the SU(N) loop dynamics is described b...
From lattice BF gauge theory to area-angle Regge calculus
Bonzom, Valentin
2009-01-01
We consider Riemannian 4d BF lattice gauge theory, on a triangulation of spacetime. Introducing the simplicity constraints which turn BF theory into simplicial gravity, some geometric quantities of Regge calculus, areas, and 3d and 4d dihedral angles, are identified. The parallel transport conditions are taken care of to ensure a consistent gluing of simplices. We show that these gluing relations, together with the simplicity constraints, contain the constraints of area-angle Regge calculus in a simple way, via the group structure of the underlying BF gauge theory. This provides a precise road from constrained BF theory to area-angle Regge calculus. Doing so, a framework combining variables of lattice BF theory and Regge calculus is built. The action takes a form {\\it \\`a la Regge} and includes the contribution of the Immirzi parameter. In the absence of simplicity constraints, the standard spin foam model for BF theory is recovered. Insertions of local observables are investigated, leading to Casimir inserti...
New approach to the Dirac spectral density in lattice gauge theory applications
Fodor, Zoltan; Kuti, Julius; Mondal, Santanu; Nogradi, Daniel; Wong, Chik Him
2016-01-01
We report tests and results from a new approach to the spectral density and the mode number distribution of the Dirac operator in lattice gauge theories. The algorithm generates the spectral density of the lattice Dirac operator as a continuous function over all scales of the complete eigenvalue spectrum. This is distinct from an earlier method where the integrated spectral density (mode number) was calculated efficiently for some preselected fixed range of the integration. The new algorithm allows global studies like the chiral condensate from the Dirac spectrum at any scale including the cutoff-dependent IR and UV range of the spectrum. Physics applications include the scale-dependent mass anomalous dimension, spectral representation of composite fermion operators, and the crossover transition from the $\\epsilon$-regime of Random Matrix Theory to the p-regime in chiral perturbation theory. We present thorough tests of the algorithm in the 2-flavor sextet SU(3) gauge theory that we continue to pursue for its...
Study of compact U(1) flux tubes in 3+1 dimensions in lattice gauge theory using GPU's
Amado, André; Cardoso, Marco; Bicudo, Pedro
2012-01-01
We utilize Polyakov loop correlations to study (3+1)D compact U(1) flux tubes and the static electron-positron potential in lattice gauge theory. By using field operators it is possible in U(1) lattice gauge theory to probe directly the electric and magnetic fields. In order to improve the signal-to-noise ratio in the confinement phase, we apply the L\\"uscher-Weiss multilevel algorithm. Our code is written in CUDA, and we run it in NVIDIA FERMI generation GPU's, in order to achieve the necessary performance for our computations.
Hamiltonian Study of Improved $U(1)_{2+1}$ Lattice Gauge Theory
Loan, M; Hamer, C; Loan, Mushtaq; Byrnes, Tim; Hamer, Chris
2003-01-01
Monte Carlo results are presented, in the Hamiltonian limit, for the string tension and antisymmetric mass gap for U(1) lattice gauge theory in (2+1) dimensions, using mean-field improved anisotropic Wilson action, are presented. Evidence of scaling in the string tension and antisymmetric mass gap is observed in the weak coupling regime of the theory. The results are compared to previous simulation data using the standard Wilson action and we find that a more accurate determination of the string tension and scalar glueball masses has been achieved. The scaling behaviour observed is in good agreement with the results from other numerical calculations. Finally comparisons are made with previous estimates obtained in the Hamiltonian limit by various other studies.
Optimizing the performance of Lattice Gauge Theory simulations with Streaming SIMD extensions
Srinivasan, Shyam
2013-01-01
Two factors, which affect simulation quality are the amount of computing power and implementation. The Streaming SIMD (single instruction multiple data) extensions (SSE) present a technique for influencing both by exploiting the processor's parallel functionalism. In this paper, we show how SSE improves performance of lattice gauge theory simulations. We identified two significant trends through an analysis of data from various runs. The speed-ups were higher for single precision than double precision floating point numbers. Notably, though the use of SSE significantly improved simulation time, it did not deliver the theoretical maximum. There are a number of reasons for this: architectural constraints imposed by the FSB speed, the spatial and temporal patterns of data retrieval, ratio of computational to non-computational instructions, and the need to interleave miscellaneous instructions with computational instructions. We present a model for analyzing the SSE performance, which could help factor in the bot...
Phase transitions in strongly coupled 3d Z(N) lattice gauge theories at finite temperature
Borisenko, O; Cortese, G; Fiore, R; Gravina, M; Papa, A; Surzhikov, I
2012-01-01
We perform an analytical and numerical study of the phase transitions in three-dimensional Z(N) lattice gauge theories at finite temperature for N>4. In the strong coupling limit these models are equivalent to a generalized version of the vector Potts models in two dimensions, where Polyakov loops play the role of Z(N) spins. The effective couplings of these two-dimensional spin models are calculated explicitly. It is argued that the effective spin models have two phase transitions of BKT type. This is confirmed by large-scale Monte Carlo simulations. Using a cluster algorithm we locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices, compute the helicity modulus, the average action and the specific heat. A scaling formula for the critical points with N is proposed.
Gauge-invariant implementation of the Abelian Higgs model on optical lattices
Bazavov, Alexei; Tsai, Shan-Wen; Unmuth-Yockey, Judah; Zhang, Jin
2015-01-01
We present a gauge-invariant effective action for the Abelian Higgs model (scalar electrodynamics) with a chemical potential $\\mu$ on a 1+1 dimensional lattice. This formulation provides an expansion in the hopping parameter $\\kappa$ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling $\\beta_{pl}$ and small values of the scalar self-coupling $\\lambda$. In the opposite limit of infinitely large $\\lambda$, the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Their numerical implementation requires truncations but there is no sign problem for arbitrary values of $\\mu$. We show that the time continuum limit of the blocked transfer matrix can be obtained numerically and, in the limit of infinite $\\beta_{pl}$ and with a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large onsite repulsion. We extend this proced...
Smooth Gauge Strings and D > 2 Lattice Yang-Mills Theories
Dubin, A Yu
2000-01-01
Employing the nonabelian duality transformation \\cite{Dub2}, I derive theGauge String representation of certain D>2 lattice Yang-Mills theories in theSC phase. With the judicious choice of the actions, in D>2 our constructiongeneralizes the Gross-Taylor stringy reformulation of the continuous YM_{2} ona 2d manifold. Using the Twisted Eguchi-Kawai model as an example, we developethe algorithm to determine the weights w[\\tilde{M}] for connected YM-fluxworldsheets $\\tilde{M}$ immersed, \\tilde{M}->T, into a given 2d cell-complex T.Owing to the invariance of w[\\tilde{M}] under a continuous group ofarea-preserving worldsheet homeomorphisms, the weights {w[\\tilde{M}]} can bereadily used to define the theory of the smooth YM-fluxes which unambiguouslyrefers to a particular continuous YM_{D} system. I argue that the latter YM_{D}models (with a finite ultraviolet cut-off \\Lambda) for sufficiently largevalues of the coupling constant(s) are reproduced, to all orders in 1/N, by thesmooth Gauge String thus associated. The...
Institute of Scientific and Technical Information of China (English)
LI Jie-Ming; CHEN Qi-Zhou; GUO Shuo-Hong
2001-01-01
The random phase approximation is applied to the coupled-cluster expansions of lattice gauge theory (LGT). Using this method, wavefunctions are approximated by linear combination of graphs consisting of only one connected Wilson loop. We study the excited state energy and wavefunction in (2 + 1)-D SU(3) LGT up to thc third order. The glueballmass shows a good scaling behavior.``
Fortran code for SU(3) lattice gauge theory with and without MPI checkerboard parallelization
Berg, Bernd A.; Wu, Hao
2012-10-01
We document plain Fortran and Fortran MPI checkerboard code for Markov chain Monte Carlo simulations of pure SU(3) lattice gauge theory with the Wilson action in D dimensions. The Fortran code uses periodic boundary conditions and is suitable for pedagogical purposes and small scale simulations. For the Fortran MPI code two geometries are covered: the usual torus with periodic boundary conditions and the double-layered torus as defined in the paper. Parallel computing is performed on checkerboards of sublattices, which partition the full lattice in one, two, and so on, up to D directions (depending on the parameters set). For updating, the Cabibbo-Marinari heatbath algorithm is used. We present validations and test runs of the code. Performance is reported for a number of currently used Fortran compilers and, when applicable, MPI versions. For the parallelized code, performance is studied as a function of the number of processors. Program summary Program title: STMC2LSU3MPI Catalogue identifier: AEMJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 26666 No. of bytes in distributed program, including test data, etc.: 233126 Distribution format: tar.gz Programming language: Fortran 77 compatible with the use of Fortran 90/95 compilers, in part with MPI extensions. Computer: Any capable of compiling and executing Fortran 77 or Fortran 90/95, when needed with MPI extensions. Operating system: Red Hat Enterprise Linux Server 6.1 with OpenMPI + pgf77 11.8-0, Centos 5.3 with OpenMPI + gfortran 4.1.2, Cray XT4 with MPICH2 + pgf90 11.2-0. Has the code been vectorised or parallelized?: Yes, parallelized using MPI extensions. Number of processors used: 2 to 11664 RAM: 200 Mega bytes per process. Classification: 11
Revisiting Chiral Extrapolation by Studying a Lattice Quark Propagator
Institute of Scientific and Technical Information of China (English)
ZHANG Yan-Bin; SUN Wei-Min; L(U) Xiao-Fu; ZONG Hong-Shi
2009-01-01
The quark propagator in the Landau gauge is studied on the lattice,including the quenched and the unquenched results.No obvious unquenched effects are found by comparing the quenched quark propagator with the dynamical one.For the quenched and unquenched configurations,the results with different quark masses have been computed.For the quark mass function,a nonlinear chiral extrapolating behavior is found in the in/tared region for both the quenched and dynamical results.
Gattringer, Christof; Marchis, Carlotta
2017-03-01
We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over "abelian color cycles" (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).
Program package for multicanonical simulations of U(1) lattice gauge theory-Second version
Bazavov, Alexei; Berg, Bernd A.
2013-03-01
A new version STMCMUCA_V1_1 of our program package is available. It eliminates compatibility problems of our Fortran 77 code, originally developed for the g77 compiler, with Fortran 90 and 95 compilers. New version program summaryProgram title: STMC_U1MUCA_v1_1 Catalogue identifier: AEET_v1_1 Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html Programming language: Fortran 77 compatible with Fortran 90 and 95 Computers: Any capable of compiling and executing Fortran code Operating systems: Any capable of compiling and executing Fortran code RAM: 10 MB and up depending on lattice size used No. of lines in distributed program, including test data, etc.: 15059 No. of bytes in distributed program, including test data, etc.: 215733 Keywords: Markov chain Monte Carlo, multicanonical, Wang-Landau recursion, Fortran, lattice gauge theory, U(1) gauge group, phase transitions of continuous systems Classification: 11.5 Catalogue identifier of previous version: AEET_v1_0 Journal Reference of previous version: Computer Physics Communications 180 (2009) 2339-2347 Does the new version supersede the previous version?: Yes Nature of problem: Efficient Markov chain Monte Carlo simulation of U(1) lattice gauge theory (or other continuous systems) close to its phase transition. Measurements and analysis of the action per plaquette, the specific heat, Polyakov loops and their structure factors. Solution method: Multicanonical simulations with an initial Wang-Landau recursion to determine suitable weight factors. Reweighting to physical values using logarithmic coding and calculating jackknife error bars. Reasons for the new version: The previous version was developed for the g77 compiler Fortran 77 version. Compiler errors were encountered with Fortran 90 and Fortran 95 compilers (specified below). Summary of revisions: epsilon=one/10**10 is replaced by epsilon/10.0D10 in the parameter statements of the subroutines u1_bmha.f, u1_mucabmha.f, u1wl
Finite Size Scaling and the Universality Class of SU(2) Lattice Gauge Theory
Staniford-Chen, Stuart Gresley
For a system near a second order phase transition, the correlation length becomes extremely large. This gives rise to much interesting physics such as the existence of critical exponents and the division of physical theories into universality classes. SU(2) lattice gauge theory has such a phase transition at finite temperature and it has been persuasively argued in the literature that it should be in the same universality class as the Ising model in a space with dimensionality one less than the gauge theory. This is in the sense that the effective theory for the SU(2) Wilson lines is universal with the Ising model. This prediction has been checked for d = 3 + 1 SU(2) by comparing the critical exponents, and those checks appear to confirm it to the modest accuracy currently available. However, the theory of finite size scaling predicts a very rich set of objects which should be the same across universality classes. For example, the shape of the graph of various observables against temperature near the transition is universal. Not only that, but whole collections of probability distributions as a function of temperature can be given a scaling form and the shape of this object is universal. I develop a methodology for comparing such sets of distributions. This gives a two dimensional surface for each theory which can then be used in comparisons. I then use this approach and compare the surface for the order parameter in SU(2) with that in phi^4. The visual similarity is very striking. I perform a semi-quantitative error analysis which does not reveal significant differences between the two surfaces. This strengthens the idea that the SU(2) effective line theory is in the Ising universality class. I conclude by discussing the advantages and disadvantages of the method used here.
Research in Lattice Gauge Theory and in the Phenomenology of Neutrinos and Dark Matter
Energy Technology Data Exchange (ETDEWEB)
Meurice, Yannick L [Univ. of Iowa, Iowa City, IA (United States); Reno, Mary Hall [Univ. of Iowa, Iowa City, IA (United States)
2016-06-23
Research in theoretical elementary particle physics was performed by the PI Yannick Meurice and co-PI Mary Hall Reno. New techniques designed for precision calculations of strong interaction physics were developed using the tensor renormalization group method. Large-scale Monte Carlo simulations with dynamical quarks were performed for candidate models for Higgs compositeness. Ab-initio lattice gauge theory calculations of semileptonic decays of B-mesons observed in collider experiments and relevant to test the validity of the standard model were performed with the Fermilab/MILC collaboration. The phenomenology of strong interaction physics was applied to new predictions for physics processes in accelerator physics experiments and to cosmic ray production and interactions. A research focus has been on heavy quark production and their decays to neutrinos. The heavy quark contributions to atmospheric neutrino and muon fluxes have been evaluated, as have the neutrino fluxes from accelerator beams incident on heavy targets. Results are applicable to current and future particle physics experiments and to astrophysical neutrino detectors such as the IceCube Neutrino Observatory.
Phase Structure of lattice $SU(2) x U_{S}(1)$ three-dimensional Gauge Theory
Farakos, K; McNeill, D
1999-01-01
We discuss a phase diagram for a relativistic SU(2) x U_{S}(1) lattice gauge theory, with emphasis on the formation of a parity-invariant chiral condensate, in the case when the $U_{S}(1)$ field is infinitely coupled, and the SU(2) field is moved away from infinite coupling by means of a strong-coupling expansion. We provide analytical arguments on the existence of (and partially derive) a critical line in coupling space, separating the phase of broken SU(2) symmetry from that where the symmetry is unbroken. We review uncoventional (Kosterlitz-Thouless type) superconducting properties of the model, upon coupling it to external electromagnetic potentials. We discuss the rôle of instantons of the unbroken subgroup U(1) of SU(2), in eventually destroying superconductivity under certain circumstances. The model may have applications to the theory of high-temperature superconductivity. In particular, we argue that in the regime of the couplings leading to the broken SU(2) phase, the model may provide an explanati...
An O(a) modified lattice set-up of the Schr\\"odinger functional in SU(3) gauge theory
Pérez-Rubio, Paula; Takeda, Shinji
2011-01-01
The set-up of the QCD Schr\\"odinger functional (SF) on the lattice with staggered quarks requires an even number of points $L/a$ in the spatial directions, while the Euclidean time extent of the lattice, $T/a$, must be odd. Identifying a unique renormalisation scale, $L=T$, is then only possible up to O($a$) lattice artefacts. In this article we study such lattices in the pure SU(3) gauge theory, where we can also compare to the standard set-up. We consider the SF coupling as obtained from the variation of an SU(3) Abelian and spatially constant background field. The O($a$) lattice artefacts can be cancelled by the existing O($a$) boundary counterterm. However, its coefficient, $\\ct$, differs at the tree-level from its standard value, so that one first needs to re-determine the induced background gauge field. The perturbative one-loop correction to the coupling allows to determine $\\ct$ to one-loop order. A few numerical simulations serve to demonstrate that residual cutoff effects in the step scaling functio...
Path Integral Monte Carlo Approach to the U(1) Lattice Gauge Theory in (2+1) Dimensions
Loan, M; Sloggett, C; Hamer, C; Loan, Mushtaq; Brunner, Michael; Sloggett, Clare; Hamer, Chris
2003-01-01
Path Integral Monte Carlo simulations have been performed for U(1) lattice gauge theory in (2+1) dimensions on anisotropic lattices. We extract the static quark potential, the string tension and the low-lying "glueball" spectrum. The Euclidean string tension and mass gap decrease exponentially at weak coupling in excellent agreement with the predictions of Polyakov and G{\\" o}pfert and Mack, but their magnitudes are five times bigger than predicted. Extrapolations are made to the extreme anisotropic or Hamiltonian limit, and comparisons are made with previous estimates obtained in the Hamiltonian formulation.
Edwards, Sam
2009-01-01
We present a precision determination of the critical coupling beta_c for the deconfinement transition in pure SU(2) gauge theory in 2+1 dimensions. This is possible from universality, by intersecting the center vortex free energy as a function of the lattice coupling beta with the exactly known value of the interface free energy in the 2D Ising model at criticality. Results for lattices with different numbers of sites N_t along the Euclidean time direction are used to determine how beta varies with temperature for a given N_t around the deconfinement transition.
Energy Technology Data Exchange (ETDEWEB)
Szirmai, G.; Szirmai, E. [ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona) (Spain); Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest (Hungary); Zamora, A. [ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona) (Spain); Lewenstein, M. [ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona) (Spain); ICREA-Institucio Catalana de Recerca i Estudis Avancats, Lluis Companys 23, E-08010 Barcelona (Spain)
2011-07-15
We propose an experimentally feasible setup with ultracold alkaline-earth-metal atoms to simulate the dynamics of U(1) lattice gauge theories in 2 + 1 dimensions with a Chern-Simons term. To this end we consider the ground-state properties of spin-5/2 alkaline-earth-metal fermions in a honeycomb lattice. We use the Gutzwiller projected variational approach in the strongly repulsive regime in the case of filling 1/6. The ground state of the system is a chiral spin-liquid state with 2{pi}/3 flux per plaquette, which violates time-reversal invariance. We demonstrate that due to the breaking of time-reversal symmetry the system exhibits quantum Hall effect and chiral edge states. We relate the experimentally accessible spin fluctuations to the emerging gauge-field dynamics. We discuss also properties of the lowest energy competing orders.
Amado, A; Bicudo, P
2013-01-01
We utilize Polyakov loop correlations to study d=3+1 compact U (1) flux tubes and the static electron-positron potential in lattice gauge theory. With the plaquette field operator, in U(1) lattice gauge theory, we probe directly the components of the electric and magnetic fields. In order to improve the signal-to-noise ratio in the confinement phase, we apply the L\\"uscher-Weiss multilevel algorithm. Our code is written in CUDA, and we run it in NVIDIA FERMI generation GPUs, in order to achieve the necessary efficiency for our computations. We measure in detail the quantum widening of the flux tube, as a function of the intercharge distance and at different finite temperatures T < Tc . Our results are compatible with the Effective String Theory.
Dong, S J; Horváth, I; Lee, F X; Liu, K F; Mathur, N; Zhang, J B
2003-01-01
The quenched chiral logs are examined on a $16^3 \\times 28$ lattice with Iwasaki gauge action and overlap fermions. The pion decay constant $f_{\\pi}$ is used to set the lattice spacing, $a = 0.200(3)$ fm. With pion mass as low as $\\sim 180 {\\rm MeV}$, we see the quenched chiral logs clearly in $m_{\\pi}^2/m$ and $f_P$, the pseudoscalar decay constant. We analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory ($\\chi$PT) to apply. With the constrained curve fitting, we are able to extract the quenched chiral log parameter $\\delta$ together with the chiral cutoff $\\Lambda_{\\chi}$ and other parameters. Only for $m_{\\pi} \\leq 300 {\\rm MeV}$ do we obtain a consistent and stable fit with a constant $\\delta$ which we determine to be 0.23(2). By comparing to the $12^3 \\times 28$ lattice, we estimate the finite volume effect to be about 1.8% for the smallest pion mass. We also study the quenched non-analytic terms in the nucleon and the $\\rho$ masses...
Sakane, Shinya; Matsui, Tetsuo
2016-01-01
We consider a system of two-level quantum quasi-spins and gauge bosons put on a 3+1D lattice. As a model of neural network of the brain functions, these spins describe neurons quantum-mechanically, and the gauge bosons describes weights of synaptic connections. It is a generalization of the Hopfield model to a quantum network with dynamical synaptic weights. At the microscopic level, this system becomes a model of quantum brain dynamics proposed by Umezawa et al., where spins and gauge field describe water molecules and photons, respectively. We calculate the phase diagram of this system under quantum and thermal fluctuations, and find that there are three phases; confinement, Coulomb, and Higgs phases. Each phase is classified according to the ability to learn patterns and recall them. By comparing the phase diagram with that of classical networks, we discuss the effect of quantum fluctuations and thermal fluctuations (noises in signal propagations) on the brain functions.
Ding, H -T; Kaczmarek, O; Karsch, F; Laermann, E; Soeldner, W
2010-01-01
We calculate the vector current correlation function for light valence quarks in the deconfined phase of QCD. The calculations have been performed in quenched lattice QCD at T=1.45 Tc for four values of the lattice cut-off on lattices up to size 128^3x48. This allows to perform a continuum extrapolation of the correlation function in the Euclidean time interval tau*T -in [0.2, 0.5], which extends to the largest temporal separations possible at finite temperature, to better than 1% accuracy. In this interval, at the value of the temperature investigated, we find that the vector correlation function never deviates from the free correlator for massless quarks by more than 9%. We also determine the first two non-vanishing thermal moments of the vector meson spectral function. The second thermal moment deviates by less than 7% from the free value. With these constraints, we then proceed to extract information on the spectral representation of the vector correlator and discuss resulting consequences for the electri...
Hofstadter butterflies and magnetically induced band-gap quenching in graphene antidot lattices
DEFF Research Database (Denmark)
Pedersen, Jesper Goor; Pedersen, Thomas Garm
2013-01-01
We study graphene antidot lattices (GALs) in magnetic fields. Using a tight-binding model and a recursive Green's function technique that we extend to deal with periodic structures, we calculate Hofstadter butterflies of GALs. We compare the results to those obtained in a simpler gapped graphene...
Institute of Scientific and Technical Information of China (English)
应和平; 董绍静; 张剑波
2003-01-01
With an exact chiral symmetry, overlap fermions allow us to reach very light quark region. In the minimummps = 179 MeV, the quenched chiral logarithm diverge is examined. The chiral logarithm parameter δ is calculatedfrom both the pseudo-scalar meson mass mp2s diverge channel and the pseudo-scalar decay constant f p channel.In both the cases, we obtain δ = 0.25 ± 0.03. We also observe that the quenchedchiral logarithm diverge occursonly in the mps ≤400 MeV region.
Hasenfratz, Anna
2012-02-10
I investigate an SU(3) gauge model with 12 fundamental fermions. The physically interesting region of this strongly coupled system can be influenced by an ultraviolet fixed point due to lattice artifacts. I suggest to use a gauge action with an additional negative adjoint plaquette term that lessens this problem. I also introduce a new analysis method for the 2-lattice matching Monte Carlo renormalization group technique that significantly reduces finite volume effects. The combination of these two improvements allows me to measure the bare step scaling function in a region of the gauge coupling where it is clearly negative, indicating a positive renormalization group β function and infrared conformality.
Gauge cooling in complex Langevin for lattice QCD with heavy quarks
Energy Technology Data Exchange (ETDEWEB)
Seiler, Erhard, E-mail: ehs@mppmu.mpg.de [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München (Germany); Sexty, Dénes, E-mail: d.sexty@thphys.uni-heidelberg.de [Institut für Theoretische Physik, Universität Heidelberg (Germany); Stamatescu, Ion-Olimpiu, E-mail: I.O.Stamatescu@thphys.uni-heidelberg.de [Institut für Theoretische Physik, Universität Heidelberg (Germany)
2013-06-10
We employ a new method, “gauge cooling”, to stabilize complex Langevin simulations of QCD with heavy quarks. The results are checked against results obtained with reweighting; we find agreement within the estimated errors, except for strong gauge coupling in the confinement region. The method allows us to go to previously unaccessible high densities.
Cluster algorithm for two-dimensional U(1) lattice gauge theory
Sinclair, R.
1992-03-01
We use gauge fixing to rewrite the two-dimensional U(1) pure gauge model with Wilson action and periodic boundary conditions as a nonfrustrated XY model on a closed chain. The Wolff single-cluster algorithm is then applied, eliminating critical slowing down of topological modes and Polyakov loops.
Overlap Quark Propagator in Coulomb Gauge QCD
Mercado, Ydalia Delgado; Schröck, Mario
2014-01-01
The chirally symmetric Overlap quark propagator is explored in Coulomb gauge. This gauge is well suited for studying the relation between confinement and chiral symmetry breaking, since confinement can be attributed to the infrared divergent Lorentz-vector dressing function. Using quenched gauge field configurations on a $20^4$ lattice, the quark propagator dressing functions are evaluated, the dynamical quark mass is extracted and the chiral limit of these quantities is discussed. By removing the low-lying modes of the Dirac operator, chiral symmetry is artificially restored. Its effect on the dressing functions is discussed.
Grady, Michael
2011-01-01
SU(2) lattice gauge theory is extended to a larger coupling space where the coupling parameter for horizontal (spacelike) plaquettes, $\\beta_H$, differs from that for vertical (Euclidean timelike) plaquettes, $\\beta_V$. When $\\beta_H \\rightarrow \\infty$ the system, when in Coulomb Gauge, splits into multiple independent 3-d O(4) Heisenberg models on spacelike hyperlayers. Through consideration of the robustness of the Heisenberg model phase transition to small perturbations, and illustrated by Monte Carlo simulations, it is shown that the ferromagnetic phase transition in this model persists for $\\beta_H < \\infty$. Once it has entered the phase-plane it must continue to another edge due to its symmetry-breaking nature, and therefore must necessarily cross the $\\beta_V = \\beta_H$ line at a finite value. Indeed, a higher-order SU(2) phase transition is found at $\\beta = 3.18 \\pm 0.08$, from a finite-size scaling analysis of the Coulomb gauge magnetization from Monte Carlo simulations, which also yields criti...
NSPT study of the three-loop lattice gluon propagator in Landau gauge
Torrero, C; Ilgenfritz, E -M; Perlt, H; Schiller, A
2010-01-01
By means of Numerical Stochastic Perturbation Theory (NSPT), we calculate the lattice gluon propagator up to three loops of perturbation theory in the limits of infinite volume and vanishing lattice spacing. Based on known anomalous dimensions and a parametrization of both the hypercubic symmetry group H(4) and finite-size effects, we calculate the non-leading-log and non-logarithmic contributions iteratively, starting with the first-loop expression.
Six-dimensional regularization of chiral gauge theories on a lattice
Fukaya, Hidenori; Yamamoto, Shota; Yamamura, Ryo
2016-01-01
We propose a six-dimensional regularization of four dimensional chiral gauge theories. We consider a massive Dirac fermion in six dimensions with two different operators having domain-wall profiles in the fifth and the sixth directions, respectively. A Weyl fermion appears as a localized mode at the junction of the two domain-walls. In our formulation, the Stora-Zumino chain of the anomaly descent equations, starting from the axial $U(1)$ anomaly in six-dimensions to the gauge anomaly in four-dimensions, is naturally embedded. Moreover, a similar inflow of the global anomalies is found. The anomaly free condition is equivalent to requiring that the axial $U(1)$ anomaly and the parity anomaly are canceled among the six-dimensional Dirac fermions. Putting the gauge field at the four- dimensional junction and extending it to the bulk using the Yang-Mills gradient flow, as recently proposed by Grabowska and Kaplan, we define the four-dimensional path integral of the target chiral gauge theory.
Final Report for "Infrared Fixed Points in Multiflavor Lattice Gauge Theory"
Energy Technology Data Exchange (ETDEWEB)
Meurice, Yannick; Sinclair, Donald K.
2013-09-27
The goal of the grant was to apply methods that we have developed with spin and pure gauge models to models with dynamical fermions which are considered as candidates for an alternative to the Higgs mechanism. The work on SU(3) with fundamental quarks and with sextet quarks is described.
Zero-momentum modes and chiral limit in compact lattice QED
Bogolubsky, I L; Müller-Preussker, M; Zverev, N V
2001-01-01
The influence of zero-momentum gauge modes on physical observables is investigated for compact lattice QED with dynamical and quenched Wilson fermions. Within the Coulomb phase, zero-momentum modes are shown to hide the critical behaviour of gauge invariant fermion observables near the chiral limit. Methods for eliminating zero-momentum modes are discussed.
Fujiwara, T
2000-01-01
We investigate the index of the Neuberger's Dirac operator in abelian gauge theories on finite lattices by numerically analyzing the spectrum of the hermitian Wilson-Dirac operator for a continuous family of gauge fields connecting different topological sectors. By clarifying the characteristic structure of the spectrum leading to the index theorem we show that the index coincides to the topological charge for a wide class of gauge field configurations. We also argue that the index can be found exactly for some special but nontrivial configurations in two dimensions by directly analyzing the spectrum.
M. Laine; Philipsen, O.(Institut für Theoretische Physik, Goethe-Universität Frankfurt, Max-von-Laue-Str. 1, 60438, Frankfurt am Main, Germany); Tassler, M.
2007-01-01
Recently, a finite-temperature real-time static potential has been introduced via a Schr\\"odinger-type equation satisfied by a certain heavy quarkonium Green's function. Furthermore, it has been pointed out that it possesses an imaginary part, which induces a finite width for the tip of the quarkonium peak in the thermal dilepton production rate. The imaginary part originates from Landau-damping of low-frequency gauge fields, which are essentially classical due to their high occupation number...
Anatomy of isolated monopole in Abelian projection od SU(2) lattice gauge theory
Belavin, V A; Veselov, A I
2001-01-01
The structure of the isolated static monopolies in the maximum Abelian projection of the SU(2) gluodynamics on the lattice studied. The standard parametrization of the coupling matrix was used by determining the maximum Abelian projection of the R functional maximization relative to all scale transformations. The monopole radius R approx = 0.06 fm is evaluated
Density of States FFA analysis of SU(3) lattice gauge theory at a finite density of color sources
Giuliani, Mario; Gattringer, Christof
2017-10-01
We present a Density of States calculation with the Functional Fit Approach (DoS FFA) in SU(3) lattice gauge theory with a finite density of static color sources. The DoS FFA uses a parameterized density of states and determines the parameters of the density by fitting data from restricted Monte Carlo simulations with an analytically known function. We discuss the implementation of DoS FFA and the results for a qualitative picture of the phase diagram in a model which is a further step towards implementing DoS FFA in full QCD. We determine the curvature κ in the μ-T phase diagram and find a value close to the results published for full QCD.
Arthur, Rudy; Hansen, Martin; Hietanen, Ari; Lewis, Randy; Pica, Claudio; Sannino, Francesco
2014-01-01
We study the meson spectrum of the SU(2) gauge theory with two Wilson fermions in the fundamental representation. The theory unifies both Technicolor and composite Goldstone Boson Higgs models of electroweak symmetry breaking. We have calculated the masses of the lightest spin one vector and axial vector mesons. In addition, we have also obtained preliminary results for the mass of the lightest scalar (singlet) meson state. The simulations have been done with multiple masses and two different lattice spacings for chiral and continuum extrapolations. The spin one meson masses set lower limits for accelerator experiments, whereas the scalar meson will mix with a pGB of the theory and produce two scalar states. The lighter of the states is the 125 GeV Higgs boson, and the heavier would be a new yet unobserved scalar state.
Degrand, Thomas
2011-12-01
I carry out a finite-size scaling study of the correlation length in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions, using recent data published by Fodor, Holland, Kuti, Nógradi and Schroeder [Z. Fodor, K. Holland, J. Kuti, D. Nogradi, and C. Schroeder, Phys. Lett. B 703, 348 (2011).PYLBAJ0370-269310.1016/j.physletb.2011.07.037]. I make the assumption that the system is conformal in the zero-mass, infinite volume limit, that scaling is violated by both nonzero fermion mass and by finite volume, and that the scaling function in each channel is determined self-consistently by the data. From several different observables I extract a common exponent for the scaling of the correlation length ξ with the fermion mass mq, ξ˜mq-1/ym with ym˜1.35. Shortcomings of the analysis are discussed.
Höllwieser, Roman; Heller, Urs M
2011-01-01
Intersections of thick, plane vortices are characterized by the topological charge $|Q|=1/2$. We compare such intersections with the distribution of zeromodes of the Dirac operator in the fundamental and adjoint representation using both the overlap and asqtad staggered fermion formulations in SU(2)-lattice gauge theory. We analyze configurations with four intersections and find that the probability density distribution of fundamental zeromodes in the intersection plane differs significantly from the one obtained analytically in [Phys.\\ Rev.\\ D 66, 85004 (2002)]. The Dirac eigenmodes are clearly sensitive to the traces of the Polyakov (Wilson) lines and do not exactly locate topological charge contributions. Although, the adjoint Dirac operator is able to produce zeromodes for configurations with topological charge $|Q|=1/2$, they do not locate single vortex intersections, as we prove by forming arbitrary linear combinations of these zeromodes - their scalar density peaks at least at two intersection points. ...
Ochiai, Tetsuyuki
2017-02-01
We study the effects of a synthetic gauge field and pseudospin-orbit interaction in a stacked two-dimensional ring-network model. The model was introduced to simulate light propagation in the corresponding ring-resonator lattice, and is thus completely bosonic. Without these two items, the model exhibits Floquet-Weyl and Floquet-topological-insulator phases with topologically gapless and gapped band structures, respectively. The synthetic magnetic field implemented in the model results in a three-dimensional Hofstadter-butterfly-type spectrum in a photonic platform. The resulting gaps are characterized by the winding number of relevant S-matrices together with the Chern number of the bulk bands. The pseudospin-orbit interaction is defined as the mixing term between two pseudospin degrees of freedom in the rings, namely, the clockwise and counter-clockwise modes. It destroys the Floquet-topological-insulator phases, while the Floquet-Weyl phase with multiple Weyl points can be preserved by breaking the space-inversion symmetry. Implementing both the synthetic gauge field and pseudospin-orbit interaction requires a certain nonreciprocity.
Heavy Quark Thermalization in Classical Lattice Gauge Theory Lessons for Strongly-Coupled QCD
Laine, Mikko; Philipsen, Owe; Tassler, Marcus
2009-01-01
Thermalization of a heavy quark near rest is controlled by the correlator of two electric fields along a temporal Wilson line. We address this correlator within real-time, classical lattice Yang-Mills theory, and elaborate on the analogies that exist with the dynamics of hot QCD. In the weak-coupling limit, it can be shown analytically that the dynamics on the two sides are closely related to each other. For intermediate couplings, we carry out non-perturbative simulations within the classical theory, showing that the leading term in the weak-coupling expansion significantly underestimates the heavy quark thermalization rate. Our analytic and numerical results also yield a general understanding concerning the overall shape of the spectral function corresponding to the electric field correlator, which may be helpful in subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo simulations.
θ dependence of the vacuum energy in SU(3) gauge theory from the lattice
Giusti, Leonardo; Petrarca, Silvano; Taglienti, Bruno
2007-11-01
We report on a precise computation of the topological charge distribution in the SU(3) Yang-Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the definition of the topological charge suggested by Neuberger’s fermions. We observe significant deviations from a Gaussian distribution. Our results disfavor the θ behavior of the vacuum energy predicted by dilute instanton models, while they are compatible with the expectation from the large Nc expansion.
Theta dependence of the vacuum energy in the SU(3) gauge theory from the lattice
Giusti, Leonardo; Taglienti, B
2007-01-01
We report on a precise computation of the topological charge distribution in the SU(3) Yang--Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the definition of the topological charge suggested by Neuberger's fermions. We observe significant deviations from a Gaussian distribution. Our results disfavour the theta behaviour of the vacuum energy predicted by instanton models, while they are compatible with the expectation from the large Nc expansion.
Negative refraction of ultra-cold atoms in optical lattices with nonuniform artificial gauge fields
Energy Technology Data Exchange (ETDEWEB)
Zhang, Ai-Xia, E-mail: zhangax@nwnu.edu.cn; Xue, Ju-Kui
2016-07-01
We theoretically study the reflection and refraction of ultra-cold atoms in optical lattices exposed to a nonuniform artificial magnetic field. The introduction of the nonuniform artificial magnetic field to the optical lattice for suitable designer magnetic potential barrier can lead to a series of intriguing reflection and refraction phenomena of atoms, including reflection, positive refraction, negative refraction and atomic matter wave splitting. Both the occurrence and the distribution of these reflection and refraction scenarios can be coherently controlled by the nonuniform artificial magnetic field. In particular, the regions close to the boundary of reflection demonstrate two more interesting propagation modes, i.e., a reflected branch of atoms comprising a positive or negative refracted branch of atoms with almost same atom population will be excited simultaneously at the magnetic potential barrier. The results can be a guide for the coherent control of the matter waves in optical lattices and the design of new atom optics devices. - Highlights: • Ultra-cold atoms in OL with nonuniform magnetic field are studied. • Matter wave reflection, refraction and splitting are coherently controlled. • Results provide a guide for the design of new atomic optics devices.
Unquenched Gluon Propagator in Landau Gauge
2004-01-01
Using lattice quantum chromodynamics (QCD) we perform an unquenched calculation of the gluon propagator in Landau gauge. We use configurations generated with the AsqTad quark action by the MILC collaboration for the dynamical quarks and compare the gluon propagator of quenched QCD (i.e., the pure Yang-Mills gluon propagator) with that of 2+1 flavor QCD. The effects of the dynamical quarks are clearly visible and lead to a significant reduction of the nonperturbative infrared enhancement relat...
Nataf, Pierre; Lajkó, Miklós; Wietek, Alexander; Penc, Karlo; Mila, Frédéric; Läuchli, Andreas M.
2016-10-01
We show that, in the presence of a π /2 artificial gauge field per plaquette, Mott insulating phases of ultracold fermions with SU (N ) symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by an approximate ground space of N low-lying singlets for periodic boundary conditions, and by chiral edge states described by the SU(N ) 1 Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for N between 3 and 9, and by a parton construction based on a set of N Gutzwiller projected fermionic wave functions with flux π /N per triangular plaquette. Experimental implications are briefly discussed.
Isotriplet Dark Matter on the Lattice: SO(4)-gauge theory with two Vector Wilson fermions
Hietanen, Ari; Sannino, Francesco; Søndergaard, Ulrik Ishøj
2012-01-01
We present preliminary results for simulations of SO(4)-gauge theory with two Dirac Wilson fermions transforming according to the vector representation. We map out the phase diagram including the strong coupling bulk phase transition line as well as the zero PCAC-mass line. In addition, we measure the pseudo scalar and vector meson masses, and investigate whether the theory features chiral symmetry breaking. If the theory is used for breaking the electroweak symmetry dynamically it is the orthogonal group equivalent of the Minimal Walking Technicolor model but with the following distinctive features: a] It provides a natural complex weak isotriplet of Goldstone bosons of which the neutral component can be identified with a light composite dark matter state; b] It is expected to break the global symmetry spontaneously; c] It is free from fermionic composite states made by a techniglue and a technifermion.
Qcd Thermodynamics On A Lattice
Levkova, L A
2004-01-01
Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero- temperature scale setting simulations, which determine the Karsch coefficients, allows for the calculation of the Equation of State at finite temperatures. We also report on studies of the chiral properties of dynamical domain-wall fermions combined with the DBW2 gauge action for different gauge couplings and fermion masses. For quenched theories, the DBW2 action gives a residual chiral symmetry breaking much smaller than what was found with more traditional choices for the gauge action. Our goal is to investigate the possibilities which this and further improvemen...
Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
Silvi, Pietro; Dalmonte, Marcello; Tschirsich, Ferdinand; Montangero, Simone
2016-01-01
We investigate the finite-density phase diagram of a non-abelian SU(2) lattice gauge theory, encoding Yang-Mills microscopical dynamics, in (1+1)-dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the filling and of the matter-field coupling, individuating different phases, some of them appearing only at finite densities. At unit filling, we find a meson BCS liquid phase, which at strong coupling undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we individuate two tri-critical points between the chiral and the two liquid phases which are compatible with a SU(2)$_2$ Wess-Zumino-Novikov-Witten model.
Giuliani, Mario
2016-01-01
We apply a recently developed variant of the Density of States (DoS) method, the so-called Functional Fit Approach (FFA) to two different models: the SU(3) spin model and SU(3) lattice gauge theory with static quarks. Both models can be derived from QCD and inherit the complex action problem at finite density. We discuss the implementation of DoS FFA in the two models and compute observables related to the particle density. For the SU(3) spin model we show that the results are in good agreement with the results from a Monte Carlo simulation in the dual formulation, which is free of the complex action problem. For the case of SU(3) lattice gauge theory with static quarks we present first results for the particle number as a function of the coupling for different values of the chemical potential.
Quenching and dipole-dipole interactions in Sr{sub 2}Al{sub 2}SiO{sub 7}:Ce{sup 3+} host lattice
Energy Technology Data Exchange (ETDEWEB)
Kolte, M.; Dhoble, S.J. [R.T.M. Nagpur University, Department of Physics, Nagpur (India); Pawade, V.B. [R.T.M. Nagpur University, Department of Applied-Physics, Laxminarayan Institute of Technology, Nagpur (India)
2016-02-15
This article reports novel results on the optical properties of Ce{sup 3+}-doped Sr{sub 2}Al{sub 2}SiO{sub 7} host lattice which has been synthesized by the combustion method at 550 C for the first time. Sr{sub 2}Al{sub 2}SiO{sub 7}: Ce{sup 3+} phosphor shows the blue emission bands at 430 nm due to 5d-4f allowed transition of Ce{sup 3+} ion, keeping the excitation wavelength constant at 357 nm. Some theoretical study is carried out on the critical distance of energy transfer, concentration quenching and type of interaction in host and rare earth ion, and it is done by using the equation reported by Van Uiltert et al. Further phosphor is well characterized by XRD, SEM and EDS analysis to study phase purity, surface morphology and elemental analysis. (orig.)
Z(2) gauge neural network and its phase structure
Takafuji, Yusuke; Nakano, Yuki; Matsui, Tetsuo
2012-11-01
We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable Si=±1 on the i-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable J=±1 describes a state of the synaptic connection between j-th and i-th neurons. The gauge symmetry allows for a self-coupling energy among J’s such as JJJ, which describes reverberation of signals. Explicitly, we consider the three models; (I) an annealed model with full and partial connections of J, (II) a quenched model with full connections where J is treated as a slow quenched variable, and (III) a quenched three-dimensional lattice model with the nearest-neighbor connections. By numerical simulations, we examine their phase structures paying attention to the effect of the reverberation term, and compare them with each other and with the annealed 3D lattice model which has been studied beforehand. By noting the dependence of thermodynamic quantities upon the total number of sites and the connectivity among sites, we obtain a coherent interpretation to understand these results. Among other things, we find that the Higgs phase of the annealed model is separated into two stable spin-glass phases in the quenched models (II) and (III).
Bulava, John; Heitger, Jochen; Wittemeier, Christian
2015-01-01
The coefficient c_A required for O(a) improvement of the axial current in lattice QCD with N_f=3 flavors of Wilson fermions and the tree-level Symanzik-improved gauge action is determined non-perturbatively. The standard improvement condition using Schroedinger functional boundary conditions is employed at constant physics for a range of couplings relevant for simulations at lattice spacings of ~ 0.09 fm and below. We define the improvement condition projected onto the zero topological charge sector of the theory, in order to avoid the problem of possibly insufficient tunneling between topological sectors in our simulations at the smallest bare coupling. An interpolation formula for c_A(g_0^2) is provided together with our final results.
Bulava, John; Heitger, Jochen; Wittemeier, Christian
2016-01-01
We non-perturbatively determine the renormalization factor of the axial vector current in lattice QCD with $N_f=3$ flavors of Wilson-clover fermions and the tree-level Symanzik-improved gauge action. The (by now standard) renormalization condition is derived from the massive axial Ward identity and it is imposed among Schr\\"{o}dinger functional states with large overlap on the lowest lying hadronic state in the pseudoscalar channel, in order to reduce kinematically enhanced cutoff effects. We explore a range of couplings relevant for simulations at lattice spacings of $\\approx 0.09$ fm and below. An interpolation formula for $Z_A(g_0^2)$, smoothly connecting the non-perturbative values to the 1-loop expression, is provided together with our final results.
Diquark correlations in baryons on the lattice with overlap quarks
Energy Technology Data Exchange (ETDEWEB)
Babich, R.; Howard, J.; Rebbi, C. [Boston Univ., MA (United States). Dept. of Physics; Garron, N. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Hoelbling, C. [Wuppertal Univ. (Gesamthochschule) (Germany). Fachbereich Physik; Lellouch, L. [CNRS Luminy, Marseille (France). Centre de Physique Theorique]|[Wuppertal Univ. (Gesamthochschule) (Germany). Fachbereich Physik
2007-01-15
We evaluate baryon wave functions in both the Coulomb and Landau gauge in lattice QCD. These are constructed from quark propagators calculated with the overlap Dirac operator on quenched gauge configurations at {beta}=6. By comparing baryon states that differ in their diquark content, we find evidence for enhanced correlation in the scalar diquark channel, as favored by quark models. We also summarize earlier results for diquark masses in the Landau gauge, casting them in a form more easily compared with subsequent studies. (orig.)
Supergravity from Gauge Theory
Berkowitz, Evan
2016-01-01
Gauge/gravity duality is the conjecture that string theories have dual descriptions as gauge theories. Weakly-coupled gravity is dual to strongly-coupled gauge theories, ideal for lattice calculations. I will show precision lattice calculations that confirm large-N continuum D0-brane quantum mechanics correctly reproduces the leading-order supergravity prediction for a black hole's internal energy---the first leading-order test of the duality---and constrains stringy corrections.
Quenched mesonic spectrum at large N
Del Debbio, Luigi; Patella, Agostino; Pica, Claudio
2008-01-01
We compute the masses of the $\\pi$ and of the $\\rho$ mesons in the quenched approximation on a lattice with fixed lattice spacing $a \\simeq 0.145 \\ \\mathrm{fm}$ for SU($N$) gauge theory with $N = 2,3,4,6$. We find that a simple linear expression in $1/N^2$ correctly captures the features of the lowest-lying meson states at those values of $N$. This enables us to extrapolate to $N = \\infty$ the behaviour of $m_{\\pi}$ as a function of the quark mass and of $m_{\\rho}$ as a function of $m_{\\pi}$. Our results for the latter agree within 5% with recent predictions obtained in the AdS/CFT framework.
Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics
Energy Technology Data Exchange (ETDEWEB)
Buividovich, P.V. [Joint Institute for Nuclear Research, Dubna (Russian Federation); Institute for Theoretical and Experimental Physics ITEP, Moscow (Russian Federation); Kalaydzhyan, T. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Institute for Theoretical and Experimental Physics ITEP, Moscow (Russian Federation); Polikarpov, M.I. [Institute for Theoretical and Experimental Physics ITEP, Moscow (Russian Federation)
2011-11-15
We study the effect of cooling on the spatial distribution of the topological charge density in quenched SU(2) lattice gauge theory with overlap fermions. We show that as the gauge field configurations are cooled, the Hausdorff dimension of regions where the topological charge is localized gradually changes from d=2/3 towards the total space dimension. Hence the cooling procedure destroys some of the essential properties of the topological charge distribution. (orig.)
A numerical investigation of orientifold planar equivalence for quenched mesons
Lucini, Biagio; Patella, Agostino; Rago, Antonio
2010-01-01
We measure on the lattice the quenched pseudoscalar and vector meson masses at a fixed value of the lattice spacing for SU(N) gauge theory with fermions in the adjoint, in the symmetric and in the antisymmetric representations of the gauge group. Simulations are performed for N=3,4,6 in all those representations, with the addition of N=2 for the adjoint representation. We illustrate a strategy for separating the even from the odd-power contributions in 1/N in the masses. Using this technique, we extrapolate the vector mass to the large-N limit in the chiral region and show that at N = infty this mass is the same within errors in all the three representations, as predicted by orientifold planar equivalence. Possible implications of our investigation for studying orientifold planar equivalence in the dynamical case are discussed.
Bazavov, Alexei; Tsai, Shan-Wen; Unmuth-Yockey, Judah; Zhang, Jin
2015-01-01
We present a gauge-invariant effective action for the Abelian-Higgs model in 1+1 dimensions. It is constructed by integrating out the gauge field and then using the hopping parameter expansion. The latter is tested with Monte Carlo simulations for small values of the scalar self-coupling. In the opposite limit, at infinitely large self-coupling, the Higgs mode is frozen and the partition function can be written in terms of local tensors and the tensor renormalization group blocking can be applied. The numerical implementation requires truncations and the time continuum limit of the blocked transfer matrix can be obtained numerically. At zero gauge coupling and with a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large onsite repulsion. The procedure is extended to finite gauge coupling and we derive a spin-1 approximation of the Hamiltonian which involves terms corresponding to transitions among the two species i...
Exploring the structure of the quenched QCD vacuum with overlap fermions
Energy Technology Data Exchange (ETDEWEB)
Ilgenfritz, E.M. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Koller, K. [Muenchen Univ. (Germany). Sektion Physik; Koma, Y. [Mainz Univ. (Germany). Inst. fuer Kernphysik; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Streuer, T. [Kentucky Univ., Lexington, KY (United States). Dept. of Physics and Astronomy; Weinberg, V. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Freie Univ. Berlin (Germany). Inst. fuer Theoretische Physik
2007-05-15
Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects of quenched gauge field configurations. This includes the localization and chiral properties of the eigenmodes, the local structure of the ultraviolet filtered field strength tensor, as well as the structure of topological charge fluctuations. We conclude that the vacuum has a multifractal structure. (orig.)
Numerical analysis of the spectrum of the Dirac operator in four-dimensional SU(2) gauge fields
Kalkreuter, T
1995-01-01
Two numerical algorithms for the computation of eigenvalues of Dirac operators in lattice gauge theories are described: one is an accelerated conjugate gradient method, the other one a standard Lanczos method. Results obtained by Cullum's and Willoughby's variant of the Lanczos method (whose convergence behaviour is closely linked with the local spectral density) are presented for euclidean Wilson fermions in quenched and unquenched SU(2) gauge fields. Complete spectra are determined on lattices up to 8^3 \\cdot 12, and we derive numerical values for fermionic determinants and results for spectral densities.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Establishment of the Coulomb law in the layer phase of a pure U(1) lattice gauge theory
Farakos, K
2008-01-01
In this article we examine the Layer phase of the five dimensional, anisotropic, Abelian gauge model. Our results are to be compared with the ones of the 4D U(1) gauge model in an attempt to verify that four dimensional physics governs the four dimensional layers. The main results are: i) From the analysis of Wilson loops we verified the $\\frac{1}{R}$ behavior, in the layered phase, for the potential between heavy charges. The renormalized fine structure constant in the layer phase is found to be equal to that of 4D Coulomb phase,$\\alpha_{layer}$=$\\alpha_{4D}$. ii) Based on the helicity modulus analysis we show that the layers are in the Coulomb phase while the transverse bulk space is in the confining phase. We also calculated the renormalized coupling $\\beta_{R}$ and found results compatible with those obtained from the Coulomb potential. Finally we calculated the potential in the 5D Coulomb phase and found $\\frac{1}{R^{2}}$ behavior for the static $q \\bar{q}$ potential. From the study of the helicity modul...
Lattice Study of Planar Equivalence: The Quark Condensate
Armoni, Adi; Patella, Agostino; Pica, Claudio
2008-01-01
We study quenched SU(N) gauge theories with fermions in the two-index symmetric, antisymmetric and the adjoint representations. Our main motivation is to check whether at large number of colours those theories become non-perturbatively equivalent. We prove the equivalence assuming that the charge-conjugation symmetry is not broken in pure Yang-Mills theory. We then carry out a quenched lattice simulation of the quark condensate in the symmetric, antisymmetric and the adjoint representations for SU(2), SU(3), SU(4), SU(6) and SU(8). We show that the data support the equivalence and discuss the size of subleading corrections.
Gauge engineering and propagators
Maas, Axel
2016-01-01
Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and properties of these additional gauge copies will be investigated. Based on these properties gauge conditions are constructed to account for these gauge copies. The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.
Gauge engineering and propagators
Maas, Axel
2017-03-01
Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and properties of these additional gauge copies will be investigated. Based on these properties gauge conditions are constructed to account for these gauge copies. The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.
Ochiai, Tetsuyuki
2016-01-01
Synthetic gauge field and pseudospin-orbit interaction are implemented in the stacked two-dimensional ring network model proposed by the present author. The model was introduced to simulate light propagation in the corresponding ring-resonator network, and is thus completely bosonic. Without these two items, the system exhibits Floquet-Weyl and Floquet-topological-insulator phases with topologically gapless and gapped band structures, respectively. The synthetic magnetic field implemented in the model results in a three-dimensional Hofstadter-butterfly-type spectrum in a photonic platform. The resulting gaps are characterization by the winding number of relevant S-matrices together with the Chern number of the bulk bands. The pseudospin-orbit interaction is defined as the mixing term between two pseudospin degrees of freedom in the rings, namely, the clockwise and counter-clockwise modes in the rings. It destroys the Floquet-topological-insulator phases, while the Floquet-Weyl phase with multiple Weyl points ...
Puhr, Matthias; Buividovich, P. V.
2017-05-01
We demonstrate the nonrenormalization of the chiral separation effect (CSE) in quenched finite-density QCD in both confinement and deconfinement phases using a recently developed numerical method which allows us, for the first time, to address the transport properties of exactly chiral, dense lattice fermions. This finding suggests that CSE can be used to fix renormalization constants for axial current density. Explaining the suppression of the CSE which we observe for topologically nontrivial gauge field configurations on small lattices, we also argue that CSE vanishes for self-dual non-Abelian fields inside instanton cores.
The three-loop $\\beta$-function of SU(N) lattice gauge theories with overlap fermions
Constantinou, M
2007-01-01
We briefly report our calculation of the 2-loop coefficient of the coupling constant renormalization function Z_g in lattice perturbation theory. The quantity under study is defined through g_0 = Z_g g, where g_0 (g) is the bare (renormalized) coupling constant. The 2-loop expression for Z_g can be directly related to the 3-loop bare beta-function beta_L(g_0). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. Our results depend explicitly on the number of fermion flavors (N_f) and colors (N). Since the dependence of Z_g on the overlap parameter rho cannot be extracted analytically, we tabulate our results for different values of rho in the allowed range (0
QCD thermodynamics on a lattice
Levkova, Ludmila A.
Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero-temperature scale setting simulations, which determine the Karsch coefficients, allows for the calculation of the Equation of State at finite temperatures. We also report on studies of the chiral properties of dynamical domain-wall fermions combined with the DBW2 gauge action for different gauge couplings and fermion masses. For quenched theories, the DBW2 action gives a residual chiral symmetry breaking much smaller than what was found with more traditional choices for the gauge action. Our goal is to investigate the possibilities which this and further improvements provide for the study of QCD thermodynamics and other simulations at stronger couplings.
Exploratory study of the 3-gluon vertex on the lattice
Parrinello, C
1994-01-01
We define and evaluate on the lattice the amputated 3-gluon vertex function in momentum space. We give numerical results for 16^3 \\times 40 and 24^3 \\times 40 quenched lattices at \\beta=6.0. A good numerical signal is obtained, at the price of enforcing the gauge-fixing condition with high accuracy. By comparing results from two different lattice volumes, we try to investigate the crucial issue of finite volume effects. We also outline a method for the lattice evaluation of the QCD running coupling constant as defined from the 3-gluon vertex, while being aware that a realistic calculation will require larger \\beta values and very high statistics.
Brambilla, Michele
2013-01-01
Numerical Stochastic Perturbation Theory was able to get three- (and even four-) loop results for finite Lattice QCD renormalization constants. More recently, a conceptual and technical framework has been devised to tame finite size effects, which had been reported to be significant for (logarithmically) divergent renormalization constants. In this work we present three-loop results for fermion bilinears in the Lattice QCD regularization defined by tree-level Symanzik improved gauge action and n_f=2 Wilson fermions. We discuss both finite and divergent renormalization constants in the RI'-MOM scheme. Since renormalization conditions are defined in the chiral limit, our results also apply to Twisted Mass QCD, for which non-perturbative computations of the same quantities are available. We emphasize the importance of carefully accounting for both finite lattice space and finite volume effects. In our opinion the latter have in general not attracted the attention they would deserve.
Itou, Etsuko
2012-01-01
We give a summary report for the nonperturbative behaviors of the twisted Polyakov loop (TPL) coupling constant for the SU(3) gauge theory, which is one of the nonperturbative renormalized coupling constants defined in finite volume. We reveal several properties for the lattice gauge theory with the twisted boundary condition and carry out the numerical simulations in the cases of the quenched QCD and N_f=12 SU(3) theories. At first, we study the quenched QCD theory by using the plaquette gauge action. The TPL coupling constant shows a fake fixed point in the Coulomb phase even in the quenched QCD. We discuss this property and show the nonperturbative running coupling constant. We also investigate the system coupled with fundamental fermions. In the simulation, we use the naive staggered fermion and the minimum number of flavor is 12 in this lattice setup because of the twisted boundary condition. The N_f=12 SU(3) gauge theory is expected that the running coupling constant shows the different behavior form th...
Unquenched Effects and Quark Mass Dependence of Lattice Gluon Propagator in Infrared Region
Institute of Scientific and Technical Information of China (English)
ZHANG Yan-Bin; PING Jia-Lun; LU Xiao-Fu; ZONG Hong-Shi
2008-01-01
In this paper,the gluon propagator in Landau gauge has been studied on a lattice,including the quenched and the unquenehed one.The small geometry size of lattice we use is 163×32,and the big one is 203×64.For the quenched approximation,we fit the numerical results and give a little different fitting values.We also obtain unquenched effects by comparing the gluon propagator resulting from the quenched and unquenehed configurations,for both the two-flavor and three-flavor cases.For the unquenched configurations,an obvious quark mass dependence has not been found in the small quark mass case,but is found in the three-flavor case when the quark mass is big.
Gauge engineering and propagators
Directory of Open Access Journals (Sweden)
Maas Axel
2017-01-01
The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.
Lenz, F
2009-01-01
By superposition of regular gauge instantons or merons, ensembles of gauge fields are constructed which describe the confining phase of SU(2) Yang-Mills theory. Various properties of the Wilson loops, the gluon condensate and the topological susceptibility are found to be in qualitative agreement with phenomenology or results of lattice calculations. Limitations in the application to the glueball spectrum and small size Wilson loops are discussed.
Effects of non-perturbatively improved dynamical fermions in QCD at fixed lattice spacing
Allton, C R; Bowler, K C; Garden, J; Hart, A; Hepburn, D; Irving, A C; Joó, B; Kenway, R D; Maynard, C M; McNeile, C; Michael, C; Pickles, S M; Sexton, J C; Sharkey, K J; Sroczynski, Z; Talevi, M; Teper, M; Wittig, H
2002-01-01
We present results for the static inter-quark potential, lightest glueballs, light hadron spectrum and topological susceptibility using a non-perturbatively improved action on a $16^3\\times 32$ lattice at a set of values of the bare gauge coupling and bare dynamical quark mass chosen to keep the lattice size fixed in physical units ($\\sim 1.7$ fm). By comparing these measurements with a matched quenched ensemble, we study the effects due to two degenerate flavours of dynamical quarks. With the greater control over residual lattice spacing effects which these methods afford, we find some evidence of charge screening and some minor effects on the light hadron spectrum over the range of quark masses studied ($M_{PS}/M_{V}\\ge0.58$). More substantial differences between quenched and unquenched simulations are observed in measurements of topological quantities.
Energy Technology Data Exchange (ETDEWEB)
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-23
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-23
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
A new scheme for the running coupling constant in gauge theories using Wilson loops
Energy Technology Data Exchange (ETDEWEB)
Kurachi, Masafumi [Los Alamos National Laboratory; Bilgici, Erek [AUSTRIA; Flachi, Antonion [KYOTO UNIV; Itou, Etsuko [KOGAKUIN UNIV; David Lin, C J [NATIONAL CHIAO-TUNG UNIV; Matsufuru, Hideo [KEK; Ohki, Hiroshi [KYOTO UNIV; Onogi, Tetsuya [KYOTO UNIV; Yamazaki, Takeshi [UNIV OF TSUKUBA
2009-01-01
We propose a new renormalization scheme of the running coupling constant in general gauge theories defined by using the Wilson loops. The renormalized coupling constant is obtained from the Cretz ratio in lattice simulations and the corresponding perturbative coefficient at the leading order. The latter calculation is performed by adopting the zeta-function resummation techniques. We make a benchmark test of our scheme in quenched QCD with the plaquette gauge action. The running of the coupling constant is determined by applying the step scaling procedure. Using several methods to improve the statistical accuracy, we show that the running coupling constant can be determined in a wide range of energy scales with relatively small number of gauge configurations.
Full CKM matrix with lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Okamoto, Masataka; /Fermilab
2004-12-01
The authors show that it is now possible to fully determine the CKM matrix, for the first time, using lattice QCD. |V{sub cd}|, |V{sub cs}|, |V{sub ub}|, |V{sub cb}| and |V{sub us}| are, respectively, directly determined with the lattice results for form factors of semileptonic D {yields} {pi}lv, D {yields} Klv, B {yields} {pi}lv, B {yields} Dlv and K {yields} {pi}lv decays. The error from the quenched approximation is removed by using the MILC unquenced lattice gauge configurations, where the effect of u, d and s quarks is included. The error from the ''chiral'' extrapolation (m{sub l} {yields} m{sub ud}) is greatly reduced by using improved staggered quarks. The accuracy is comparable to that of the Particle Data Group averages. In addition, |V{sub ud}|, |V{sub ts}|, |V{sub ts}| and |V{sub td}| are determined by using unitarity of the CKM matrix and the experimental result for sin (2{beta}). In this way, they obtain all 9 CKM matrix elements, where the only theoretical input is lattice QCD. They also obtain all the Wolfenstein parameters, for the first time, using lattice QCD.
Atomic Quantum Simulations of Abelian and non-Abelian Gauge Theories
CERN. Geneva
2014-01-01
Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, in a collaboration of atomic and particle physicists, we have constructed a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum link models which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows investigations of string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods. Similarly, using ultracold alkaline-earth atoms in optical lattices, we have constructed a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at non-zero temperature or baryon density. Unlike classical simulations, a quantum ...
Maas, Axel
2012-01-01
QCD can be formulated using any gauge group. One particular interesting choice is to replace SU(3) by the exceptional group G2. Conceptually, this group is the simplest group with a trivial center. It thus permits to study the conjectured relevance of center degrees of freedom for QCD. Practically, since all its representation are real, it is possible to perform lattice simulations for this theory also at finite baryon densities. It is thus an excellent environment to test methods and to investigate general properties of gauge theories at finite densities. We review the status of our understanding of gauge theories with the gauge group G2, including Yang-Mills theory, Yang-Mills-Higgs theory, and QCD both in the vacuum and in the phase diagram.
Quenched heavy-light decay constants
Energy Technology Data Exchange (ETDEWEB)
Baxter, R.M.; Booth, S.P.; Bowler, K.C.; Collins, S.; Henty, D.S.; Kenway, R.D.; Richards, D.G.; Shanahan, H.P.; Simone, J.N.; Simpson, A.D.; Wilkes, B.E. (Department of Physics, The University of Edinburgh, Edinburgh EH9 3JZ (United Kingdom)); Ewing, A.K.; Lellouch, L.; Sachrajda, C.T.; Wittig, H. (Physics Department, The University, Southampton SO9 5NH (United Kingdom)); (UKQCD Collaboration)
1994-02-01
We present results for heavy-light decay constants, using both propagating quarks and the static approximation, in [ital O]([ital a])-improved, quenched lattice QCD. At [beta]=6.2 on a 24[sup 3][times]48 lattice we find [ital f][sub [ital D
Building projected entangled pair states with a local gauge symmetry
Zohar, Erez; Burrello, Michele
2016-04-01
Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and as a tool for the analysis of the recent proposals for quantum simulations of lattice gauge theories. In this paper we present a framework for describing locally gauge invariant states on lattices using PEPS. The PEPS constructed hereby shall include both bosonic and fermionic states, suitable for all combinations of matter and gauge fields in lattice gauge theories defined by either finite or compact Lie groups.
Building Projected Entangled Pair States with a Local Gauge Symmetry
Zohar, Erez
2015-01-01
Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and as a tool for the analysis of the recent proposals for quantum simulations of lattice gauge theories. In this paper we present a framework for describing locally gauge invariant states on lattices using PEPS. The PEPS constructed hereby shall include both bosonic and fermionic states, suitable for all combinations of matter and gauge fields in lattice gauge theories defined by either finite or compact Lie groups.
Quenched hadron spectroscopy with improved staggered quark action
Bernard, C W; DeGrand, T A; DeTar, C E; Gottlieb, S; Heller, U M; Hetrick, J E; McNeile, C; Rummukainen, K; Sugar, B; Toussaint, D; Bernard, Claude; Blum, Tom; Grand, Thomas A. De; Tar, Carleton De; Gottlieb, Steven; Heller, Urs M.; Hetrick, James; Neile, Craig Mc; Sugar, Bob; Toussaint, Doug
1998-01-01
We investigate light hadron spectroscopy with an improved quenched staggered quark action. We compare the results obtained with an improved gauge plus an improved quark action, an improved gauge plus standard quark action, and the standard gauge plus standard quark action. Most of the improvement in the spectroscopy results is due to the improved gauge sector. However, the improved quark action substantially reduces violations of Lorentz invariance, as evidenced by the meson dispersion relations.
Effects of quenching and partial quenching on QCD penguin matrix elements
Golterman, Maarten; Pallante, Elisabetta
2002-01-01
We point out that chiral transformation properties of penguin operators change in the transition from unquenched to (partially) quenched QCD. The way in which this affects the lattice determination of weak matrix elements can be understood in the framework of (partially) quenched chiral perturbation
Framework for improved lattice calculations of epsilion'/epsilon
Laiho, Jack
In this thesis we show that it is possible to construct epsilon '/epsilon to NLO using both full and partially quenched chiral perturbation theory (PQChPT) from amplitudes that are computable using numerical lattice gauge theory. We find that the electro-weak penguin (Delta I = 3/2 and 1/2) contributions to epsilon'/epsilon in PQChPT can be determined to NLO using only degenerate (mK = mpi) K → pi computations without momentum insertion. All one-loop formulas needed to extract the necessary NLO constants from the lattice are presented in this work. Issues pertaining to power divergent contributions, originating from mixing with lower dimensional operators in a lattice regularization, are addressed. In embedding the QCD penguin left-right operator onto PQChPT an ambiguity arises when the number of light sea quarks is not the physical value of three, as first emphasized by Golterman and Pallante. In the quenched theory they have pointed out that there are additional effective operators that appear in the quenched chiral perturbation theory needed to make contact with K → pipi amplitudes at physical kinematics. They have also proposed a method for determining the leading order low-energy constant, aNSq , associated with the new operators. We show that their method has difficulties due to power divergent contributions and propose a new method to obtain this constant from the lattice which does not suffer from this problem. Using this alternative method, we obtain aNSq , and show that our value implies a large ambiguity in the quenched contribution of Q6 to epsilon'/epsilon.
A non-perturbative study of massive gauge theories
DEFF Research Database (Denmark)
Della Morte, Michele; Hernandez, Pilar
2013-01-01
We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists and the ...
General Gauge Mediation and Deconstruction
McGarrie, Moritz
2010-01-01
We locate a supersymmetry breaking hidden sector and supersymmetric standard model on different lattice points of an orbifold moose. The hidden sector is encoded in a set of current correlators and the effects of the current correlators are mediated by the lattice site gauge groups with "lattice hopping" functions and through the bifundamental matter that links the lattice sites together. We show how the gaugino mass, scalar mass and Casimir energy of the lattice can be computed for a general set of current correlators and then give specific formulas when the hidden sector is specified to be a generalised messenger sector coupled to a supersymmetry breaking spurion. The results reproduce the effect of five dimensional gauge mediation from a purely four dimensional construction.
Flavor symmetry breaking and scaling for improved staggered actions in quenched QCD
Cheng, M; Jung, C; Karsch, F; Mawhinney, R D; Petreczky, P; Petrov, K V
2006-01-01
We present a study of the flavor symmetry breaking in the pion spectrum for various improved staggered fermion actions. To study the effects of link fattening and tadpole improvement, we use three different variants of the p4 action - p4fat3, p4fat7, and p4fat7tad. These are compared to Asqtad and also to naive staggered. To study the pattern of symmetry breaking, we measure all 15 meson masses in the 4-flavor staggered theory. The measurements are done on a quenched gauge background, generated using a one-loop improved Symanzik action with $\\beta=10/g^2 = 7.40, 7.75,$ and 8.00, corresponding to lattice spacings of approximately a = .31 fm., .21 fm., and .14 fm. We also study how the lattice scale set by the $\\rho$ mass on each of these ensembles compares to one set by the static quark potential.
Trigiante, Mario
2016-01-01
We give a general review of extended supergravities and their gauging using the duality-covariant embedding tensor formalism. Although the focus is on four-dimensional theories, an overview of the gauging procedure and the related tensor hierarchy in the higher-dimensional models is given. The relation of gauged supergravities to flux compactifications is discussed and examples are worked out in detail.
Trigiante, Mario
2017-03-01
We give a general review of extended supergravities and their gauging using the duality-covariant embedding tensor formalism. Although the focus is on four-dimensional theories, an overview of the gauging procedure and the related tensor hierarchy in the higher-dimensional models is given. The relation of gauged supergravities to flux compactifications is discussed and examples are worked out in detail.
Lipstein, Arthur E
2014-01-01
We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces associated with each fundamental cube of the lattice. If we take the gauge group to be $U(1)$, the theory reduces to the well-known abelian gerbe theory in the continuum limit. We also propose a very simple and natural non-abelian generalization with gauge group $U(N) \\times U(N)$, which gives rise to $U(N)$ Yang-Mills theory upon dimensional reduction. Formulating the theory on a lattice has several other advantages. In particular, it is possible to compute many observables, such as the expectation value of Wilson surfaces, analytically at strong coupling and numerically for any value of the coupling.
Weatherall, James Owen
2015-01-01
I consider two usages of the expression "gauge theory". On one, a gauge theory is a theory with excess structure; on the other, a gauge theory is any theory appropriately related to classical electromagnetism. I make precise one sense in which one formulation of electromagnetism, the paradigmatic gauge theory on both usages, may be understood to have excess structure, and then argue that gauge theories on the second usage, including Yang-Mills theory and general relativity, do not generally have excess structure in this sense.
Stout-link smearing in lattice fermion actions
Zhang, J B; Bowman, Patrick O; Leinweber, Derek B; Williams, Anthony G
2009-01-01
The properties of the momentum space quark propagator in Landau gauge are studied for the overlap quark action in quenched lattice QCD. Numerical calculations are performed over four ensembles of gauge configurations, where three are smeared using either 1, 3, or 6 sweeps of stout-link smearing. We calculate the non-perturbative wave function renormalization function $Z(p)$ and the non-perturbative mass function $M(p)$ for a variety of bare quark masses. We find that the wave-function renormalization function is slightly sensitive to the number of stout-link smearing sweeps. For the mass function we find the effect of the stout-link smearing algorithm to be small for moderate to light bare quark masses. For a heavy bare quark mass we find a strong dependence on the number of smearing sweeps.
Magnetic vortices in gauge/gravity duality
Energy Technology Data Exchange (ETDEWEB)
Strydom, Migael
2014-07-18
We study strongly-coupled phenomena using gauge/gravity duality, with a particular focus on vortex solutions produced by magnetic field and time-dependent problems in holographic models. The main result is the discovery of a counter-intuitive effect where a strong non-abelian magnetic field induces the formation of a triangular vortex lattice ground state in a simple holographic model. Gauge/gravity duality is a powerful theoretical tool that has been used to study strongly-coupled systems ranging from the quark-gluon plasma produced at particle colliders to condensed matter theories. The most important idea is that of duality: a strongly coupled quantum field theory can be studied by investigating the properties of a particular gravity background described by Einstein's equations. One gravity background we study in this dissertation is AdS-Schwarzschild with an SU(2) gauge field. We switch on the gauge field component that gives the field theory an external magnetic field. When the magnetic field is above a critical value, we find that the system is unstable, indicating a superconducting phase transition. We find the instability in two ways. Firstly, we do a quasinormal mode analysis, studying fluctuations about the background. Secondly, we rewrite the equations in Schroedinger form and numerically find that, as the magnetic field is increased, the potential deepens until it is capable of supporting a bound state. Next we show that the resulting superconducting ground state is a triangular vortex lattice. This is done by performing a perturbative expansion in a small parameter proportional to the condensate size. After solving the equations to third order, we use the holographic dictionary to calculate the total energy of different lattice solutions and identify the minimum energy state. In addition, we show that the result holds in an AdS-hard wall model as well, which is dual to a confining theory. Next we extend the simple gravity model to include a
Bulava, John; Heitger, Jochen; Wittemeier, Christian
2013-01-01
We report on an ongoing non-perturbative determination of the improvement coefficient of the axial current, $c_\\mathrm A$, with three flavours of dynamical $\\mathrm O(a)$ improved Wilson quarks and tree-level Symanzik improved gauge action. Our computations are based on simulations with the openQCD code. The improvement condition for a range of couplings is formulated with Schr\\"odinger functional boundary conditions and imposed along a line of constant physics in parameter space. Our analysis involves correlation functions with boundary wave functions such that a large sensitivity to $c_\\mathrm A$ can be reached by exploiting the PCAC relation with two different pseudoscalar states.
Aspects of baryon structure in lattice QCD
Babich, Ronald
Despite the long success of Quantum Chromodynamics (QCD) as the theory of the strong interactions, there remains much to be understood about the structure of hadrons and the consequences of QCD in the nonperturbative regime. Lattice gauge theory, a framework nearly as old as QCD itself, makes calculations in this regime possible, starting from first principles. With advances in theoretical understanding, methods, and computer technology, the lattice has found application to an ever-widening range of problems. In this dissertation, I consider two such problems having to do with the structure of baryons. The first concerns the contribution of sea quarks, and the strange quark in particular, to form factors of the nucleon. This has been a long-standing challenge for the lattice, because such contributions involve the insertion of a current on a quark loop, demanding the full inversion of the discretized Dirac operator, conceptually a large sparse matrix. I discuss methods for addressing this challenge and present a calculation of the strange scalar form factor and the related parameter fTs. The latter is of great theoretical interest, since it enters into the cross section for the scattering of dark matter off nuclei in supersymmetric extensions of the standard model. As such, it represents a major uncertainty in the interpretation of direct detection experiments. I also present results for the strange quark contribution to the nucleon's axial and electromagnetic form factors, which are themselves the subject of active experimental programs. These calculations were performed using the Wilson fermion formulation on a 243 x 64 anisotropic lattice. In the second part of the dissertation, I turn to the valence sector and address the role of diquark correlations in the observed spectrum of hadrons and their properties. A diquark is a correlated pair of quarks, thought to play an important role in certain phenomenological models of hadrons. I present results for baryon wave
Framework For Improved Lattice Calculations Of Epsilion'/epsilon
Laiho, J
2004-01-01
In this thesis we show that it is possible to construct ε ′/ε to NLO using both full and partially quenched chiral perturbation theory (PQChPT) from amplitudes that are computable using numerical lattice gauge theory. We find that the electro- weak penguin (Δ I = 3/2 and 1/2) contributions to ε′/ε in PQChPT can be determined to NLO using only degenerate (mK = mπ) K → π computations without momentum insertion. All one-loop formulas needed to extract the necessary NLO constants from the lattice are presented in this work. Issues pertaining to power divergent contributions, originating from mixing with lower dimensional operators in a lattice regularization, are addressed. In embedding the QCD penguin left-right operator onto PQChPT an ambiguity arises when the number of light sea quarks is not the physical value of three, as first emphasized by Golterman and Pallante. In the quenched theory they have pointed out that there...
Non-degenerate light quark masses from 2+1f lattice QCD+QED
Energy Technology Data Exchange (ETDEWEB)
Drury, Shane [Southampton U.; Blum, Thomas [RIKEN BNL; Hayakawa, Masashi [Nagoya U.; Izubuchi, Taku [RIKEN BNL; Sachrajda, Chris [Southampton U.; Zhou, Ran [Indiana U.
2014-01-01
We report on a calculation of the effects of isospin breaking in Lattice QCD+QED. This involves using Chiral Perturbation Theory with Electromagnetic corrections to find the renormalized, non-degenerate, light quark masses. The calculations are carried out on QCD ensembles generated by the RBC and UKQCD collaborations using Domain Wall Fermions and the Iwasaki and Iwasaki+DSDR Gauge Actions with unitary pion masses down to 170 MeV. Non-compact QED is treated in the quenched approximation. The simulations use a $32^3$ lattice size with $a^{-1}=2.28(3)$ GeV (Iwasaki) and 1.37(1) (Iwasaki+DSDR). This builds on previous work from the RBC/UKQCD collaboration with lattice spacing $a^{-1}=1.78(4)$ GeV.
Topological index theorem on the lattice through the spectral flow of staggered fermions
Energy Technology Data Exchange (ETDEWEB)
Azcoiti, V., E-mail: azcoiti@azcoiti.unizar.es [Departamento de Física Teórica, Universidad de Zaragoza, Calle Pedro Cerbuna 12, E-50009 Zaragoza (Spain); Follana, E., E-mail: efollana@unizar.es [Departamento de Física Teórica, Universidad de Zaragoza, Calle Pedro Cerbuna 12, E-50009 Zaragoza (Spain); Vaquero, A., E-mail: Alejandro.Vaquero@mib.infn.it [Departamento de Física Teórica, Universidad de Zaragoza, Calle Pedro Cerbuna 12, E-50009 Zaragoza (Spain); Di Carlo, G., E-mail: giuseppe.dicarlo@lngs.infn.it [Laboratori Nazionali del Gran Sasso, Via G. Acitelli, 22, 67100 Assergi L' Aquila (Italy)
2015-05-11
We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic (quenched) gauge configurations. We obtain clear numerical evidence that the definition works as expected: there is a clear separation between crossings near and far away from the origin, and the topological charge defined through the crossings near the origin agrees, for most configurations, with the one defined through the near-zero modes of large taste-singlet chirality of the staggered Dirac operator. The crossings are much closer to the origin if we improve the Dirac operator used in the definition, and they move towards the origin as we decrease the lattice spacing.
Cardoso, Nuno; Bicudo, Pedro; Oliveira, Orlando
2012-01-01
In this paper we present and explore the performance of Landau gauge fixing in GPUs using CUDA. We consider the steepest descent algorithm with Fourier acceleration, and compare the GPU performance with a parallel CPU implementation. Using $32^4$ lattice volumes, we find that the computational power of a single Tesla C2070 GPU is equivalent to approximately 256 CPU cores.
Puhr, M
2016-01-01
We use exactly chiral overlap lattice fermions to investigate the Chiral Separation Effect in quenched QCD at finite density. We employ a recently developed numerical method which allows, for the first time, to address the transport properties of exactly chiral lattice fermions with non-zero chemical potential. Studying the axial current along the external magnetic field, we find a linear dependence consistent with the free fermion result for topologically trivial gauge field configurations. However, for configurations with nontrivial topology in the confinement regime the axial current is strongly suppressed due to contributions of topological modes of the Dirac operator, which suggests that non-perturbative corrections to the Chiral Separation Effect have topological origin.
Hofmann, Ralf; Hofmann, Ralf; Keil, Mathias Th.
2002-01-01
Based on thermal equilibrium between the vacuum and its relevant excitations a model for cosmic inflation is presented. Due to a vacuum dominating, U(1) gauged inflaton field an inflationary regime can be reached without explicitly imposing slow-roll conditions. Thereby, nontrivial euclidean BPS saturation of the inflaton bans gravity from the field equations and masquerades the gauge symmetry as a $Z_{N+1}$ symmetry at the point where thermal equilibrium breaks down. Solving the vacuum dynamics of the gauge field in the inflaton background in the spirit of a Born-Oppenheimer approximation, a temperature dependent cosmological constant $\\La=\\La(T)$ is obtained. The $T$ dependence of $\\La$ competes with the black body radiation of the (massive) gauge field during cosmic expansion. This leads to (initial condition independent) inflation at some critical value of the inflaton amplitude. The model allows for a closed, noncollapsing universe with Planckian initial density, and hence it resolves the flatness proble...
Energy Technology Data Exchange (ETDEWEB)
Schaefer, Stefan [DESY (Germany). Neumann Inst. for Computing
2016-11-01
These configurations are currently in use in many on-going projects carried out by researchers throughout Europe. In particular this data will serve as an essential input into the computation of the coupling constant of QCD, where some of the simulations are still on-going. But also projects computing the masses of hadrons and investigating their structure are underway as well as activities in the physics of heavy quarks. As this initial project of gauge field generation has been successful, it is worthwhile to extend the currently available ensembles with further points in parameter space. These will allow to further study and control systematic effects like the ones introduced by the finite volume, the non-physical quark masses and the finite lattice spacing. In particular certain compromises have still been made in the region where pion masses and lattice spacing are both small. This is because physical pion masses require larger lattices to keep the effects of the finite volume under control. At light pion masses, a precise control of the continuum extrapolation is therefore difficult, but certainly a main goal of future simulations. To reach this goal, algorithmic developments as well as faster hardware will be needed.
Lewis, Randy
2014-01-01
Several collaborations have recently performed lattice calculations aimed specifically at dark matter, including work with SU(2), SU(3), SU(4) and SO(4) gauge theories to represent the dark sector. Highlights of these studies are presented here, after a reminder of how lattice calculations in QCD itself are helping with the hunt for dark matter.
Analytic Variational Investigation of Euclidean SU(3) Gauge Theory
Dass, N D H
1993-01-01
Analytic variational techniques for lattice gauge theories based on the Rayleigh-Ritz(RR) method were previously developed for euclidean SU(2) gauge theories in 3 and 4 dimensions. Their extensions to SU(3) gauge theory including applications to correlation functions and mass gaps are presented here.
GPU implementation of a Landau gauge fixing algorithm
Cardoso, Nuno; Oliveira, Orlando; Bicudo, Pedro
2012-01-01
We discuss how the steepest descent method with Fourier acceleration for Laudau gauge fixing in lattice SU(3) simulations can be implemented using CUDA. The scaling of the gauge fixing code was investigated using a Tesla C2070 Fermi architecture, and compared with a parallel CPU gauge fixing code.
Even parity excitations of the nucleon in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
B. G. Lasscock; J. N. Hedditch; W. Kamleh; D. B. Leinweber; W. Melnitchouk; A. G. Williams; J. M. Zanotti
2007-09-01
We study the spectrum of the even parity excitations of the nucleon in quenched lattice QCD. We extend our earlier analysis by including an expanded basis of nucleon interpolating fields, increasing the physical size of the lattice, including more configurations to enhance statistics and probing closer to the chiral limit. With a review of world lattice data, we conclude that there is little evidence of the Roper resonance in quenched lattice QCD.
Alkofer, R; Von Smekal, L; Alkofer, Reinhard; Fischer, Christian S.; Smekal, Lorenz von
2003-01-01
The Kugo-Ojima confinement criterion and its relation to the infrared behaviour of the gluon and ghost propagators in Landau gauge QCD are reviewed. The realization of this confinement criterion (which in Landau gauge relates to Zwanziger's horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson-Schwinger equations provide an explicit example for the anticipated infrared behaviour. These results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, $\\alpha(0) = 8.9/N_c$. Solutions for the coupled system of Dyson-Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry is found. In the quenched approximation the quark propagator functions agree well with th...
HQET at order 1/m. Pt. 1. Non-perturbative parameters in the quenched approximation
Energy Technology Data Exchange (ETDEWEB)
Blossier, Benoit [Paris XI Univ., 91 - Orsay (France). Lab. de Physique Theorique; Della Morte, Michele [Mainz Univ. (Germany). Inst. fuer Kernphysik; Garron, Nicolas [Universidad Autonoma de Madrid (Spain). Dept. Fisica Teorica y Inst. de Fisica Teorica UAM/CSIC; Edinburgh Univ. (United Kingdom). School of Physics and Astronomy - SUPA; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2010-01-15
We determine non-perturbatively the parameters of the lattice HQET Lagrangian and those of heavy-light axial-vector and vector currents in the quenched approximation. The HQET expansion includes terms of order 1/m{sub b}. Our results allow to compute, for example, the heavy-light spectrum and B-meson decay constants in the static approximation and to order 1/m{sub b} in HQET. The determination of the parameters is separated into universal and non-universal parts. The universal results can be used to determine the parameters for various discretizations. The computation reported in this paper uses the plaquette gauge action and the ''HYP1/2'' action for the b-quark described by HQET. The parameters of the currents also depend on the light-quark action, for which we choose non-perturbatively O(a)-improved Wilson fermions. (orig.)
G_2 gauge theory at finite temperature
Cossu, Guido; Di Giacomo, Adriano; Lucini, Biagio; Pica, Claudio
2007-01-01
The gauge group being centreless, $G_2$ gauge theory is a good laboratory for studying the role of the centre of the group for colour confinement in Yang-Mills gauge theories. In this paper, we investigate $G_2$ pure gauge theory at finite temperature on the lattice. By studying the finite size scaling of the plaquette, the Polyakov loop and their susceptibilities, we show that a deconfinement phase transition takes place. The analysis of the pseudocritical exponents give strong evidence of the deconfinement transition being first order. Implications of our findings for scenarios of colour confinement are discussed.
Exact formulas in noncommutative gauge theories
Wallet, Jean-Christophe
2016-01-01
The noncommutative space $\\mathbb{R}^3_\\lambda$, a deformation of $\\mathbb{R}^3$, supports a $3$-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of $\\mathbb{R}^3_\\lambda$. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Domain decomposition, multi-level integration and exponential noise reduction in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Ce, Marco [Scuola Normale Superiore, Pisa (Italy); INFN, Sezione di Pisa (Italy); Giusti, Leonardo [Univ. di Milano-Bicocca (Italy). Dipt. di Fisica; INFN, Sezione di Milano-Bicocca (Italy); Schaefer, Stefan [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2016-01-15
We explore the possibility of computing fermionic correlators on the lattice by combining a domain decomposition with a multi-level integration scheme. The quark propagator is expanded in series of terms with a well defined hierarchical structure. The higher the order of a term, the (exponentially) smaller its magnitude, the less local is its dependence on the gauge field. Once inserted in a Wick contraction, the gauge-field dependence of the terms in the resulting series can be factorized so that it is suitable for multi-level Monte Carlo integration. We test the strategy in quenched QCD by computing the disconnected correlator of two flavor-diagonal pseudoscalar densities, and a nucleon two-point function. In either cases we observe a significant exponential increase of the signal-to-noise ratio.
Rho Meson Decay into pi+pi- on Asymmetrical Lattices
Pelissier, Craig S.
The computation of the lowest-lying hadron masses was the earliest success of lattice QCD. Current spectroscopy is faced with the task of computing excited-states. This is particularly challenging when excited-states appear as scattering resonances. In this case, the resonance parameters have to be determined by studying the energies of the scattering states. Currently it is only computationally feasible to compute resonances of the simplest systems. In our work, we carry out a calculation of the ρ(770) resonance seen in the isospin l = 1 two-pion system in the l = 1 channel. To determine the resonance parameters, we compute the scattering phase shifts from the two-pion spectrum using Luscher's formula. Unlike other studies which employ the moving frame formalism, we use lattices with one spatial direction elongated. To vary the momentum of the two-pion state, we adjust the length of the elongated direction. With this approach, the two-pion momentum can be tuned more finely, which allows one to map out the resonance more accurately. In this work, we employed nHYP-smeared clover fermions with two mass-degenerate quarks. The lattice computations were carried out on large elongated lattices with spatial volumes ≥ 33 fm3. We carried out an exploratory quenched study and found the two-pion spectrum to be compatible with the results obtained using dynamical fermions. Our results showed a disagreement with the physical decay at the level of 20% which is typical for quenched simulations. After completing the quenched study, we recomputed the resonance parameters on fully dynamical gauge configurations with a pion mass of 304(2) MeV. We found a value mρ = 827(3)(5) MeV and gρππ = 6.67(42) for the resonance mass and coupling constant. Our results are consistent with other lattice studies at similar pion masses and are in good agreement with the prediction from unitarized Chiral Perturbation Theory at NLO. The scattering phase shifts we computed are more evenly
Gauge-fixing and the Gribov-Singer ambiguity
Energy Technology Data Exchange (ETDEWEB)
Maas, Axel [Institute for Theoretical Physics, University of Jena (Germany)
2013-07-01
Gauge-fixing is a useful tool in intermediate steps of calculations in quantum gauge field theories. However, in non-Abelian gauge theories it is complicated non-perturbatively by the Gribov-Singer ambiguity. Several aspects of this ambiguity and proposals for its resolution in the class of Landau gauges are presented, especially in view of the necessity to perform the same type of gauge-fixing both in the continuum and on the lattice. This has implications also for global residual gauge symmetries, like the BRST symmetry or the breaking of global symmetries by the Higgs mechanism.
Energy Technology Data Exchange (ETDEWEB)
Burnier, Yannis [Institut de Théorie des Phénomènes Physiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland); Kaczmarek, Olaf [Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld (Germany); Rothkopf, Alexander [Institute for Theoretical Physics, Heidelberg University, Philosophenweg 16, D-69120 Heidelberg (Germany)
2016-01-22
We report recent results of a non-perturbative determination of the static heavy-quark potential in quenched and dynamical lattice QCD at finite temperature. The real and imaginary part of this complex quantity are extracted from the spectral function of Wilson line correlators in Coulomb gauge. To obtain spectral information from Euclidean time numerical data, our study relies on a novel Bayesian prescription that differs from the Maximum Entropy Method. We perform simulations on quenched 32{sup 3} × N{sub τ} (β = 7.0, ξ = 3.5) lattices with N{sub τ} = 24, …, 96, which cover 839MeV ≥ T ≥ 210MeV. To investigate the potential in a quark-gluon plasma with light u,d and s quarks we utilize N{sub f} = 2 + 1 ASQTAD lattices with m{sub l} = m{sub s}/20 by the HotQCD collaboration, giving access to temperatures between 286MeV ≥ T ≥ 148MeV. The real part of the potential exhibits a clean transition from a linear, confining behavior in the hadronic phase to a Debye screened form above deconfinement. Interestingly its values lie close to the color singlet free energies in Coulomb gauge at all temperatures. We estimate the imaginary part on quenched lattices and find that it is of the same order of magnitude as in hard-thermal loop perturbation theory. From among all the systematic checks carried out in our study, we discuss explicitly the dependence of the result on the default model and the number of datapoints.
Energy Technology Data Exchange (ETDEWEB)
ORGINOS,K.
2003-01-07
I review the current status of hadronic structure computations on the lattice. I describe the basic lattice techniques and difficulties and present some of the latest lattice results; in particular recent results of the RBC group using domain wall fermions are also discussed. In conclusion, lattice computations can play an important role in understanding the hadronic structure and the fundamental properties of Quantum Chromodynamics (QCD). Although some difficulties still exist, several significant steps have been made. Advances in computer technology are expected to play a significant role in pushing these computations closer to the chiral limit and in including dynamical fermions. RBC has already begun preliminary dynamical domain wall fermion computations [49] which we expect to be pushed forward with the arrival of QCD0C. In the near future, we also expect to complete the non-perturbative renormalization of the relevant derivative operators in quenched QCD.
A Nonperturbative Regulator for Chiral Gauge Theories
Grabowska, Dorota M
2015-01-01
We propose a nonperturbative gauge invariant regulator for $d$-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in $d+1$ dimensions with quantum gauge fields that reside on one $d$-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local $d$-dimensional interpretation if and only if the chiral fermion representation is anomaly free. A physical realization of this construction leads to mirror fermions in the Standard Model with soft form factors for gauge fields and gravity. These mirror particles could evade detection except by sensitive probes at extremely low energy, and yet still affect vacuum topology, and could gravitate differently than conventional matter.
Critical slowing down and error analysis in lattice QCD simulations
Energy Technology Data Exchange (ETDEWEB)
Virotta, Francesco
2012-02-21
In this work we investigate the critical slowing down of lattice QCD simulations. We perform a preliminary study in the quenched approximation where we find that our estimate of the exponential auto-correlation time scales as {tau}{sub exp}(a){proportional_to}a{sup -5}, where a is the lattice spacing. In unquenched simulations with O(a) improved Wilson fermions we do not obtain a scaling law but find results compatible with the behavior that we find in the pure gauge theory. The discussion is supported by a large set of ensembles both in pure gauge and in the theory with two degenerate sea quarks. We have moreover investigated the effect of slow algorithmic modes in the error analysis of the expectation value of typical lattice QCD observables (hadronic matrix elements and masses). In the context of simulations affected by slow modes we propose and test a method to obtain reliable estimates of statistical errors. The method is supposed to help in the typical algorithmic setup of lattice QCD, namely when the total statistics collected is of O(10){tau}{sub exp}. This is the typical case when simulating close to the continuum limit where the computational costs for producing two independent data points can be extremely large. We finally discuss the scale setting in N{sub f}=2 simulations using the Kaon decay constant f{sub K} as physical input. The method is explained together with a thorough discussion of the error analysis employed. A description of the publicly available code used for the error analysis is included.
Precocious scaling in lattice gauge theories
Gliozzi, F.; Ravanini, F.; Sciuto, S.
1982-12-01
We propose a method to evaluate numerically and in some cases analytically the two-loop contributions to physical quantities without computing Feynman graphs. Such contributions are negligible for the SU(2) Wilson action, which shows a precocious scaling; on the contrary they are important for other actions (including Manton and heat kernel ones) and account for the observed violations of universality.
Lattice Gauge Field Theory and Prismatic Sets
DEFF Research Database (Denmark)
Akyar, Bedia; Dupont, Johan Louis
We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set and the prismatic star of . Both have the same homotopy type as and in part......We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set and the prismatic star of . Both have the same homotopy type...
Hadron spectrum, quark masses and decay constants from light overlap fermions on large lattices
Energy Technology Data Exchange (ETDEWEB)
Galletly, D.; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Guertler, M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Division, Dept. of Mathematical Sciences; Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC]|[Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Streuer, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC]|[Freie Univ. Berlin (Germany). Inst. fuer Theoretische Physik
2006-07-15
We present results from a simulation of quenched overlap fermions with Luescher-Weisz gauge field action on lattices up to 24{sup 3} 48 and for pion masses down to {approx}250 MeV. Among the quantities we study are the pion, rho and nucleon masses, the light and strange quark masses, and the pion decay constant. The renormalization of the scalar and axial vector currents is done nonperturbatively in the RI-MOM scheme. The simulations are performed at two different lattice spacings, a {approx}0.1 fm and {approx}0.15 fm, and on two different physical volumes, to test the scaling properties of our action and to study finite volume effects. We compare our results with the predictions of chiral perturbation theory and compute several of its low-energy constants. The pion mass is computed in sectors of fixed topology as well. (orig.)
Short-distance matrix elements for $D$-meson mixing for 2+1 lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Chang, Chia Cheng [Univ. of Illinois, Champaign, IL (United States)
2015-01-01
We study the short-distance hadronic matrix elements for D-meson mixing with partially quenched N_{f} = 2+1 lattice QCD. We use a large set of the MIMD Lattice Computation Collaboration's gauge configurations with a^{2} tadpole-improved staggered sea quarks and tadpole-improved Lüscher-Weisz gluons. We use the a^{2} tadpole-improved action for valence light quarks and the Sheikoleslami-Wohlert action with the Fermilab interpretation for the valence charm quark. Our calculation covers the complete set of five operators needed to constrain new physics models for D-meson mixing. We match our matrix elements to the MS-NDR scheme evaluated at 3 GeV. We report values for the Beneke-Buchalla-Greub-Lenz-Nierste choice of evanescent operators.
Gauge fixing and BRST formalism in non-Abelian gauge theories
Ghiotti, Marco; Williams, A G
2007-01-01
In this Thesis we present a comprehensive study of perturbative and non-perturbative non-Abelian gauge theories in the light of gauge-fixing procedures, focusing our attention on the BRST formalism in Yang-Mills theory. We propose first a model to re-write the Faddeev-Popov quantisation method in terms of group-theoretical techniques and then we give a possible way to solve the no-go theorem of Neuberger for lattice Yang-Mills theory with double BRST symmetry. In the final part we present a study of the Batalin-Vilkovisky quantisation method for non-linear gauges in non-Abelian gauge theories.
Baryon spectroscopy in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Derek B. Leinweber; Wolodymyr Melnitchouk; David Richards; Anthony G. Williams; James Zanotti
2004-04-01
We review recent developments in the study of excited baryon spectroscopy in lattice QCD. After introducing the basic methods used to extract masses from correlation functions, we discuss various interpolating fields and lattice actions commonly used in the literature. We present a survey of results of recent calculations of excited baryons in quenched QCD, and outline possible future directions in the study of baryon spectra.
Lattice QCD for nuclear physics
Meyer, Harvey
2015-01-01
With ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter. Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun, and many new observables will be calculated at the new computational facilities. The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems, and in particular to nuclear physics. A wide variety of topics are covered, including continuum field theory, lattice discretizations, hadron spect...
Mangiarotti, L
1998-01-01
This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed;
A gauge invariant Debye mass for the complex heavy-quark potential
Burnier, Yannis
2016-01-01
The concept of a screening mass is a powerful tool to simplify the intricate physics of in-medium test charges surrounded by light charge carriers. While it has been successfully used to describe electromagnetic properties, its definition and computation in QCD is plagued by questions of gauge invariance and the presence of non-perturbative contributions from the magnetic sector. Here we present a recent alternative definition of a gauge invariant Debye mass parameter following closely the original idea of Debye and Hueckel. Our test charges are a static heavy quark-antiquark pair whose complex potential and its in-medium modification can be extracted using lattice QCD. By combining in a generalized Gauss-Law the non-perturbative aspects of quark binding with a perturbative ansatz for the medium effects, we succeed to describe the lattice values of the potential with a single temperature dependent parameter, in turn identified with a Debye mass. We find that its behavior, as evaluated in a recent quenched lat...
Energy Technology Data Exchange (ETDEWEB)
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
Interquark potential with finite quark mass from lattice QCD.
Kawanai, Taichi; Sasaki, Shoichi
2011-08-26
We present an investigation of the interquark potential determined from the q ̄q Bethe-Salpeter (BS) amplitude for heavy quarkonia in lattice QCD. The q ̄q potential at finite quark mass m(q) can be calculated from the equal-time and Coulomb gauge BS amplitude through the effective Schrödinger equation. The definition of the potential itself requires information about a kinetic mass of the quark. We then propose a self-consistent determination of the quark kinetic mass on the same footing. To verify the proposed method, we perform quenched lattice QCD simulations with a relativistic heavy-quark action at a lattice cutoff of 1/a≈2.1 GeV in a range 1.0≤m(q)≤3.6 GeV. Our numerical results show that the q ̄q potential in the m(q)→∞ limit is fairly consistent with the conventional one obtained from Wilson loops. The quark-mass dependence of the q ̄q potential and the spin-spin potential are also examined. © 2011 American Physical Society
Kugo-Ojima confinement and QCD Green's functions in covariant gauges
Alkofer, R; Von Smekal, L; Alkofer, Reinhard; Fischer, Christian S.; Smekal, Lorenz von
2003-01-01
In Landau gauge QCD the Kugo-Ojima confinement criterion and its relation to the infrared behaviour of the gluon and ghost propagators are reviewed. It is demonstrated that the realization of this confinement criterion (which is closely related to the Gribov-Zwanziger horizon condition) results from quite general properties of the ghost Dyson-Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson--Schwinger equations provide an explicit example for the anticipated infrared behaviour. The results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, $\\alpha(0) = 8.915/N_c$. Solutions for the coupled system of Dyson--Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry takes place. In the quenched approximation the quark propag...
Ohno, T; Ichinose, I; Matsui, T; Ohno, Takuya; Arakawa, Gaku; Ichinose, Ikuo; Matsui, Tetsuo
2004-01-01
We study the phase structure of the random-plaquette Z_2 lattice gauge model in three dimensions. In this model, the "gauge coupling" for each plaquette is a quenched random variable that takes the value \\beta with the probability 1-p and -\\beta with the probability p. This model is relevant for the recently proposed quantum memory of toric code. The parameter p is the concentration of the plaquettes with "wrong-sign" couplings -\\beta, and interpreted as the error probability per qubit in quantum code. In the gauge system with p=0, i.e., with the uniform gauge couplings \\beta, it is known that there exists a second-order phase transition at a certain critical "temperature", T(\\equiv \\beta^{-1}) = T_c =1.31, which separates an ordered(Higgs) phase at TT_c. As p increases, the critical temperature T_c(p) decreases. In the p-T plane, the curve T_c(p) intersects with the Nishimori line T_{N}(p) at the certain point (p_c, T_{N}(p_c)). The value p_c is just the accuracy threshold for a fault-tolerant quantum memory...
Heavy quarkonium potential from Bethe-Salpeter wave function on the lattice
Kawanai, Taichi
2013-01-01
We propose a novel method for the determination of the interquark potential together with quark "kinetic mass'' $m_Q$ from the equal-time $Q\\bar{Q}$ Bethe-Salpeter (BS) amplitude in lattice QCD. Our approach allows us to calculate spin-dependent $Q\\bar{Q}$ potentials, e.g. the spin-spin potential, as well. In order to investigate several systematic uncertainties on such $Q\\bar{Q}$ potentials, we carry out lattice QCD simulations using quenched gauge configurations generated with the single plaquette gauge action with three different lattice spacings, $a \\approx$ 0.093, 0.068 and 0.047 fm, and two different physical volumes, $L \\approx$ 2.2 and 3.0 fm. For heavy quarks, we employ the relativistic heavy quark (RHQ) action which can control large discretization errors introduced by large quark mass $m_Q$. The spin-independent central $Q\\bar{Q}$ potential for the charmonium system yields the "Coulomb plus linear'' behavior with good scaling and small volume dependence. We explore the quark mass dependence over th...
International Lattice Data Grid
Davies, C T H; Kenway, R D; Maynard, C M
2002-01-01
We propose the co-ordination of lattice QCD grid developments in different countries to allow transparent exchange of gauge configurations in future, should participants wish to do so. We describe briefly UKQCD's XML schema for labelling and cataloguing the data. A meeting to further develop these ideas will be held in Edinburgh on 19/20 December 2002, and will be available over AccessGrid.
Testing gauge-invariant perturbation theory
Törek, Pascal
2016-01-01
Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In ...
Electrically tunable artificial gauge potential for polaritons
Lim, Hyang-Tag; Togan, Emre; Kroner, Martin; Miguel-Sanchez, Javier; Imamoğlu, Atac
2017-01-01
Neutral particles subject to artificial gauge potentials can behave as charged particles in magnetic fields. This fascinating premise has led to demonstrations of one-way waveguides, topologically protected edge states and Landau levels for photons. In ultracold neutral atoms, effective gauge fields have allowed the emulation of matter under strong magnetic fields leading to realization of Harper-Hofstadter and Haldane models. Here we show that application of perpendicular electric and magnetic fields effects a tunable artificial gauge potential for two-dimensional microcavity exciton polaritons. For verification, we perform interferometric measurements of the associated phase accumulated during coherent polariton transport. Since the gauge potential originates from the magnetoelectric Stark effect, it can be realized for photons strongly coupled to excitations in any polarizable medium. Together with strong polariton–polariton interactions and engineered polariton lattices, artificial gauge fields could play a key role in investigation of non-equilibrium dynamics of strongly correlated photons. PMID:28230047
Gauge fermions with flat bands and anomalous transport via chiral modes from breaking gauge symmetry
Luo, Xi
2016-01-01
The dispersionless longitudinal photon in Maxwell theory is thought of as a redundant degree of freedom due to the gauge symmetry. We find that when there exist exactly flat bands with zero energy in a condensed matter system, the fermion field may locally transform as a gauge field and the system possesses a gauge symmetry. As the longitudinal photon, the redundant degrees of freedom from the flat bands must be gauged away from the physical states. As an example, we study spinless fermions on a generalized Lieb lattice in three dimensions. The flat band of the longitudinal fermion induces a gauge symmetry. An external magnetic field breaks this gauge symmetry and emerges a bunch of non-topologically chiral modes. Combining these emergent chiral modes with the chiral anomaly mode which is of an opposite chirality, rich anomalous electric transport phenomena exhibit and are expected to be observed in Pd$_3$Bi$_2$S$_2$ and Ag$_3$Se$_2$Au.
Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.
Andreev, Oleg
2009-05-29
We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range.
Signatures of confinement in Landau gauge QCD
Pawlowski, J M; Nedelko, S; Von Schmekal, L
2005-01-01
We summarise an analysis of the infrared regime of Landau gauge QCD by means of a flow equation approach. The infrared behaviour of gluon and ghost propagators is evaluated. The results provide further evidence for the Kugo-Ojima confinement scenario. We also discuss their relation to results obtained with other functional methods as well as the lattice.
Thermal mass and dispersion relations of quarks in the deconfined phase of quenched QCD
Kaczmarek, Olaf; Kitazawa, Masakiyo; Soeldner, Wolfgang
2012-01-01
Temporal quark correlation functions are analyzed in quenched lattice QCD for two values of temperature above the critical temperature (Tc) for deconfinement, T=1.5Tc and 3Tc. A two-pole ansatz for the quark spectral function is used to determine the bare quark mass and the momentum dependence of excitation spectra on large lattices of size up to 128^3x16. The dependence of the quark correlator on these parameters as well as the finite volume dependence of the excitation energies are analyzed in detail in order to examine the reliability of our analysis. Our results suggest the existence of quasi-particle peaks in the quark spectrum. We furthermore find evidence that the dispersion relation of the plasmino mode has a minimum at non-zero momentum even in the non-perturbative region near Tc. We also elaborate on the enhancement of the quark correlator near the chiral limit which is observed at T=1.5Tc on about half of the gauge configurations. We attribute this to the presence of near zero-modes of the fermion ...
Resummation of Cactus Diagrams in Lattice QCD
Panagopoulos, H
1998-01-01
We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, this expansion yields results remarkably close to corresponding nonperturbative estimates.
Application of Noncommutative Differential Geometry on Lattice to Anomaly
Fujiwara, T; Wu, K; Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
1999-01-01
The chiral anomaly in lattice abelian gauge theory is investigated by applying the geometric and topological method in noncommutative differential geometry(NCDG). A new kind of double complex and descent equation are proposed on infinite hypercubic lattice in arbitrary even dimensional Euclidean space, in the framework of NCDG. Using the general solutions to proposed descent equation, we derive the chiral anomaly in Abelian lattice gauge theory. The topological origin of anomaly is nothing but the Chern classes in NCDG.
Quenching parameter in a holographic thermal QCD
Patra, Binoy Krishna
2016-01-01
We have calculated the quenching parameter, $\\hat{q}$ in a model-independent way using the gauge-gravity duality. In earlier calculations, the geometry in the gravity side at finite temperature was usually taken as the pure AdS blackhole metric for which the dual gauge theory becomes conformally invariant unlike QCD. Therefore we use a metric which incorporates the fundamental quarks by embedding the coincident D7 branes in the Klebanov-Tseytlin background and a finite temperature is switched on by inserting a black hole into the background, known as OKS-BH metric. Further inclusion of an additional UV cap to the metric prepares the dual gauge theory to run similar to thermal QCD. Moreover $\\hat{q}$ is usually defined in the literature from the Glauber-model perturbative QCD evaluation of the Wilson loop, which has no reasons to hold if the coupling is large and is thus against the main idea of gauge-gravity duality. Thus we use an appropriate definition of $\\hat{q}$: $\\hat{q} L^- = 1/L^2$, where $L$ is the s...
QCD Thermodynamics with an Improved Lattice Action
Bernard, C W; DeGrand, T A; Wingate, M; DeTar, C E; Gottlieb, S; Heller, U M; Rummukainen, K; Toussaint, D; Sugar, R L; Bernard, Claude; Hetrick, James E.; Grand, Thomas De; Wingate, Matthew; Tar, Carleton De; Gottlieb, Steven; Heller, Urs M.; Rummukainen, Kari; Toussaint, Doug; Sugar, Robert L.
1997-01-01
We have investigated QCD with two flavors of degenerate fermions using a Symanzik-improved lattice action for both the gauge and fermion actions. Our study focuses on the deconfinement transition on an $N_t=4$ lattice. Having located the thermal transition, we performed zero temperature simulations nearby in order to compute hadronic masses and the static quark potential. We find that the present action reduces lattice artifacts present in thermodynamics with the standard Wilson (gauge and fermion) actions. However, it does not bring studies with Wilson-type quarks to the same level as those using the Kogut--Susskind formulation.
An exploratory study of heavy domain wall fermions on the lattice
Energy Technology Data Exchange (ETDEWEB)
Boyle, P. [School of Physics and Astronomy, University of Edinburgh,Edinburgh, EH9 3JZ (United Kingdom); Jüttner, A. [School of Physics and Astronomy, University of Southampton,Southampton, SO17 1BJ (United Kingdom); Marinković, M. Krstić [School of Physics and Astronomy, University of Southampton,Southampton, SO17 1BJ (United Kingdom); Theoretical Physics Department, CERN,Geneva (Switzerland); Sanfilippo, F.; Spraggs, M.; Tsang, J.T. [School of Physics and Astronomy, University of Southampton,Southampton, SO17 1BJ (United Kingdom); Collaboration: The RBC/UKQCD collaboration
2016-04-06
We report on an exploratory study of domain wall fermions (DWF) as a lattice regularisation for heavy quarks. Within the framework of quenched QCD with the tree-level improved Symanzik gauge action we identify the DWF parameters which minimise discretisation effects. We find the corresponding effective 4d overlap operator to be exponentially local, independent of the quark mass. We determine a maximum bare heavy quark mass of am{sub h}≈0.4, below which the approximate chiral symmetry and O(a)-improvement of DWF are sustained. This threshold appears to be largely independent of the lattice spacing. Based on these findings, we carried out a detailed scaling study for the heavy-strange meson dispersion relation and decay constant on four ensembles with lattice spacings in the range 2.0–5.7 GeV. We observe very mild a{sup 2} scaling towards the continuum limit. Our findings establish a sound basis for heavy DWF in dynamical simulations of lattice QCD with relevance to Standard Model phenomenology.
An exploratory study of heavy domain wall fermions on the lattice
Boyle, Peter; Marinkovic, Marina Krstic; Sanfilippo, Francesco; Spraggs, Matthew; Tsang, Justus Tobias
2016-01-01
We report on an exploratory study of domain wall fermions (DWF) as a lattice regularisation for heavy quarks. Within the framework of quenched QCD with the tree-level improved Symanzik gauge action we identify the DWF parameters which minimise discretisation effects. We find the corresponding effective 4$d$ overlap operator to be exponentially local, independent of the quark mass. We determine a maximum bare heavy quark mass of $am_h\\approx 0.4$, below which the approximate chiral symmetry and O(a)-improvement of DWF are sustained. This threshold appears to be largely independent of the lattice spacing. Based on these findings, we carried out a detailed scaling study for the heavy-strange meson dispersion relation and decay constant on four ensembles with lattice spacings in the range $2.0-5.7\\,\\mathrm{GeV}$. We observe very mild $a^2$ scaling towards the continuum limit. Our findings establish a sound basis for heavy DWF in dynamical simulations of lattice QCD with relevance to Standard Model phenomenology.
Lattice quantum chromodynamics practical essentials
Knechtli, Francesco; Peardon, Michael
2017-01-01
This book provides an overview of the techniques central to lattice quantum chromodynamics, including modern developments. The book has four chapters. The first chapter explains the formulation of quarks and gluons on a Euclidean lattice. The second chapter introduces Monte Carlo methods and details the numerical algorithms to simulate lattice gauge fields. Chapter three explains the mathematical and numerical techniques needed to study quark fields and the computation of quark propagators. The fourth chapter is devoted to the physical observables constructed from lattice fields and explains how to measure them in simulations. The book is aimed at enabling graduate students who are new to the field to carry out explicitly the first steps and prepare them for research in lattice QCD.
Eight light flavors on large lattice volumes
Schaich, David
2013-01-01
I present first results from large-scale lattice investigations of SU(3) gauge theory with eight light flavors in the fundamental representation. Using leadership computing resources at Argonne, we are generating gauge configurations with lattice volumes up to $64^3\\times128$ at relatively strong coupling, in an attempt to access the chiral regime. We use nHYP-improved staggered fermions, carefully monitoring finite-volume effects and other systematics. Here I focus on analyses of the light hadron spectrum and chiral condensate, measured on lattice volumes up to $48^3\\times96$ with fermion masses as light as m=0.004 in lattice units. We find no clear indication of spontaneous chiral symmetry breaking in these observables. I discuss the implications of these initial results, and prospects for further physics projects employing these ensembles of gauge configurations.
Noaki, J I; Aoki, Y; Burkhalter, R; Ejiri, S; Fukugita, M; Hashimoto, S; Ishizuka, N; Iwasaki, Y; Izubuchi, T; Kanaya, K; Kaneko, T; Kuramashi, Y; Lesk, V I; Nagai, K I; Okawa, M; Taniguchi, Y; Ukawa, A; Yoshié, T
2001-01-01
We explore application of the domain wall fermion formalism of lattice QCD to calculate the $K\\to\\pi\\pi$ decay amplitudes in terms of the $K\\to\\pi$ and $K\\to 0$ hadronic matrix elements through relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD using domain-wall fermion action for quarks and an RG-improved gauge action for gluons on a $16^3\\times 32\\times 16$ and $24^3\\times 32\\times 16$ lattice at $\\beta=2.6$ corresponding to the lattice spacing $1/a\\approx 2$GeV. Quark loop contractions which appear in Penguin diagrams are calculated by the random noise method, and the $\\Delta I=1/2$ matrix elements which require subtractions with the quark loop contractions are obtained with a statistical accuracy of about 10%. We confirm the chiral properties required of the $K\\to\\pi$ matrix elements. Matching the lattice matrix elements to those in the continuum at $\\mu=1/a$ using the perturbative renormalization factor to one loop order, and running to the scale $\\mu=m...
Gauge Theories on the Light-Front
Brodsky, S J
2004-01-01
The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitary, and a trivial vacuum. The light-front Hamiltonian form of QCD provides an alternative to lattice gauge theory for the computation of nonperturbative quantities such as the hadronic spectrum and the corresponding eigenfunctions. In the case of the electroweak theory, spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field. Light-front quantization then leads to an elegant ghost-free theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions, as well as the Goldstone boson equivalence theorem.
Gauge invariance and Weyl-polymer quantization
Strocchi, Franco
2016-01-01
The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases -- typically in the presence of a gauge symmetry -- non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra. In general, a gauge invariant ground state defines a non-regular representation of the gauge dependent Weyl operators, providing a mathematically consistent treatment of familiar quantum systems -- such as the electron in a periodic potential (Bloch electron), the Quantum Hall electron, or the quantum particle on a circle -- where the gauge transformations are, respectively, the lattice translations, the magne...
Basketter, D
2000-11-01
Fragrance chemicals are a frequently reported cause of allergic contact dermatitis (ACD), a matter which has recently come into considerable prominence, to the point that legislation in Europe is under serious consideration. Certain skin-sensitizing fragrance chemicals have been reported by the producing industry to be rendered safe (quenched), at least in terms of ACD, when they are used in the presence of a specific quenching agent. Accordingly, it seemed timely to review this apparent quenching phenomenon, considering the available data and potential mechanistic hypotheses that might be used to explain it. If it is correct, it should be a phenomenon of potentially enormous value in the elimination of the allergenic properties of at least a proportion of common skin sensitizers. Whilst there is some evidence in man for the occurrence of quenching during the induction of skin sensitization, a much more substantial body of work has failed to find supportive evidence in various animals models, at a chemical level or at elicitation in human subjects with existing allergy. On balance, it is concluded that quenching of fragrance allergens is a phenomenon still awaiting positive evidence of existence.
Phase structure of lattice N=4 super Yang-Mills
DEFF Research Database (Denmark)
Catterall, Simon; Damgaard, Poul H.; DeGrand, Thomas;
2012-01-01
We make a first study of the phase diagram of four-dimensional N = 4 super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results are consi...
5D Maximally Supersymmetric Yang-Mills on the Lattice
Joseph, Anosh
2016-01-01
We provide details of the lattice construction of five-dimensional maximally supersymmetric Yang-Mills theory. The lattice theory is supersymmetric, gauge invariant and free from spectrum doublers. Such a supersymmetric lattice formulation is interesting as it can be used for non-perturbative explorations of the five-dimensional theory, which has a known gravitational dual.
Quench dynamics of the anisotropic Heisenberg model.
Liu, Wenshuo; Andrei, Natan
2014-06-27
We develop an analytical approach for the study of the quench dynamics of the anisotropic Heisenberg model (XXZ model) on the infinite line. We present the exact time-dependent wave functions after a quench in an integral form for any initial state and for any anisotropy Δ by means of a generalized Yudson contour representation. We calculate the evolution of several observables from two particular initial states: starting from a local Néel state we calculate the time evolution of the antiferromagnetic order parameter-staggered magnetization; starting from a state with consecutive flipped spins (1) we calculate the evolution of the local magnetization and express it in terms of the propagation of magnons and bound state excitations, and (2) we predict the evolution of the induced spin currents. These predictions can be confronted with experiments in ultracold gases in optical lattices. We also show how the "string" solutions of Bethe ansatz equations emerge naturally from the contour approach.
Appelquist, Thomas; Brower, Richard C; Buchoff, Michael I; Fleming, George T; Kiskis, Joe; Kribs, Graham D; Lin, Meifeng; Neil, Ethan T; Osborn, James C; Rebbi, Claudio; Rinaldi, Enrico; Schaich, David; Schroeder, Chris; Syritsyn, Sergey; Voronov, Gennady; Vranas, Pavlos; Weinberg, Evan; Witzel, Oliver
2014-01-01
We present the spectrum of baryons in a new SU(4) gauge theory with fundamental fermion constituents. The spectrum of these bosonic baryons is of significant interest for composite dark matter theories. Here, we compare the spectrum and properties of SU(3) and SU(4) baryons, and then compute the dark-matter direct detection cross section via Higgs boson exchange for TeV-scale composite dark matter arising from a confining SU(4) gauge sector. Comparison with the latest LUX results leads to tight bounds on the fraction of the constituent-fermion mass that may arise from electroweak symmetry breaking. Lattice calculations of the dark matter mass spectrum and the Higgs-dark matter coupling are performed on quenched $16^{3} \\times 32$, $32^{3} \\times 64$, $48^{3} \\times 96$, and $64^{3} \\times128$ lattices with three different lattice spacings, using Wilson fermions with moderate to heavy pseudoscalar meson masses. Our results lay a foundation for future analytic and numerical study of composite baryonic dark matt...
Inhomogeneous Thermal Quenches
Sohrabi, Kiyoumars A
2015-01-01
We describe holographic thermal quenches that are inhomogeneous in space. The main characteristic of the quench is to take the system far from its equilibrium configuration. Except special extreme cases, the problem has no analytic solution. Using the numerical holography methods, we study different observables that measure thermalization such as the time evolution of the horizon, two-point Wightman function and entanglement entropy (EE). Having an extra nontrivial spacial direction, allows us to study this peculiar generalization since we categorize the problem based on whether we do the measurements along this special direction or perpendicular to it. Exciting new features appear that are absent in the common computations in the literature, the appearance of negative EE valleys surrounding the positive EE hills and abrupt quenches that occupy the whole space at their universal limit are some of the results of this paper. We have tried to provide physical explanations wherever possible. The physical picture ...
Caux, Jean-Sébastien
2016-06-01
We give a pedagogical introduction to the methodology of the Quench Action, which is an effective representation for the calculation of time-dependent expectation values of physical operators following a generic out-of-equilibrium state preparation protocol (for example a quantum quench). The representation, originally introduced in Caux and Essler (2013 Phys. Rev. Lett. 110 257203), is founded on a mixture of exact data for overlaps together with variational reasonings. It is argued to be quite generally valid and thermodynamically exact for arbitrary times after the quench (from short times all the way up to the steady state), and applicable to a wide class of physically relevant observables. Here, we introduce the method and its language, give an overview of some recent results, suggest a roadmap and offer some perspectives on possible future research directions.
Quantum quenches during inflation
Carrilho, Pedro
2016-01-01
We propose a new technique to study fast transitions during inflation, by studying the dynamics of quantum quenches in an $O(N)$ scalar field theory in de Sitter spacetime. We compute the time evolution of the system using a non-perturbative large-$N$ limit approach. We derive the self-consistent mass equation for several physically relevant transitions of the parameters of the theory, in a slow motion approximation. Our computations reveal that the effective mass after the quench evolves in the direction of recovering its value before the quench, but stopping at a different asymptotic value, in which the mass is strictly positive. Furthermore, we tentatively find situations in which the effective mass can be temporarily negative, thus breaking the $O(N)$ symmetry of the system for a certain time, only to then come back to a positive value, restoring the symmetry. We argue the relevance of our new method in a cosmological scenario.
Gauge theory and little gauge theory
Koizumi, Kozo
2016-01-01
The gauge theory is the most important type of the field theory, in which the interactions of the elementary particles are described by the exchange of the gauge bosons.In this article, the gauge theory is reexamined as geometry of the vector space, and a new concept of "little gauge theory" is introduced. A key peculiarity of the little gauge theory is that the theory is able to give a restriction for form of the connection field. Based on the little gauge theory, Cartan geometry, a charged boson and the Dirac fermion field theory are investigated. In particular, the Dirac fermion field theory leads to an extension of Sogami's covariant derivative. And it is interpreted that Higgs bosons are included in new fields introduced in this article.
Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
2016-01-01
We study full QCD at finite density and low temperature with light quark mass using the complex Langevin method. Since the singular drift problem turns out to be mild on a $4^3 \\times 8$ lattice we use, the gauge cooling is performed only to control the unitarity norm in this exploratory study. We report on our preliminary data obtained from the complex Langevin simulation up to certain Langevin time. While the data are still noisy due to lack of statistics, the onset of the baryon number density seems to occur at larger $\\mu$ than half the pion mass, which is the value for the phase quenched QCD. The validity of our simulation is tested by the recently proposed criterion based on the probability distribution of the drift term.
Lattice QCD Calculation of Nucleon Structure
Energy Technology Data Exchange (ETDEWEB)
Liu, Keh-Fei [University of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy; Draper, Terrence [University of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy
2016-08-30
It is emphasized in the 2015 NSAC Long Range Plan that "understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of strong-interaction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out first-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large-scale computer simulation. We started out by calculating the nucleon form factors -- electromagnetic, axial-vector, πNN, and scalar form factors, the quark spin contribution to the proton spin, the strangeness magnetic moment, the quark orbital angular momentum, the quark momentum fraction, and the quark and glue decomposition of the proton momentum and angular momentum. The first round of calculations were done with Wilson fermions in the `quenched' approximation where the dynamical effects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge configurations. Beginning in 2000, we have started implementing the overlap fermion formulation into the spectroscopy and structure calculations. This is mainly because the overlap fermion honors chiral symmetry as in the continuum. It is going to be more and more important to take the symmetry into account as the simulations move closer to the physical point where the u and d quark masses are as light as a few MeV only. We began with lattices which have quark masses in the sea corresponding to a pion mass at ~ 300 MeV and obtained the strange form factors, charm and strange quark masses, the charmonium spectrum and the D_{s} meson decay constant f_{Ds}, the strangeness and charmness, the meson mass
Lattice QCD Calculation of Nucleon Structure
Energy Technology Data Exchange (ETDEWEB)
Liu, Keh-Fei; Draper, Terrence
2016-08-30
It is emphasized in the 2015 NSAC Long Range Plan [1] that \\understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of strong-interaction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out rst-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large scale computer simulation. We started out by calculating the nucleon form factors { electromagnetic [2], axial-vector [3], NN [4], and scalar [5] form factors, the quark spin contribution [6] to the proton spin, the strangeness magnetic moment [7], the quark orbital angular momentum [8], the quark momentum fraction [9], and the quark and glue decomposition of the proton momentum and angular momentum [10]. These rst round of calculations were done with Wilson fermions in the `quenched' approximation where the dynamical e ects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge con gurations. Beginning in 2000, we have started implementing the overlap fermion formulation into the spectroscopy and structure calculations [11, 12]. This is mainly because the overlap fermion honors chiral symmetry as in the continuum. It is going to be more and more important to take the symmetry into account as the simulations move closer to the physical point where the u and d quark masses are as light as a few MeV only. We began with lattices which have quark masses in the sea corresponding to a pion mass at 300 MeV and obtained the strange form factors [13], charm and strange quark masses, the charmonium spectrum and the Ds meson decay constant fDs [14], the strangeness and charmness [15], the
Chakrabarti, J; Bagchi, B; Chakrabarti, Jayprokas; Basu, Asis; Bagchi, Bijon
2000-01-01
Fermions on the lattice have bosonic excitations generated from the underlying periodic background. These, the lattice bosons, arise near the empty band or when the bands are nearly full. They do not depend on the nature of the interactions and exist for any fermion-fermion coupling. We discuss these lattice boson solutions for the Dirac Hamiltonian.
$B_{K}$ from quenched overlap QCD
Garron, N; Hölbling, C; Lellouch, L P; Rebbi, C
2003-01-01
We present an exploratory calculation of the standard model Delta S=2 matrix element relevant for indirect CP violation in K -> pi pi decays. The computation is performed with overlap fermions in the quenched approximation at beta=6.0 on a 16^3x32 lattice. The resulting bare matrix element is renormalized non-perturbatively. Our preliminary result is B_K^{NDR}(2 GeV)=0.61(7), where the error does not yet include an estimate of systematic uncertainties.
Exact partition functions for gauge theories on Rλ3
Directory of Open Access Journals (Sweden)
Jean-Christophe Wallet
2016-11-01
Full Text Available The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Exact partition functions for gauge theories on Rλ3
Wallet, Jean-Christophe
2016-11-01
The noncommutative space R,SUB>λ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of R&x03bb;3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
The three-quark potential and perfect Abelian dominance in SU(3) lattice QCD
Suganuma, Hideo
2015-01-01
We study the static three-quark (3Q) potential for more than 300 different patterns of 3Q systems with high statistics, i.e., 1000-2000 gauge configurations, in SU(3) lattice QCD at the quenched level. For all the distances, the 3Q potential is found to be well described by the Y-ansatz, i.e., one-gluon-exchange (OGE) Coulomb plus Y-type linear potential. Also, we investigate Abelian projection of quark confinement in the context of the dual superconductor picture proposed by Yoichiro~Nambu~{\\it et al.} in SU(3) lattice QCD. Remarkably, quark confinement forces in both Q$\\bar{\\rm Q}$ and 3Q systems can be described only with Abelian variables in the maximally Abelian gauge, i.e., $\\sigma_{\\rm Q \\bar Q} \\simeq \\sigma_{\\rm Q \\bar Q}^{\\rm Abel} \\simeq \\sigma_{\\rm 3Q} \\simeq \\sigma_{\\rm 3Q}^{\\rm Abel}$, which we call ``perfect Abelian dominance'' of quark confinement.
$B_K$ from quenched QCD with exact chiral symmetry
Garron, N; Hölbling, C; Lellouch, L P; Rebbi, C; Garron, Nicolas; Giusti, Leonardo; Hoelbling, Christian; Lellouch, Laurent; Rebbi, Claudio
2004-01-01
We present a calculation of the standard model Delta S=2 matrix element relevant to indirect CP violation in K->pipi decays which uses Neuberger's chiral formulation of lattice fermions. The computation is performed in the quenched approximation on a 16^3x32 lattice that has a lattice spacing asim 0.1 fm. The resulting bare matrix element is renormalized non-perturbatively. Our main result is B_K^{RGI}=0.87(8)^{+2+14}_{-1-14}, where the first error is statistical, the second is systematic and the third is an estimate of the uncertainty associated with the quenched approximation and with the fact that our kaons are composed of degenerate s and d quarks with masses sim m_s/2.
More on the properties of the first Gribov region in Landau gauge
Maas, Axel
2015-01-01
Complete gauge-fixing beyond perturbation theory in non-Abelian gauge theories is a non-trivial problem. This is particularly evident in covariant gauges, where the Gribov-Singer ambiguity gives an explicit formulation of the problem. In practice, this is a problem if gauge-dependent quantities between different methods, especially lattice and continuum methods, should be compared: Only when treating the Gribov-Singer ambiguity in the same way is the comparison meaningful. To provide a better basis for such a comparison the structure of the first Gribov region in Landau gauge, a subset of all possible gauge copies satisfying the perturbative Landau gauge condition, will be investigated. To this end, lattice gauge theory will be used to investigate a two-dimensional projection of the region for SU(2) Yang-Mills theory in two, three, and four dimensions for a wide range of volumes and discretizations.
More on the properties of the first Gribov region in Landau gauge
Maas, Axel
2016-03-01
Complete gauge fixing beyond perturbation theory in non-Abelian gauge theories is a nontrivial problem. This is particularly evident in covariant gauges, where the Gribov-Singer ambiguity gives an explicit formulation of the problem. In practice, this is a problem if gauge-dependent quantities between different methods, especially lattice and continuum methods, should be compared: Only when treating the Gribov-Singer ambiguity in the same way is the comparison meaningful. To provide a better basis for such a comparison the structure of the first Gribov region in Landau gauge, a subset of all possible gauge copies satisfying the perturbative Landau gauge condition, will be investigated. To this end, lattice gauge theory will be used to investigate a two-dimensional projection of the region for SU(2) Yang-Mills theory in two, three, and four dimensions for a wide range of volumes and discretizations.
A lattice approach to spinorial quantum gravity
Renteln, Paul; Smolin, Lee
1989-01-01
A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.
Elimination of spurious lattice fermion solutions and noncompact lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Lee, T.D.
1997-09-22
It is well known that the Dirac equation on a discrete hyper-cubic lattice in D dimension has 2{sup D} degenerate solutions. The usual method of removing these spurious solutions encounters difficulties with chiral symmetry when the lattice spacing l {ne} 0, as exemplified by the persistent problem of the pion mass. On the other hand, we recall that in any crystal in nature, all the electrons do move in a lattice and satisfy the Dirac equation; yet there is not a single physical result that has ever been entangled with a spurious fermion solution. Therefore it should not be difficult to eliminate these unphysical elements. On a discrete lattice, particle hop from point to point, whereas in a real crystal the lattice structure in embedded in a continuum and electrons move continuously from lattice cell to lattice cell. In a discrete system, the lattice functions are defined only on individual points (or links as in the case of gauge fields). However, in a crystal the electron state vector is represented by the Bloch wave functions which are continuous functions in {rvec {gamma}}, and herein lies one of the essential differences.
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another
Classical Loop Actions of Gauge Theories
Armand-Ugon, D; Griego, J R; Setaro, L; Armand-Ugon, Daniel; Gambini, Rodolfo; Griego, Jorge; Setaro, Leonardo
1994-01-01
Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply it in the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing to do Montecarlo calculations in a gauge invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ``confining phase''.
Screening Masses of Hot SU(2) Gauge Theory from the 3D Adjoint Higgs Model
Karsch, Frithjof; Petreczky, P
1999-01-01
We study the Landau gauge propagators of the lattice SU(2) 3d adjoint Higgs model, considered as an effective theory of high temperature 4d SU(2) gauge theory. From the long distance behaviour of the propagators we extract the screening masses. It is shown that the pole masses extracted from the propagators agree well with the screening masses obtained recently in finite temperature SU(2) theory. The relation of the propagator masses to the masses extracted from gauge invariant correlators is also discussed. In so-called lambda gauges non-perturbative evidence is given for the gauge independence of pole masses within this class of gauges.
A Lattice Study of the Glueball Spectrum
Institute of Scientific and Technical Information of China (English)
LIU Chuan
2001-01-01
The glueball spectrum is studied using an improved gluonic action on asymmetric lattices in the pure SU(3) lattice gauge theory. The smallest spatial lattice spacing is about 0.08 fm which makes the extrapolation to the ontinuum limit more reliable. Converting our lattice results to physical units using the scale set by the static quark potential, we obtain the following results for the glueball masses: MG(0++) -＝ 1730(90) MeV for the scalarglueball and MG(2++) ＝ 2400(95) MeV for the tensor glueball.
Quench studies of ILC cavities
Energy Technology Data Exchange (ETDEWEB)
Eremeev, Grigory; Geng, Rongli; Palczewski, Ari; Dai, Jin
2011-07-01
Quench limits accelerating gradient in SRF cavities to a gradient lower than theoretically expected for superconducting niobium. Identification of the quenching site with thermometry and OST, optical inspection, and replica of the culprit is an ongoing effort at Jefferson Lab aimed at better understanding of this limiting phenomenon. In this contribution we present our finding with several SRF cavities that were limited by quench.
de Wild Propitius, M.D.F.; Bais, F.A.
1999-01-01
In these lectures, we present a self-contained treatment of planar gauge theories broken down to some finite residual gauge group $H$ via the Higgs mechanism. The main focus is on the discrete $H$ gauge theory describing the long distance physics of such a model. The spectrum features global $H$ cha
Validation of a novel fiber optic strain gauge in a cryogenic and high magnetic field environment
Baxter, Scott; Lakrimi, M.'hamed; Thomas, Adrian M.; Gao, Yunxin; Blakes, Hugh; Gibbens, Paul; Looi, Mengche
2010-10-01
We report on the first operation of an easy to use low cost novel fiber optic strain gauge (FOSG) in cryogenic and magnetic field environments. The FOSGs were mounted on a superconducting coil and resin impregnated. The gauges detected resin shrinkage upon curing. On cooldown, the FOSG monitored the thermal contraction strains of the coil and the electromagnetic strain during energization. The coil was deliberately quenched, in excess of 175 times, and again the FOSG detected the quenches and measured the thermal expansion-induced strains and subsequent re-cooling of the coil after a quench. Agreement with FEA predictions was very good.
Quenched effective population size
Sagitov, Serik; Vatutin, Vladimir
2010-01-01
We study the genealogy of a geographically - or otherwise - structured version of the Wright-Fisher population model with fast migration. The new feature is that migration probabilities may change in a random fashion. Applying Takahashi's results on Markov chains with random transition matrices, we establish convergence to the Kingman coalescent, as the population size goes to infinity. This brings a novel formula for the coalescent effective population size (EPS). We call it a quenched EPS to emphasize the key feature of our model - random environment. The quenched EPS is compared with an annealed (mean-field) EPS which describes the case of constant migration probabilities obtained by averaging the random migration probabilities over possible environments.
Salgado, C A; Salgado, Carlos A.; Wiedemann, Urs Achim
2003-01-01
We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation (Baier-Dokshitzer-Mueller-Peign\\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and in the single hard scattering approximation (N=1 opacity approximation). By comparison, we establish a simple relation between transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus colli...
Phenomenology of Holographic Quenches
da Silva, Emilia; Lopez, Esperanza; Mas, Javier; Serantes, Alexandre
2015-10-01
We study holographic models related to global quantum quenches in finite size systems. The holographic set up describes naturally a CFT, which we consider on a circle and a sphere. The enhanced symmetry of the conformal group on the circle motivates us to compare the evolution in both cases. Depending on the initial conditions, the dual geometry exhibits oscillations that we holographically interpret as revivals of the initial field theory state. On the sphere, this only happens when the energy density created by the quench is small compared to the system size. However on the circle considerably larger energy densities are compatible with revivals. Two different timescales emerge in this latter case. A collapse time, when the system appears to have dephased, and the revival time, when after rephasing the initial state is partially recovered. The ratio of these two times depends upon the initial conditions in a similar way to what is observed in some experimental setups exhibiting collapse and revivals.
Lattice quantum chromodynamics with approximately chiral fermions
Energy Technology Data Exchange (ETDEWEB)
Hierl, Dieter
2008-05-15
In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)
Extra-dimensional models on the lattice
Knechtli, Francesco
2016-01-01
In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergencies by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include non-perturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime for various extra-dimensional models.
Chiral Fermions on the Lattice
Bietenholz, Wolfgang
2010-01-01
In the last century the non-perturbative regularization of chiral fermions was a long-standing problem. We review how this problem was finally overcome by the formulation of a modified but exact form of chiral symmetry on the lattice. This also provides a sound definition of the topological charge of lattice gauge configurations. We illustrate a variety of applications to QCD in the p-, the epsilon- and the delta-regime, where simulation results can now be related to Random Matrix Theory and Chiral Perturbation Theory. The latter contains Low Energy Constants as free parameters, and we comment on their evaluation from first principles of QCD.
DEFF Research Database (Denmark)
2016-01-01
The invention relates to a strain gauge of a carrier layer and a meandering measurement grid positioned on the carrier layer, wherein the strain gauge comprises two reinforcement members positioned on the carrier layer at opposite ends of the measurement grid in the axial direction....... The reinforcement members are each placed within a certain axial distance to the measurement grid with the axial distance being equal to or smaller than a factor times the grid spacing. The invention further relates to a multi-axial strain gauge such as a bi-axial strain gauge or a strain gauge rosette where each...... of the strain gauges comprises reinforcement members. The invention further relates to a method for manufacturing a strain gauge as mentioned above....
Quantum Gauge General Relativity
Institute of Scientific and Technical Information of China (English)
WU Ning
2004-01-01
Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein's field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.
Quenching parameter in a holographic thermal QCD
Patra, Binoy Krishna; Arya, Bhaskar
2017-01-01
We have calculated the quenching parameter, q ˆ in a model-independent way using the gauge-gravity duality. In earlier calculations, the geometry in the gravity side at finite temperature was usually taken as the pure AdS black hole metric for which the dual gauge theory becomes conformally invariant unlike QCD. Therefore we use a metric which incorporates the fundamental quarks by embedding the coincident D7 branes in the Klebanov-Tseytlin background and a finite temperature is switched on by inserting a black hole into the background, known as OKS-BH metric. Further inclusion of an additional UV cap to the metric prepares the dual gauge theory to run similar to thermal QCD. Moreover q ˆ is usually defined in the literature from the Glauber model perturbative QCD evaluation of the Wilson loop, which has no reasons to hold if the coupling is large and is thus against the main idea of gauge-gravity duality. Thus we use an appropriate definition of q ˆ : q ˆ L- = 1 /L2, where L is the separation for which the Wilson loop is equal to some specific value. The above two refinements cause q ˆ to vary with the temperature as T4 always and to depend linearly on the light-cone time L- with an additional (1 /L-) correction term in the short-distance limit whereas in the long-distance limit, q ˆ depends only linearly on L- with no correction term. These observations agree with other holographic calculations directly or indirectly.
Loop Equations in Abelian Gauge Theories
Di Bartolo, C; Pe~na, F; Bartolo, Cayetano Di; Leal, Lorenzo; Peña, Francisco
2005-01-01
The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme for studying these loop-equations for lattice Maxwell theory is presented. The approximation leads to a partial difference equation in the area and length variables of the loop, and certain physically motivated ansatz is seen to reproduce the mean field results from a geometrical perspective.
Lattice BRST without Neuberger 0/0 problem
von Smekal, Lorenz
2013-01-01
We illustrate in a simple toy model how the methods of SUSY quantum mechanics and topological quantum field theory can be used for covariant gauge-fixing with unbroken BRST symmetry on a finite lattice.
An improved single-plaquette gauge action
Energy Technology Data Exchange (ETDEWEB)
Banerjee, D. [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics,University of Bern, Sidlerstr. 5, 3012 Bern (Switzerland); NIC, DESY,Platanenallee 6, 15738, Zeuthen (Germany); Bögli, M. [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics,University of Bern, Sidlerstr. 5, 3012 Bern (Switzerland); Department of Physics, Chung-Yuan Christian University (CYCU),Chung-Li 32023, Taiwan (China); Holland, K. [Physics Department, University of the Pacific, 3601 Pacific Avenue, Stockton, CA 95211 (United States); Niedermayer, F. [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics,University of Bern, Sidlerstr. 5, 3012 Bern (Switzerland); Pepe, M. [INFN - Sezione di Milano-Bicocca,Edificio U2, Piazza della Scienza 3, 20126 Milano (Italy); Wenger, University; Wiese, UniversityJ. [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics,University of Bern, Sidlerstr. 5, 3012 Bern (Switzerland)
2016-03-17
We describe and test a nonperturbatively improved single-plaquette lattice action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large fluctuations of the plaquette, without requiring the naive continuum limit for smooth fields. We tune the action parameters based on torelon masses in moderate cubic physical volumes, and investigate the size of cut-off effects in other physical quantities, including torelon masses in asymmetric spatial volumes, the static quark potential, and gradient flow observables. In 2-d O(N) models similarly constructed nearest-neighbor actions have led to a drastic reduction of cut-off effects, down to the permille level, in a wide variety of physical quantities. In the gauge theories, we find significant reduction of lattice artifacts, and for some observables, the coarsest lattice result is very close to the continuum value. We estimate an improvement factor of 40 compared to using the Wilson gauge action to achieve the same statistical accuracy and suppression of cut-off effects.
An Improved Single-Plaquette Gauge Action
Banerjee, Debasish; Holland, Kieran; Niedermayer, Ferenc; Pepe, Michele; Wenger, Urs; Wiese, Uwe-Jens
2015-01-01
We describe and test a nonperturbatively improved single-plaquette lattice action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large fluctuations of the plaquette, without requiring the naive continuum limit for smooth fields. We tune the action parameters based on torelon masses in moderate cubic physical volumes, and investigate the size of cut-off effects in other physical quantities, including torelon masses in asymmetric spatial volumes, the static quark potential, and gradient flow observables. In 2-d O(N) models similarly constructed nearest-neighbor actions have led to a drastic reduction of cut-off effects, down to the permille level, in a wide variety of physical quantities. In the gauge theories, we find significant reduction of lattice artifacts, and for some observables, the coarsest lattice result is very close to the continuum value. We estimate an improvement factor of 40 compared to using the Wilson gauge action to achieve the same statistical accuracy and suppression of cut-of...
Gauge Theory On The Fuzzy Torus
Bigatti, D
2001-01-01
In this paper a formulation of U(1) gauge theory on a fuzzy torus is discussed. The theory is regulated in both the infrared and ultraviolet. It can be thought of as a non-commutative version of lattice gauge theory on a periodic lattice. The construction of Wilson loops is particularly transparent in this formulation. Following Ishibashi, Iso, Kawai and Kitazawa, we show that certain Fourier modes of open Wilson lines are gauge invariant. We also introduce charged matter fields which can be thought of as fundamentals of the gauge group. These particles behave like charges in a strong magnetic field and are frozen into the lowest Landau levels. The resulting system is a simple matrix quantum mechanics which should reflect much of the physics of charged particles in strong magnetic fields. The present results were first presented as a talk at the Institute for Mathematical Science, Chennai, India; the author wishes to thank Prof. T. R. Govindarajan and the IMS for hospitality and financial support, and the aud...
Wang, Da-Wei; Zhu, Shi-Yao; Scully, Marlan O
2014-01-01
We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in the momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on an electromagnetically induced transparency (EIT) system. For a one-dimensional SL, we need the coupling field of the EIT system to be a standing wave. The detuning between the two components of the standing wave introduces an effective electric field. The quantum behaviours of electrons in lattices, such as Bloch oscillations, Wannier-Stark ladders, Bloch band collapsing and dynamic localization can be observed in the SL. The SL can be extended to two, three and even higher dimensions where no analogous real space lattices exist and new physics are waiting to be explored.
Bukenov, A K; Polikarpov, M I; Polley, L; Wiese, U J
1992-01-01
We develop a formalism for the quantization of topologically stable excitations in the 4-dimensional abelian lattice gauge theory. The excitations are global and local (Abrikosov-Nielsen-Olesen) strings and monopoles. The operators of creation and annihilation of string states are constructed; the string Green functions are represented as a path integral over random surfaces. Topological excitations play an important role in the early universe. In the broken symmetry phase of the $U(1)$ spin model, closed global cosmic strings arise, while in the Higgs phase of the noncompact gauge-Higgs model, local cosmic strings are present. The compact gauge-Higgs model also involves monopoles. Then the strings can break if their ends are capped by monopoles. The topology of the Euclidean string world sheets are studied by numerical simulations.
Fermion propagator in quenched QED3 in the light of the Landau-Khalatnikov-Fradkin tranformation
Energy Technology Data Exchange (ETDEWEB)
Bashir, A. [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Apartado Postal 2-82, Morelia, Michoacan 58040 (Mexico); Raya, A. [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Col. Villa San Sebastian, Colima, Colima 28045 (Mexico)
2005-04-15
We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynamical symmetry breaking, in the light of its Landau-Khalatnikov-Fradkin transformation (LKFT). In the former case, starting with the massive bare propagator in the Landau gauge, we obtain non perturbative propagator in an arbitrary covariant gauge. Carrying out a perturbative expansion of this result, it yields correct wavefunction renormalization and the mass function up to the terms independent of the gauge parameter. Also, we obtain valuable information for the higher order perturbative expansion of the propagator. As for the case of dynamical chiral symmetry breaking, we start by approximating the numerical solution in Landau gauge in the rainbow approximation in terms of analytic functions. We then use LKFT to obtain the dynamically generated fermion propagator in an arbitrary covariant gauge. We find that the results obtained have all the required qualitative features. We also go beyond the rainbow and encounter similar desirable qualitative features.
Composite operators in lattice QCD nonperturbative renormalization
Göckeler, M; Oelrich, H; Perlt, H; Petters, D; Rakow, P; Schäfer, A; Schierholz, G; Schiller, A
1999-01-01
We investigate the nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.
Mixed action computations on fine dynamical lattices
Bernardoni, F; Hernandez, P; Necco, S; Pena, C
2009-01-01
We report on our first experiences in simulating Neuberger valence fermions on CLS $N_f=2$ configurations with light sea quark masses and small lattice spacings. Valence quark masses are considered that allow to explore the matching to (partially quenched) chiral perturbation theory both in the $\\epsilon$- and $p$-regimes. The setup is discussed, and first results are presented for spectral observables.
Working Group Report: Lattice Field Theory
Energy Technology Data Exchange (ETDEWEB)
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Commensurability effects in holographic homogeneous lattices
Andrade, Tomas; Krikun, Alexander
2016-01-01
An interesting application of the gauge/gravity duality to condensed matter physics is the description of a lattice via breaking translational invariance on the gravity side. By making use of global symmetries, it is possible to do so without scarifying homogeneity of the pertinent bulk solutions, which we thus term as "homogeneous holographic lattices." Due to their technical simplicity, these configurations have received a great deal of attention in the last few years and have been shown to...
Perfect Lattice Actions for Staggered Fermions
Bietenholz, W; Chandrasekharan, S; Wiese, U J
1996-01-01
We construct a perfect lattice action for staggered fermions by blocking from the continuum. The locality, spectrum and pressure of such perfect staggered fermions are discussed. We also derive a consistent fixed point action for free gauge fields and discuss its locality as well as the resulting static quark-antiquark potential. This provides a basis for the construction of (classically) perfect lattice actions for QCD using staggered fermions.
Lattice QCD and the Jefferson Laboratory Program
Energy Technology Data Exchange (ETDEWEB)
Jozef Dudek, Robert Edwards, David Richards, Konstantinos Orginos
2011-06-01
Lattice gauge theory provides our only means of performing \\textit{ab initio} calculations in the non-perturbative regime. It has thus become an increasing important component of the Jefferson Laboratory physics program. In this paper, we describe the contributions of lattice QCD to our understanding of hadronic and nuclear physics, focusing on the structure of hadrons, the calculation of the spectrum and properties of resonances, and finally on deriving an understanding of the QCD origin of nuclear forces.
Generalized Higher Gauge Theory
Ritter, Patricia; Schmidt, Lennart
2015-01-01
We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between the canonical exact Courant Lie 2-algebroid $TM\\oplus T^*M$ over some manifold $M$ and a semistrict gauge Lie 2-algebra. We discuss generalized curvatures and their infinitesimal gauge transformations. Finite gauge transformation as well as global kinematical data are then obtained from principal 2-bundles over 2-spaces. As dynamical principle, we consider first the canonical Chern-Simons action for such a gauge theory. We then show that a previously proposed 3-Lie algebra model for the six-dimensional (2,0) theory is very naturally interpreted as a generalized higher gauge theory.
Gauge symmetry from decoupling
Energy Technology Data Exchange (ETDEWEB)
Wetterich, C., E-mail: c.wetterich@thphys.uni-heidelberg.de
2017-02-15
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang–Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
Gauge symmetry from decoupling
Directory of Open Access Journals (Sweden)
C. Wetterich
2017-02-01
Full Text Available Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang–Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
Gauge symmetry from decoupling
Wetterich, C.
2017-02-01
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
Quenched Heavy-Light Decay Constants
Baxter, R M; Bowler, K C; Collins, S; Henty, D S; Kenway, R D; Richards, D G; Shanahan, H P; Simone, J N; Simpson, A D; Wilkes, B E; Ewing, A K; Lellouch, L P; Sachrajda, Christopher T C; Wittig, H
1994-01-01
We present results for heavy-light decay constants, using both propagating quarks and the static approximation, in O(a)-improved, quenched lattice QCD. At beta=6.2 on a 24^3x48 lattice we find f_D=185 +4-3(stat)+42-7(syst) MeV, f_B=160 +6-6 +53-19 MeV, f_{D_s}/f_D=1.18 +2-2 and f_{B_s}/f_B=1.22 +4-3, in good agreement with earlier studies. From the static theory we obtain f_B^stat=253 +16-15 +105-14 MeV. We also present results from a simulation at beta=6.0 on a 16^3x48 lattice, which are consistent with those at beta=6.2. In order to study the effects of improvement, we present a direct comparison of the results using both the Wilson and the improved action at beta=6.0.
Screening in two-dimensional gauge theories
Korcyl, Piotr
2012-01-01
We analyze the problem of screening in 1+1 dimensional gauge theories. Using QED2 as a warm-up for the non-abelian models we show the mechanism of the string breaking, in particular the vanishing overlap of the Wilson loops to the broken-string ground state that has been conjectured in higher-dimensional analyses. We attempt to extend our analysis to non-integer charges in the quenched and unquenched cases, in pursuit of the numerical check of a renowned result for the string tension between arbitrarily-charged fermions in the massive Schwinger model.
Screening in two-dimensional gauge theories
Energy Technology Data Exchange (ETDEWEB)
Korcyl, Piotr [Uniwersytet Jagiellonski, Cracow (Poland). Inst. Fizyki; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Koren, Mateusz [Uniwersytet Jagiellonski, Cracow (Poland). Inst. Fizyki
2012-12-15
We analyze the problem of screening in 1+1 dimensional gauge theories. Using QED{sub 2} as a warmup for the non-abelian models we show the mechanism of the string breaking, in particular the vanishing overlap of the Wilson loops to the broken-string ground state that has been conjectured in higher-dimensional analyses. We attempt to extend our analysis to non-integer charges in the quenched and unquenched cases, in pursuit of the numerical check of a renowned result for the string tension between arbitrarily-charged fermions in the massive Schwinger model.
A gauge-invariant reorganization of thermal gauge theory
Energy Technology Data Exchange (ETDEWEB)
Su, Nan
2010-07-01
This dissertation is devoted to the study of thermodynamics for quantum gauge theories. The poor convergence of quantum field theory at finite temperature has been the main obstacle in the practical applications of thermal QCD for decades. In this dissertation I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to the thermodynamics of QED and Yang-Mills theory to three-loop order. For the Abelian case, I present a calculation of the free energy of a hot gas of electrons and photons by expanding in a power series in m{sub D}/T, m{sub f}/T and e{sup 2}, where m{sub D} and m{sub f} are the photon and electron thermal masses, respectively, and e is the coupling constant. I demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e {proportional_to} 2. For the non-Abelian case, I present a calculation of the free energy of a hot gas of gluons by expanding in a power series in m{sub D}/T and g{sup 2}, where m{sub D} is the gluon thermal mass and g is the coupling constant. I show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T {proportional_to} 2 - 3 T{sub c}. The results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC. (orig.)
Design of Industrial Quenching Processes
Institute of Scientific and Technical Information of China (English)
Nikolai. I. KOBASKO; George .E. TOTTEN
2004-01-01
The method of designing industrial processes of quench cooling, in particular, the speed of the conveyor movement with regard to shape and sizes of parts to be quenched, thermal and physical properties of material and cooling capacity of quenchants has been developed. The suggested designing method and databases are the basis for the complete automation of industrial processes of quench cooling, especially for continuous conveyor lines, with the purpose of making high-strength materials. The process is controlled by infrared technique.
Hamiltonian truncation approach to quenches in the Ising field theory
Rakovszky, Tibor; Collura, Mario; Kormos, Márton; Takács, Gábor
2016-01-01
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1+1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while...
Relative weights approach to SU(3) gauge theories with dynamical fermions at finite density
Höllwieser, Roman
2016-01-01
We derive effective Polyakov line actions for SU(3) gauge theories with staggered dynamical fermions, for a small sample of lattice couplings, lattice actions, and lattice extensions in the time direction. The derivation is via the method of relative weights, and the theories are solved at finite chemical potential by mean field theory. We find in some instances that the long-range couplings in the effective action are very important to the phase structure, and that these couplings are responsible for long-lived metastable states in the effective theory. Only one of these states corresponds to the underlying lattice gauge theory.
Glueball calculations in large-$N_{c}$ gauge theory
Dalley, S
1999-01-01
We use the light-front Hamiltonian of transverse lattice gauge theory to compute from first principles the glueball spectrum and light-front wavefunctions in the leading order of the 1/N_c colour expansion. We find 0^{++}, 2^{++}, and 1^{+-} glueballs having masses consistent with N_c=3 data available from Euclidean lattice path integral methods. The wavefunctions exhibit a light-front constituent gluon structure.
Schwinger mechanism in linear covariant gauges
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2017-02-01
In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modeled by means of certain physically motivated Ansätze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ansätze are compatible with the existence of nontrivial solutions. When such Ansätze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic "zero crossing," while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.
Quantum Gravity on the Lattice
Hamber, Herbert W
2009-01-01
I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I cover the general methods and goals of the lattice approach. An underlying theme is an attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which should apply to the strong gravity regime and are inherently non-perturbative. A second theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral q...
Kagome Chiral Spin Liquid as a Gauged U(1) Symmetry Protected Topological Phase.
He, Yin-Chen; Bhattacharjee, Subhro; Pollmann, Frank; Moessner, R
2015-12-31
While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.
Kagome Chiral Spin Liquid as a Gauged U (1 ) Symmetry Protected Topological Phase
He, Yin-Chen; Bhattacharjee, Subhro; Pollmann, Frank; Moessner, R.
2015-12-01
While the existence of a chiral spin liquid (CSL) on a class of spin-1 /2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U (1 ) symmetry protected topological (SPT) phase, which upon promoting its U (1 ) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.
Effective Field Theories and Lattice QCD
Bernard, C
2015-01-01
I describe some of the many connections between lattice QCD and effective field theories, focusing in particular on chiral effective theory, and, to a lesser extent, Symanzik effective theory. I first discuss the ways in which effective theories have enabled and supported lattice QCD calculations. Particular attention is paid to the inclusion of discretization errors, for a variety of lattice QCD actions, into chiral effective theory. Several other examples of the usefulness of chiral perturbation theory, including the encoding of partial quenching and of twisted boundary conditions, are also described. In the second part of the talk, I turn to results from lattice QCD for the low energy constants of the two- and three-flavor chiral theories. I concentrate here on mesonic quantities, but the dependence of the nucleon mass on the pion mass is also discussed. Finally I describe some recent preliminary lattice QCD calculations by the MILC Collaboration relating to the three-flavor chiral limit.
A classification of 2-dim Lattice Theory
Kieburg, Mario; Zafeiropoulos, Savvas
2013-01-01
A unified classification and analysis is presented of two dimensional Dirac operators of QCD-like theories in the continuum as well as in a naive lattice discretization. Thereby we consider the quenched theory in the strong coupling limit. We do not only consider the case of a lattice which has an even number of lattice sites in both directions and is thus equivalent to the case of staggered fermions. We also study lattices with one or both directions with an odd parity to understand the general mechanism of changing the universality class via a discretization. Furthermore we identify the corresponding random matrix ensembles sharing the global symmetries of these QCD-like theories. Despite the Mermin-Wagner-Coleman theorem we find good agreement of lattice data with our random matrix predictions.
Energy Technology Data Exchange (ETDEWEB)
Bartholomew, M. J. [Brookhaven National Lab. (BNL), Upton, NY (United States)
2016-01-01
To improve the quantitative description of precipitation processes in climate models, the Atmospheric Radiation Measurement (ARM) Climate Research Facility deployed rain gauges located near disdrometers (DISD and VDIS data streams). This handbook deals specifically with the rain gauges that make the observations for the RAIN data stream. Other precipitation observations are made by the surface meteorology instrument suite (i.e., MET data stream).
N=4 supersymmetry on a space-time lattice
DEFF Research Database (Denmark)
Catterall, Simon; Schaich, David; Damgaard, Poul H.
2014-01-01
Maximally supersymmetric Yang–Mills theory in four dimensions can be formulated on a space-time lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice theory, paying particular attention to its strongly coupled regime. Targeting a theory with gauge group SU...
Comment on Pauli-Villars Lagrangian on the Lattice
Haga, K; Okuyama, K; Suzuki, H; Haga, Kazunobu; Igarashi, Hiroshi; Okuyama, Kiyoshi; Suzuki, Hiroshi
1997-01-01
It is interesting to superimpose the Pauli--Villars regularization on the lattice regularization. We illustrate how this scheme works by evaluating the axial anomaly in a simple lattice fermion model, the Pauli--Villars Lagrangian with a gauge non-invariant Wilson term. The gauge non-invariance of the axial anomaly, caused by the Wilson term, is remedied by a compensation between Pauli--Villars regulators in the continuum limit. A subtlety in Frolov--Slavnov's scheme for an {\\it odd\\/} number of chiral fermions in an anomaly free complex gauge representation, which requires an infinite number of regulators, is briefly mentioned.
A Lattice Study of the Glueball Spectrum
Institute of Scientific and Technical Information of China (English)
LIU Chuan
2001-01-01
Glueball spectrum is studied using an improved gluonic action on asymmetric lattices in the pure SU(3)gauge theory. The smallest spatial lattice spacing is about 0.08 fm which makes the extrapolation to the continuum limit more reliable. In particular, attention is paid to the scalar glueball mass which is known to have problems in the extrapolation. Converting our lattice results to physical units using the scale set by the static quark potential,we obtain the following results for the glueball masses: MG(0++) = 1730(90) MeV for the scalar glueball mass and MG(2++) = 2400(95) MeV for the tensor glueball.
The vortex-finding property of maximal center (and other) gauges
Energy Technology Data Exchange (ETDEWEB)
Faber, M.; Greensite, J.; Olejnik, S.; Yamada, D.
1999-10-01
The authors argue that the vortex-finding property of maximal center gauge, i.e. the ability of this gauge to locate center vortices inserted by hand on any given lattice, is the key to its success in extracting the vortex content of thermalized lattice configurations. The authors explain how this property comes about, and why it is expected not only in maximal center gauge, but also in an infinite class of gauge conditions based on adjoint-representation link variables. In principle, the vortex-finding property can be foiled by Gribov copies. This fact is relevant to a gauge-fixing procedure devised by Kovacs and Tomboulis, where they show that the loss of center dominance, found in their procedure, is explained by a corresponding loss of the vortex-finding property. The dependence of center dominance on the vortex-finding property is demonstrated numerically in a number of other gauges.
Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories
Hanany, Amihay
2016-01-01
The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to a collection of semi-groups. It turns out that the unique Hilbert bases of these semi-groups are a sufficient, finite set of monopole operators which generate the entire chiral ring. Moreover, the knowledge of the properties of the minimal generators is enough to compute the Hilbert series explicitly. The techniques of this paper allow an efficient evaluation of the Hilbert series for general rank gauge groups. As an application, we provide various examples for all rank two gauge groups to demonstrate the novel interpretation.
Coulomb branches for rank 2 gauge groups in 3dN=4 gauge theories
Energy Technology Data Exchange (ETDEWEB)
Hanany, Amihay [Theoretical Physics Group, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom); Sperling, Marcus [Institut für Theoretische Physik, Leibniz Universität Hannover,Appelstraße 2, 30167 Hannover (Germany)
2016-08-02
The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to a collection of semi-groups. It turns out that the unique Hilbert bases of these semi-groups are a sufficient, finite set of monopole operators which generate the entire chiral ring. Moreover, the knowledge of the properties of the minimal generators is enough to compute the Hilbert series explicitly. The techniques of this paper allow an efficient evaluation of the Hilbert series for general rank gauge groups. As an application, we provide various examples for all rank two gauge groups to demonstrate the novel interpretation.
Vacuum polarization and chiral lattice fermions
Randjbar-Daemi, S.; Strathdee, J.
1996-02-01
The vacuum polarization due to chiral fermions on a 4-dimensional Euclidean lattice is calculated according to the overlap prescription. The fermions are coupled to weak and slowly varying background gauge and Higgs fields, and the polarization tensor is given by second order perturbation theory. In this order the overlap constitutes a gauge-invariant regularization of the fermion vacuum amplitude. Its low-energy-long-wavelength behaviour can be computed explicitly and we verify that it coincides with the Feynman graph result obtainable, for example, by dimensional regularization of continuum gauge theory. In particular, the Standard Model Callan-Symanzik RG functions are recovered. Moreover, there are no residual lattice artefacts such as a dependence on Wilson-type mass parameters.
Vacuum polarization and chiral lattice fermions
Strathdee, J A
1995-01-01
The vacuum polarization due to chiral fermions on a 4--dimensional Euclidean lattice is calculated according to the overlap prescription. The fermions are coupled to weak and slowly varying background gauge and Higgs fields, and the polarization tensor is given by second order perturbation theory. In this order the overlap constitutes a gauge invariant regularization of the fermion vacuum amplitude. Its low energy -- long wavelength behaviour can be computed explicitly and we verify that it coincides with the Feynman graph result obtainable, for example, by dimensional regularization of continuum gauge theory. In particular, the Standard Model Callan--Symanzik RG functions are recovered. Moreover, there are no residual lattice artefacts such as a dependence on Wilson--type mass parameters.
Quantum Operator Design for Lattice Baryon Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Lichtl, Adam [Carnegie Mellon Univ., Pittsburgh, PA (United States)
2006-09-07
A previously-proposed method of constructing spatially-extended gauge-invariant three-quark operators for use in Monte Carlo lattice QCD calculations is tested, and a methodology for using these operators to extract the energies of a large number of baryon states is developed. This work is part of a long-term project undertaken by the Lattice Hadron Physics Collaboration to carry out a first-principles calculation of the low-lying spectrum of QCD. The operators are assemblages of smeared and gauge-covariantly-displaced quark fields having a definite flavor structure. The importance of using smeared fields is dramatically demonstrated. It is found that quark field smearing greatly reduces the couplings to the unwanted high-lying short-wavelength modes, while gauge field smearing drastically reduces the statistical noise in the extended operators.
Monte Carlo methods in continuous time for lattice Hamiltonians
Huffman, Emilie
2016-01-01
We solve a variety of sign problems for models in lattice field theory using the Hamiltonian formulation, including Yukawa models and simple lattice gauge theories. The solutions emerge naturally in continuous time and use the dual representation for the bosonic fields. These solutions allow us to construct quantum Monte Carlo methods for these problems. The methods could provide an alternative approach to understanding non-perturbative dynamics of some lattice field theories.
Crystalline Scaling Geometries from Vortex Lattices
Bao, Ning
2013-01-01
We study magnetic geometries with Lifshitz and/or hyperscaling violation exponents (both with a hard wall cutoff in the IR and a smooth black brane horizon) which have a complex scalar field which couples to the magnetic field. The complex scalar is unstable to the production of a vortex lattice in the IR. The lattice is a normalizable mode which is relevant (i.e. grows into the IR.) When one considers linearized backreaction of the lattice on the metric and gauge field, the metric forms a crystalline structure. We analyze the scaling of the free energy, thermodynamic entropy, and entanglement in the lattice phase and find that in the smeared limit, the leading order correction to thermodynamic properties due to the lattice has the scaling behavior of a theory with a hyperscaling violation exponent between 0 and 1, indicating a flow to an effectively lower-dimensional theory in the deep IR.
Donnellan, Thomas; Maxwell, E A; Plumpton, C
1968-01-01
Lattice Theory presents an elementary account of a significant branch of contemporary mathematics concerning lattice theory. This book discusses the unusual features, which include the presentation and exploitation of partitions of a finite set. Organized into six chapters, this book begins with an overview of the concept of several topics, including sets in general, the relations and operations, the relation of equivalence, and the relation of congruence. This text then defines the relation of partial order and then partially ordered sets, including chains. Other chapters examine the properti
Dark matter from one-flavor SU(2) gauge theory
Francis, Anthony; Lewis, Randy; Tulin, Sean
2016-01-01
SU(2) gauge theory with a single fermion in the fundamental representation is a minimal non-Abelian candidate for the dark matter sector, which is presently missing from the standard model. Having only a single flavor provides a natural mechanism for stabilizing dark matter on cosmological timescales. Preliminary lattice results are presented and discussed in the context of dark matter phenomenology.
Gauge/String Duality, Hot QCD and Heavy Ion Collisions
Casalderrey-Solana, Jorge; Liu, Hong; Mateos, David; Rajagopal, Krishna; Wiedemann, Urs Achim
2014-06-01
1. Opening remarks; 2. A heavy ion phenomenology primer; 3. Results from lattice QCD at nonzero temperature; 4. Introducing the gauge/string duality; 5. A duality toolbox; 6. Bulk properties of strongly coupled plasma; 7. From hydrodynamics for far-from-equilibrium dynamics; 8. Probing strongly coupled plasma; 9. Quarkonium mesons in strongly coupled plasma; 10. Concluding remarks and outlook; Appendixes; References; Index.
Aspects of confinement in QCD from lattice simulations
Energy Technology Data Exchange (ETDEWEB)
Spielmann, Daniel
2011-01-12
We study confinement in quantum chromodynamics via numerical simulations in the framework of lattice gauge theory. In Landau gauge, the mechanism of confinement is related to the infrared behavior of the ghost and gluon propagators via the Gribov-Zwanziger and Kugo- Ojima scenarios. These scenarios entail a scaling behavior. Functional methods in the continuum allow both for this behavior and for decoupling solutions, while lattice simulations in three and four dimensions yield only the latter. A possible explanation for this mismatch is based on limitations of standard lattice gauge fixing methods. Hence, we investigate a number of alternative gauge fixing algorithms in pure SU(2) gauge theory in two, three and four dimensions. We find that stochastic quantization yields an infrared behavior of the propagators in agreement with the results of standard procedures, even though the Faddeev-Popov operator spectrum indicates some different properties. In the strong-coupling limit, our results challenge the standard picture. In particular, we find in a non-perturbative completion of Landau gauge an enormous effect of the Gribov ambiguity. It entails that no subset of infrared solutions can be excluded yet. Moreover, we study the gluon propagator with free boundary conditions. On large lattices, the results mostly show the standard behavior. We also examine non-periodic gauge transformations. Furthermore, we analyze two topics related to the phase diagram of QCD. First, we explore the sign problem for fermions on the lattice by simulating the three-dimensional Thirring model with a complex Langevin equation. The algorithm succeeds in yielding a 'Silver Blaze' behavior of observables, but it does not reliably describe the onset to a phase with non-zero density. Second, we determine properties of the deconfinement phase transition of pure SU(2) gauge theory in 2+1 dimensions, like the critical temperature, by means of the gluon propagator in Landau gauge. (orig.)
A lattice QCD calculation of the transverse decay constant of the b1(1235) meson
Jansen, K; Michael, C; Urbach, C
2009-01-01
We review various B meson decays that require knowledge of the transverse decay constant of the b1(1235) meson. We report on an exploratory lattice QCD calculation of the transverse decay constant of the b1 meson. The lattice QCD calculations used unquenched gauge configurations, at two lattice spacings, generated with two flavours of sea quarks. The twisted mass formalism is used.
Four Fermion Interactions in Non-Abelian Gauge Theory
Catterall, Simon
2013-01-01
We continue our earlier study of the phase structure of a SU(2) gauge theory whose action contains additional chirally invariant four fermion interactions. Our lattice theory uses a reduced staggered fermion formalism to generate two Dirac flavors in the continuum limit. In the current study we have tried to reduce lattice spacing and taste breaking effects by using an improved fermion action incorporating stout smeared links. As in our earlier study we observe two regimes; for weak gauge coupling the chiral condensate behaves as an order parameter differentiating a phase at small four fermi coupling where the condensate vanishes from a phase at strong four fermi coupling in which chiral symmetry is spontaneously broken. This picture changes qualitatively when the gauge coupling is strong enough to cause confinement; in this case we observe a first order phase transition for some critical value of the four fermi coupling associated with a strong enhancement of the chiral condensate. We observe that this criti...
Large-Nc Gauge Theory and Chiral Random Matrix Theory
Hanada, Masanori; Lee, Jong-Wan; Yamada, Norikazu
Effective theory approaches and the large-Nc limit are useful for studying the strongly coupled gauge theories. In this talk we consider how the chiral random matrix theory (χRMT) can be used in the study of large-Nc gauge theories. It turns out the parameter regions, in which each of these two approaches are valid, are different. Still, however, we show that the breakdown of chiral symmetry can be detected by combining the large-Nc argument and the χRMT with some cares. As a demonstration, we numerically study the four dimensional SU(Nc) gauge theory with Nf = 2 heavy adjoint fermions on a 24 lattice by using Monte-Carlo simulations, which is related to the infinite volume lattice through the Eguchi-Kawai equivalence.
Gauge coupling unification in gauge-Higgs grand unification
Yamatsu, Naoki
2016-04-01
We discuss renormalization group equations for gauge coupling constants in gauge-Higgs grand unification on five-dimensional Randall-Sundrum warped space. We show that all four-dimensional Standard Model gauge coupling constants are asymptotically free and are effectively unified in SO(11) gauge-Higgs grand unified theories on 5D Randall-Sundrum warped space.
Chung, Daniel J H
2016-01-01
We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.
National Aeronautics and Space Administration — Cog-Gauge is a portable hand-held game that can be used by astronauts and crew members during space exploration missions to assess their cognitive workload...
Healey, Richard
Those looking for holism in contemporary physics have focused their attention primarily on quantum entanglement. But some gauge theories arguably also manifest the related phenomenon of nonseparability. While the argument is strong for the classical gauge theory describing electromagnetic interactions with quantum "particles", it fails in the case of general relativity even though that theory may also be formulated in terms of a connection on a principal fiber bundle. Anandan has highlighted the key difference in his analysis of a supposed gravitational analog to the Aharonov-Bohm effect. By contrast with electromagnetism in the original Aharonov-Bohm effect, gravitation is separable and exhibits no novel holism in this case. Whether the nonseparability of classical gauge theories of nongravitational interactions is associated with holism depends on what counts as the relevant part-whole relation. Loop representations of quantized gauge theories of nongravitational interactions suggest that these conclusions about holism and nonseparability may extend also to quantum theories of the associated fields.
The QCD equation of state with charm quarks from lattice QCD
Cheng, Michael
Recently, there have been several calculations of the QCD equation of state (EoS) on the lattice. These calculations take into account the two light quarks and the strange quark, but have ignored the effects of the charm quark, assuming that the charm mass (mc ≈ 1300 MeV) is exponentially suppressed at the temperatures which are explored. However, future heavy ion collisions, such as those planned at the LHC, may well probe temperature regimes where the charm quarks play an important role in the dynamics of the QGP. We present a calculation of the charm quark contribution to the QCD EoS using p4-improved staggered fermions at Nt = 4, 6, 8. This calculation is done with a quenched charm quark, i.e. the relevant operators are measured using a valence charm quark mass on a 2+1 flavor gauge field background. The charm quark masses are determined by calculating charmonium masses (metac and mJ/Psi) and fixing these mesons to their physical masses. The interaction measure, pressure, energy density, and entropy density are calculated. We find that the charm contribution makes a significant contribution, even down to temperatures as low as the pseudo-critical temperature, Tc. However, there are significant scaling corrections at the lattice spacings that we use, preventing a reliable continuum extrapolation.
Schwinger mechanism in linear covariant gauges
Aguilar, A C; Papavassiliou, J
2016-01-01
In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully-dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modelled by means of certain physically motivated Ans\\"atze. The gauge-dependent terms contributing to this ke...
Improved Lattice Renormalization Group Techniques
Petropoulos, Gregory; Hasenfratz, Anna; Schaich, David
2013-01-01
We compute the bare step-scaling function $s_b$ for SU(3) lattice gauge theory with $N_f = 12$ massless fundamental fermions, using the non-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group two-lattice matching technique. We use a short Wilson flow to approach the renormalized trajectory before beginning RG blocking steps. By optimizing the length of the Wilson flow, we are able to determine an $s_b$ corresponding to a unique discrete $\\beta$ function, after a few blocking steps. We carry out this study using new ensembles of 12-flavor gauge configurations generated with exactly massless fermions, using volumes up to $32^4$. The results are consistent with the existence of an infrared fixed point (IRFP) for all investigated lattice volumes and number of blocking steps. We also compare different renormalization schemes, each of which indicates an IRFP at a slightly different value of the bare coupling, as expected for an IR-conformal theory.
Frampton, Paul H
2008-01-01
This third edition on the classic Gauge Field Theories is an ideal reference for researchers starting work with the Large Hadron Collider and the future International Linear Collider. This latest title continues to offer an up to date reference containing revised chapters on electroweak interactions and model building including a completely new chapter on conformality. Within this essential reference logical organization of the material on gauge invariance, quantization, and renormalization is also discussed providing necessary reading for Cosmologists and Particle Astrophysicists
Viscous conformal gauge theories
DEFF Research Database (Denmark)
Toniato, Arianna; Sannino, Francesco; Rischke, Dirk H.
2017-01-01
We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories.......We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories....
Heavy Dynamical Fermions in Lattice QCD
Hasenfratz, Anna; Hasenfratz, Anna; Grand, Thomas A. De
1994-01-01
It is expected that the only effect of heavy dynamical fermions in QCD is to renormalize the gauge coupling. We derive a simple expression for the shift in the gauge coupling induced by $N_f$ flavors of heavy fermions. We compare this formula to the shift in the gauge coupling at which the confinement-deconfinement phase transition occurs (at fixed lattice size) from numerical simulations as a function of quark mass and $N_f$. We find remarkable agreement with our expression down to a fairly light quark mass. However, simulations with eight heavy flavors and two light flavors show that the eight flavors do more than just shift the gauge coupling. We observe confinement-deconfinement transitions at $\\beta=0$ induced by a large number of heavy quarks. We comment on the relevance of our results to contemporary simulations of QCD which include dynamical fermions.
Lattice QCD on nonorientable manifolds
Mages, Simon; Tóth, Bálint C.; Borsányi, Szabolcs; Fodor, Zoltán; Katz, Sándor D.; Szabó, Kálmán K.
2017-05-01
A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a nonorientable manifold and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is that translational invariance is preserved up to exponentially small corrections. A Dirac fermion on a nonorientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.
Shear Viscosity from Lattice QCD
Mages, Simon W; Fodor, Zoltán; Schäfer, Andreas; Szabó, Kálmán
2015-01-01
Understanding of the transport properties of the the quark-gluon plasma is becoming increasingly important to describe current measurements at heavy ion collisions. This work reports on recent efforts to determine the shear viscosity h in the deconfined phase from lattice QCD. The main focus is on the integration of the Wilson flow in the analysis to get a better handle on the infrared behaviour of the spectral function which is relevant for transport. It is carried out at finite Wilson flow time, which eliminates the dependence on the lattice spacing. Eventually, a new continuum limit has to be carried out which sends the new regulator introduced by finite flow time to zero. Also the non-perturbative renormalization strategy applied for the energy momentum tensor is discussed. At the end some quenched results for temperatures up to 4 : 5 T c are presented
Babich, R; Hölbling, C; Howard, J; Lellouch, L; Rebbi, C; Babich, Ronald; Garron, Nicolas; Hoelbling, Christian; Howard, Joseph; Lellouch, Laurent; Rebbi, Claudio
2006-01-01
We present results for the \\Delta S=2 matrix elements which are required to study neutral kaon mixing in the standard model (SM) and beyond (BSM). We also provide leading chiral order results for the matrix elements of the electroweak penguin operators which give the dominant \\Delta I=3/2 contribution to direct CP violation in K->\\pi\\pi decays. Our calculations were performed with Neuberger fermions on two sets of quenched Wilson gauge configurations at inverse lattice spacings of approximately 2.2 GeV and 1.5 GeV. All renormalizations were implemented non-perturbatively in the RI/MOM scheme, where we accounted for sub-leading operator product expansion corrections and discretization errors. We find ratios of non-SM to SM matrix elements which are roughly twice as large as in the only other dedicated lattice study of these amplitudes. On the other hand, our results for the electroweak penguin matrix elements are in good agreement with two recent domain-wall fermion calculations. As a by-product of our study, ...
Holographic Quenches with a Gap
da Silva, Emilia; Mas, Javier; Serantes, Alexandre
2016-01-01
In order to holographically model quenches with a gapped final hamiltonian, we consider a gravity-scalar theory in anti-de Sitter space with an infrared hard wall. We allow a time dependent profile for the scalar field at the wall. This induces an energy exchange between bulk and wall and generates an oscillating scalar pulse. We argue that such backgrounds are the counterpart of quantum revivals in the dual field theory. We perform a qualitative comparison with the quench dynamics of the massive Schwinger model, which has been recently analyzed using tensor network techniques. Agreement is found provided the width of the oscillating scalar pulse is inversely linked to the energy density communicated by the quench. We propose this to be a general feature of holographic quenches.
Holographic quenches with a gap
da Silva, Emilia; Lopez, Esperanza; Mas, Javier; Serantes, Alexandre
2016-06-01
In order to holographically model quenches with a gapped final hamiltonian, we consider a gravity-scalar theory in anti-de Sitter space with an infrared hard wall. We allow a time dependent profile for the scalar field at the wall. This induces an energy exchange between bulk and wall and generates an oscillating scalar pulse. We argue that such backgrounds are the counterpart of quantum revivals in the dual field theory. We perform a qualitative comparison with the quench dynamics of the massive Schwinger model, which has been recently analyzed using tensor network techniques. Agreement is found provided the width of the oscillating scalar pulse is inversely linked to the energy density communicated by the quench. We propose this to be a general feature of holographic quenches.
Topics in Effective Field Theory for Lattice QCD
Walker-Loud, A
2006-01-01
In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we compare to existing lattice QCD calculations. In particular, we extend the heavy baryon Lagrangian to the next order in partially quenched chiral perturbation theory and use it to compute the masses of the lightest spin-1/2 and spin-3/2 baryons to next-to-next-to leading order. We then construct the twisted mass chiral Lagrangian for baryons and apply it to compute the lattice spacing corrections to the baryon masses simulated with twisted mass lattice QCD. We extend computations of the nucleon electromagnetic structure to account for finite volume effects, as these observables are particularly sensitive to the finite extent of the lattice. We resolve subtle peculiarities for lattice QCD simulations of polarizabilities and we show that using background field techniques, one can...
Hydrodynamics of Sakai Sugimoto model in the quenched approximation
Benincasa, Paolo; Buchel, Alex
2006-09-01
We study transport properties of the finite temperature Sakai-Sugimoto model. The model represents a holographic dual to (4 + 1)-dimensional supersymmetric SU (Nc) gauge theory compactified on a circle with anti-periodic boundary conditions for fermions, coupled to Nf left-handed quarks and Nf right-handed quarks localized at different points on the compact circle. We analytically compute the speed of sound and the sound wave attenuation in the quenched approximation. Since confinement/deconfinement (and the chiral symmetry restoration) phase transitions are first order in this model, we do not see any signature of these phase transitions in the transport properties.