A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory
Bedford, J; Spence, B; Travaglini, G; Bedford, James; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
2004-01-01
We extend the twistor string theory inspired formalism introduced in hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel representation of the gauge theory amplitudes as dispersion integrals, which are surprisingly simple to evaluate. As an application we calculate one-loop maximally helicity violating (MHV) scattering amplitudes with an arbitrary number of external legs. The result we obtain agrees precisely with the expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.
Demystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory
Chicherin, Dmitry
2016-01-01
We explain some details of the construction of composite operators in N=4 SYM that we have elaborated earlier in the context of Lorentz harmonic chiral (LHC) superspace. We give a step-by-step elementary derivation and show that the result coincides with the recent hypothesis put forward in arXiv:1603.04471 within the twistor approach. We provide the appropriate LHC-to-twistors dictionary.
Supermembrane limit of Yang-Mills theory
Lechtenfeld, Olaf
2015-01-01
We consider Yang-Mills theory with $N{=}1$ super translation group in eleven auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $\\Sigma_3\\times S^1$, where $\\Sigma_3$ is a three-dimensional Lorentzian manifold and $S^1$ is a circle. We show that in the infrared limit, when the metric on $S^1$ is scaled down, the Yang-Mills action supplemented by a Wess-Zumino-type term reduces to the action of an M2-brane.
Integrable amplitude deformations for N =4 super Yang-Mills and ABJM theory
Bargheer, Till; Huang, Yu-Tin; Loebbert, Florian; Yamazaki, Masahito
2015-01-01
We study Yangian-invariant deformations of scattering amplitudes in 4d N =4 super Yang-Mills theory and 3d N =6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Graßmannian integral for 4d N =4 supersymmetric Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Graßmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.
All tree amplitudes of supersymmetric Einstein-Yang-Mills theory
Adamo, Tim; Roehrig, Kai A; Skinner, David
2015-01-01
We present a new formula for all tree amplitudes in four dimensional supergravity coupled to super Yang-Mills. Like the Cachazo-He-Yuan formula, our expression is supported on solutions of the scattering equations, but with momenta written in terms of spinor helicity variables. Supersymmetry and parity are both manifest. In the pure gravity and pure Yang-Mills sectors, it reduces to the known twistor-string formulae. We show that the formula behaves correctly under factorization. We sketch how these amplitudes may be obtained from a four-dimensional (ambi)twistor string.
Superstring limit of Yang-Mills theories
Lechtenfeld, Olaf; Popov, Alexander D.
2016-11-01
It was pointed out by Shifman and Yung that the critical superstring on X10 =R4 ×Y6, where Y6 is the resolved conifold, appears as an effective theory for a U(2) Yang-Mills-Higgs system with four fundamental Higgs scalars defined on Σ2 ×R2, where Σ2 is a two-dimensional Lorentzian manifold. Their Yang-Mills model supports semilocal vortices on R2 ⊂Σ2 ×R2 with a moduli space X10. When the moduli of slowly moving thin vortices depend on the coordinates of Σ2, the vortex strings can be identified with critical fundamental strings. We show that similar results can be obtained for the low-energy limit of pure Yang-Mills theory on Σ2 × Tp2, where Tp2 is a two-dimensional torus with a puncture p. The solitonic vortices of Shifman and Yung then get replaced by flat connections. Various ten-dimensional superstring target spaces can be obtained as moduli spaces of flat connections on Tp2, depending on the choice of the gauge group. The full Green-Schwarz sigma model requires extending the gauge group to a supergroup and augmenting the action with a topological term.
Duality in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
Dynamical Breaking of Generalized Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
WANGDian-Fu; SONGHe-Shan
2004-01-01
The dynamical breaking of a generalized Yang-Mills theory is discussed. It is shown, in terms of the Nambu Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills theory. The combination of the generalized Yang-Mills theory and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Dynamical Breaking of Generalized Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; SONG He-Shah
2004-01-01
The dynamical breaking of a generalized Yang-Mills theory is discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills theory. The combination of the generalized Yang-Mills theory and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Perturbative spacetimes from Yang-Mills theory
Luna, Andrés; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Perturbative spacetimes from Yang-Mills theory
Luna, Andres; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2016-01-01
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Deformations of Yang-Mills theory
Cofano, Marco; Krasnov, Kirill
2015-01-01
We introduce and study a new class of power-counting non-renormalisable gauge theories in four space-time dimensions. The Lagrangian is an arbitrary function of the self-dual part of the field strength. The resulting perturbation theory has the property that whenever two derivatives act on an internal line propagator, the result is a delta-function and the line collapses to a point. This means that there remains at most one derivative on each internal line, which gives improved ulta-violet behaviour. For many purposes, this class of theories behaves just like ordinary Yang-Mills theory. In particular, they all share the Yang-Mills theory MHV amplitudes. Moreover, these theories remain constructible in the sense that higher-point tree level scattering amplitudes can be obtained from the lower-point amplitudes using the BCFW recursion relations. Also, the square of these gauge-theory amplitudes gives the scattering amplitudes of "deformations" of General Relativity, at least for the low particle numbers that we...
Yang-Mills theory in Coulomb gauge; Yang-Mills-theorie in Coulombeichung
Energy Technology Data Exchange (ETDEWEB)
Feuchter, C.
2006-07-01
In this thesis we study the Yang-Mills vacuum structure by using the functional Schroedinger picture in Coulomb gauge. In particular we discuss the scenario of colour confinement, which was originally formulated by Gribov. After a short introduction, we recall some basic aspects of Yang-Mills theories, its canonical quantization in the Weyl gauge and the functional Schroedinger picture. We then consider the minimal Coulomb gauge and the Gribov problem of the gauge theory. The gauge fixing of the Coulomb gauge is done by using the Faddeev-Popov method, which enables the resolution of the Gauss law - the constraint on physical states. In the third chapter, we variationally solve the stationary Yang-Mills Schroedinger equation in Coulomb gauge for the vacuum state. Therefor we use a vacuum wave functional, which is strongly peaked at the Gribov horizon. The vacuum energy functional is calculated and minimized resulting in a set of coupled Schwinger-Dyson equations for the gluon energy, the ghost and Coulomb form factors and the curvature in gauge orbit space. Using the angular approximation these integral equations have been solved analytically in both the infrared and the ultraviolet regime. The asymptotic analytic solutions in the infrared and ultraviolet regime are reasonably well reproduced by the full numerical solutions of the coupled Schwinger-Dyson equations. In the fourth chapter, we investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. (orig.)
One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
Brandhuber, A; Travaglini, G; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
2004-01-01
We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices, using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of MHV one-loop scattering amplitudes with an arbitrary number of external legs in N=4 super Yang-Mills. Remarkably, our approach naturally leads to a representation of the amplitudes as dispersion integrals, which we evaluate exactly. Our results for the MHV amplitudes are in precise agreement with the expressions for this class of amplitudes obtained previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.
Nonperturbative aspects of Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Schleifenbaum, Wolfgang
2008-07-01
The subject of this thesis is the theory of strong interactions of quarks and gluons, with particular emphasis on nonperturbative aspects of the gluon sector. Continuum methods are used to investigate in particular the confinement phenomenon. Confinement which states that the elementary quarks and gluons cannot be detected as free particles requires an understanding of large-scale correlations. In perturbation theory, only short-range correlations can be reliably described. A nonperturbative approach is given by the set of integral Dyson Schwinger equations involving all Green functions of the theory. A solution for the gluon propagator is obtained in the infrared and ultraviolet asymptotic limits. In chapter 1, redundant degrees of freedom of the Yang Mills gauge theory are removed by fixing the Weyl and Coulomb gauge prior to quantization. The constrained quantization in the Dirac bracket formalism is then performed explicitly to produce the quantized Yang Mills Hamiltonian. The asymptotic infrared limits of Coulomb gauge correlation functions are studied analytically in chapter 2 in the framework of the Gribov Zwanziger confinement scenario. The Coulomb potential between heavy quarks as part of the Yang Mills Hamiltonian is calculated in this limit. A connection between the infrared limits of Coulomb and Landau gauge is established. The Hamiltonian derived paves the way in chapter 3 for finding the Coulomb gauge vacuum wave functional by means of the variational principle. Numerical solutions for the propagators in this vacuum state are discussed and seen to reproduce the anticipated infrared limit. The discussion is extended to the vertex functions. The effect of the approximations on the results is examined. Chapter 4 is mainly devoted to the ultraviolet behavior of the propagators. The discussion is issued in both Coulomb and Landau gauge. A nonperturbative running coupling is defined and calculated. The ultraviolet tails of the variational solutions from
Quantum Yang-Mills field theory
Frasca, Marco
2017-01-01
We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.
Band Structure in Yang-Mills Theories
Bachas, Constantin
2016-01-01
We show how Yang-Mills theory on $S^3\\times R$ can exhibit a spectrum with continuous bands if coupled either to a topological 3-form gauge field, or to a dynamical axion with heavy Peccei-Quinn scale. The basic mechanism consists in associating winding histories to a bosonic zero mode whose role is to convert a circle in configuration space into a helix. The zero mode is, respectively, the holonomy of the 3-form field or the axion momentum. In these models different theta sectors coexist but are not mixed by local operators. Our analysis sheds light on, and extends Seiberg's proposal for modifying the topological sums in quantum field theories. It refutes a recent claim that $B+L$ violation at LHC is unsuppressed.
All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
Bern, Z; Kosower, D A; Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2004-01-01
We compute the next-to-MHV one-loop n-gluon amplitudes in N=4 super-Yang-Mills theory. These amplitudes contain three negative-helicity gluons and an arbitrary number of positive-helicity gluons, and are the first infinite series of amplitudes beyond the simplest, MHV, amplitudes. We also discuss some aspects of their twistor-space structure.
The Parisi-Sourlas Mechanism in Yang-Mills Theory?
Magpantay, J A
2000-01-01
The Parisi-Sourlas mechanism is exhibited in pure Yang-Mills theory. Using the new scalar degrees of freedom derived from the non-linear gauge condition, we show that the non-perturbative sector of Yang-Mills theory is equivalent to a 4D O(1,3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where (x^{2}+\\thetabar\\theta) is unchanged. This leads to dimensional reduction proving the equivalence of the non-perturbative sector of Yang-Mills theory to a 2D O(1,3) sigma model.
On maximally supersymmetric Yang-Mills theories
Movshev, M
2004-01-01
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L_{\\infty}- and A_{\\infty}- algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra Omega of (0, k)-forms on some supermanifold; the Lie algebra is tensor product of Omega and matrix algebra . We construct several other algebras that are quasiisomorphic to Omega and, therefore, also can be used to give BV formulation of 10D SUSY YM theory...
Curving Yang-Mills-Higgs Gauge Theories
Kotov, Alexei
2015-01-01
Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction forces like those mediated by photons and gluons. In the present article, we permit non-zero curvature also on the internal space, the target of the field map. The action functional and the symmetries are constructed in such a way that they reduce to those of standard Yang-Mills-Higgs (YMH) gauge theories precisely when the curvature on the target of the fields is turned off. For curved targets one obtains a new theory, a curved YMH gauge theory. It realizes in a mathematically consistent manner an old wish in the community: replacing structures constants by functions depending on the scalars of the theory. In addition, we provide a simple 4d toy model, where the gauge symmetry is abelian, but turning off the gauge fields, no rigid symmetry remains---another possible manife...
Generalisation of the Yang-Mills Theory
Savvidy, George
2015-01-01
We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The proposed extension is essentially based on the extension of the Poincar\\'e algebra and the existence of an appropriate transversal representations. The invariant Lagrangian is expressed in terms of new higher-rank field strength tensors. It does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan-Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. Considering the contribution of tensorgluons of all spins into the beta function we found that it is leading to the theo...
Simulations of supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Demmouche, K.; Farchioni, F.; Ferling, A.; Muenster, G.; Wuilloud, J. [Muenster Univ. (Germany); Montvay, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Scholz, E.E. [Fermi National Accelerator Lab., Batavia, IL (United States)
2009-11-15
Results of a numerical simulation concerning the low-lying spectrum of four-dimensional N = 1 SU(2) Supersymmetric Yang-Mills (SYM) theory on the lattice with light dynamical gluinos are reported. We use the tree-level Symanzik improved gauge action and Wilson fermions with stout smearing of the gauge links in the Wilson-Dirac operator. The configurations are produced with the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithm. We performed simulations on lattices up to a size of 24{sup 3}.48 at {beta}=1.6. Using QCD units with the Sommer scale being set to r{sub 0}=0.5 fm, the lattice spacing is about a {approx_equal}0.09 fm, and the spatial extent of the lattice corresponds to 2.1 fm to control finite size effects. At the lightest simulated gluino mass our results indicate a mass for the lightest gluino-glue bound state, which is considerably heavier than the values obtained for its possible superpartners. Whether supermultiplets are formed remains to be studied in upcoming simulations. (orig.)
A QCD Model Using Generalized Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; SONG He-Shan; KOU Li-Na
2007-01-01
Generalized Yang-Mills theory has a covariant derivative,which contains both vector and scalar gauge bosons.Based on this theory,we construct a strong interaction model by using the group U(4).By using this U(4)generalized Yang-Mills model,we also obtain a gauge potential solution,which can be used to explain the asymptotic behavior and color confinement.
Higher derivative super Yang-Mills theories
Bergshoeff, E.; Rakowski, M.; Sezgin, E.
1987-01-01
The most general higher derivative Yang-Mills actions of the type (F^2 + Î±^2F^4) which are globally supersymmetric up to order Î±^2 in six- and ten-dimensional spacetimes are given. The F^4-terms turn out to occur in the combination Î±^2[tr F^4 - Â¼(tr F^2)^2], where the trace is over the Lorentz i
Quantum Yang-Mills theory: an overview of a programme
Milsted, Ashley
2016-01-01
We present an overview of a programme to understand the low-energy physics of quantum Yang-Mills theory from a quantum-information perspective. Our setting is that of the hamiltonian formulation of pure Yang-Mills theory in the temporal gauge on the lattice. Firstly, inspired by recent constructions for $\\mathbb{Z}/2\\mathbb{Z}$ lattice gauge theory, in particular, Kitaev's toric code, we describe the gauge-invariant sector of hilbert space by introducing a primitive quantum gate: the quantum parallel transporter. We then develop a nonabelian generalisation of laplace interpolation to present an ansatz for the ground state of pure Yang-Mills theory which interpolates between the weak- and strong-coupling RG fixed points. The resulting state acquires the structure of a tensor network, namely, a multiscale entanglement renormalisation ansatz, and allows for the efficient computation of local observables and Wilson loops. Various refinements of the tensor network are discussed leading to several generalisations. ...
Super Yang-Mills theory from nonlinear supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Shima, Kazunari, E-mail: shima@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology Fukaya, Saitama 369-0293 (Japan); Tsuda, Motomu, E-mail: tsuda@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology Fukaya, Saitama 369-0293 (Japan)
2010-04-05
The relation between a nonlinear supersymmetric (NLSUSY) theory and a SUSY Yang-Mills (SYM) theory is studied for N=3 SUSY in two-dimensional space-time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of cancellations among Nambu-Goldstone fermion self-interaction terms.
Exact, Schwarzschild-like solution for Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Singleton, D.
1995-04-01
Exploiting the connection between general relativity and Yang-Mills theory an exact, Schwarzchild-like solution is given for an SU(N) gauge field coupled to a scalar field in the Bogomolny, Prasad, Sommerfield limit. The SU(2) solution is found using the second order Euler-Lagrange formalism, while the SU(N) generalization is given using the first order Bogomolny formalism. In analogy with the Schwarzschild solution of general relativity, these Yang-Mills solutions possess an event horizon with respect to the SU(N) charge. It is conjectured that this may be the confinement mechanism for QCD, since just as a Schwarzschild black hole will permanently confine anything which carries the charge of general relativity (mass-energy), so this Yang-Mills solution will confine any particle which carries the SU(N) charge.
Field-dependent BRST transformations in Yang-Mills theory
Lavrov, Peter M
2013-01-01
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary R_xi gauges.
Field-dependent BRST transformations in Yang-Mills theory
Lavrov, Peter M.; Lechtenfeld, Olaf
2013-10-01
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely amount to a precise change in the gauge-fixing functional. This proves the independence of the vacuum functional under any field-dependent BRST transformation. We also give a formula for the transformation parameter functional which generates a prescribed change of gauge and evaluate it for connecting two arbitrary Rξ gauges.
Perturbation Theory of Massive Yang-Mills Fields
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
Coset space dimensional reduction of Einstein-Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Chatzistavrakidis, A. [Institute of Nuclear Physics, NCSR Demokritos, 15310 Athens (Greece); Physics Department, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Manousselis, P. [Physics Department, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece); Department of Engineering Sciences, University of Patras, 26110 Patras (Greece); Prezas, N. [Theory Unit, Physics Department, 1211 Geneva (Switzerland); Zoupanos, G.
2008-04-15
In the present contribution we extend our previous work by considering the coset space dimensional reduction of higher-dimensional Einstein-Yang-Mills theories including scalar fluctuations as well as Kaluza-Klein excitations of the compactification metric and we describe the gravity-modified rules for the reduction of non-abelian gauge theories. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
From twistor string theory to recursion relations
Spradlin, Marcus; Volovich, Anastasia
2009-10-01
Witten’s twistor string theory gives rise to an enigmatic formula known as the “connected prescription” for tree-level Yang-Mills scattering amplitudes. We derive a link representation for the connected prescription by Fourier transforming it to mixed coordinates in terms of both twistor and dual twistor variables. We show that it can be related to other representations of amplitudes by applying the global residue theorem to deform the contour of integration. For six and seven particles we demonstrate explicitly that certain contour deformations rewrite the connected prescription as the Britto-Cachazo-Feng-Witten representation, thereby establishing a concrete link between Witten’s twistor string theory and the dual formulation for the S matrix of the N=4 SYM recently proposed by Arkani-Hamed Other choices of integration contour also give rise to “intermediate prescriptions.” We expect a similar though more intricate structure for more general amplitudes.
S-duality in N=4 Yang-Mills theories
Girardello, L; Porrati, Massimo; Zaffaroni, A
1995-01-01
Evidence in favor of SL(2,Z) S-duality in N=4 supersymmetric Yang-Mills theories in four dimensions and with general compact, simple gauge groups is presented. (Contribution to the Proceedings of the Strings '95 conference, March 13-18, 1995, USC, and the Proceedings of the Trieste Conference on S-Duality and Mirror Symmetry June 5-9, 1995.)
Perturbation theory of massive Yang-Mills fields
Veltman, M.J.G.
1968-01-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Primitive diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possib
Topological susceptibility for the SU(3) Yang--Mills theory
DEFF Research Database (Denmark)
Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio
2004-01-01
We present the results of a computation of the topological susceptibility in the SU(3) Yang--Mills theory performed by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to c...
Spinors, strings, integrable models, and decomposed Yang-Mills theory
Ioannidou, Theodora; Jiang, Ying; Niemi, Antti J.
2014-07-01
This paper deals with various interrelations between strings and surfaces in three-dimensional ambient space, two-dimensional integrable models, and two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three-dimensional stringlike structures. Then its relation to the structure of the su_(2) Lie algebra valued Maurer-Cartan one-form is presented, while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is shown how the Lax pair of the integrable nonlinear Schrödinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation, and it is described how a spinor-based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schrödinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to properties of flat connections in a two-dimensional decomposed SU(2) Yang-Mills theory. In addition, the connection between the decomposed Yang-Mills and the Gauß-Codazzi equation that describes surfaces in three-dimensional ambient space is presented. In that context the relation between isothermic surfaces and integrable models is discussed. Finally, the utility of the Cartan approach to differential geometry is considered. In particular, the similarities between the Cartan formalism and the structure of both two-dimensional and four-dimensional decomposed SU(2) Yang-Mills theories are discussed, while the description of two-dimensional integrable models as embedded structures in the four-dimensional decomposed SU(2) Yang-Mills theory are presented.
Deconfinement in Yang-Mills Theory through Toroidal Compactification
Energy Technology Data Exchange (ETDEWEB)
Simic, Dusan; Unsal, Mithat; /Stanford U., Phys. Dept. /SLAC
2011-08-12
We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double-trace deformation of toroidally compactified Yang-Mills theory on R{sup 2} x S{sub L}{sup 1} x S{sub {beta}}{sup 1}. At large N, fixed-L, and arbitrary {beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic component of the quark-gluon plasma at RHIC.
Emergent Yang-Mills Theories from Universal Extra Dimensions
Chkareuli, J L
2016-01-01
We study emergent Yang-Mills theories which could origin from universal extra dimensions. Particularly, some vector field potential terms or polynomial vector field constraints introduced into five-dimensional non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional 4D gauge boson candidates. As a special signature, apart from conventional gauge couplings, there appear an infinite number of the properly suppressed direct multi-boson (multi-photon in particular) interaction couplings in emergent Yang-Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in these theories an internal symmetry is also appeared spontaneously broken to its diagonal subgroups. This breaking origins from the extra vector field components playing a role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar fie...
Spectroscopy of two dimensional N=2 Super Yang Mills theory
August, Daniel; Wipf, Andreas
2016-01-01
Albeit the standard model is the most successful model of particles physics, it still has some theoretical shortcomings, for instance the hierarchy problem, the absence of dark matter, etc. Supersymmetric extensions of the standard model could be a possible solution to these problems. One of the building blocks of these supersymmetric models are supersymmetric gauge theories. It is expected that they exhibit interesting features like confinement, chiral symmetry breaking, magnetic monopoles and the like. We present new results on N=2 Super Yang Mills theory in two dimensions. The lattice action is derived by a dimensional reduction of the N=1 Super Yang Mills theory in four dimensions. By preserving the R symmetry of the four dimensional model we can exploit Ward identities to fine tune our parameters of the model to obtain the chiral and supersymmetric continuum limit. This allows us to calculate the mass spectrum at the physical point and compare these results with effective field theories.
Regge trajectories in {N} = 2 supersymmetric Yang-Mills theory
Córdova, Clay
2016-09-01
We demonstrate that {N} = 2 supersymmetric non-Abelian gauge theories have towers of BPS particles obeying a Regge relation, J ˜ m 2, between their angular momenta, J, and their masses, m. For SU( N) Yang-Mills theories, we estimate the slope of these Regge trajectories using a non-relativistic quiver quantum mechanics model. Along the way, we also prove various structure theorems for the quiver moduli spaces that appear in the calculation.
Multiscale Monte Carlo equilibration: pure Yang-Mills theory
Endres, Michael G; Detmold, William; Orginos, Kostas; Pochinsky, Andrew V
2015-01-01
We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.
Asymptotic freedom of Yang-Mills theory with gravity
Folkerts, Sarah; Pawlowski, Jan M
2011-01-01
We study the high energy behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
Asymptotic freedom of Yang-Mills theory with gravity
Energy Technology Data Exchange (ETDEWEB)
Folkerts, Sarah, E-mail: Sarah.Folkerts@physik.uni-muenchen.de [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH (United Kingdom); Pawlowski, Jan M. [Institut f. Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); ExtreMe Matter Inst. EMMI, GSI, Planckstr. 1, 64291 Darmstadt (Germany)
2012-03-19
We study the behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
The local renormalization of super-Yang-Mills theories
Gillioz, Marc
2016-01-01
We show how to consistently renormalize $\\mathcal{N} = 1$ and $\\mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportional to derivatives of the holomorphic coupling. In the $\\mathcal{N} = 2$ case, this new action is exact at all orders in perturbation theory.
Magnetic Yang-Mills Theory of the Gluon Plasma
Baker, M
2009-01-01
We propose magnetic SU(N) pure gauge theory as an effective field theory describing the long distance nonperturbative magnetic response of the deconfined phase of Yang-Mills theory. The magnetic non-Abelian Lagrangian, unlike that of electrodynamics where there is exact electromagnetic duality, is not known explicitly, but here we regard the magnetic SU(N) Yang-Mills Lagrangian as the leading term in the long distance effective gauge theory of the plasma phase. In this treatment, which is applicable for a range of temperatures in the interval T_c < T < 3 T_c accessible in heavy ion experiments, formation of the magnetic energy profile around a spatial Wilson loop in the deconfined phase parallels the formation of an electric flux tube in the confined phase. We use the effective theory to calculate spatial Wilson loops and the magnetic charge density induced in the plasma by the corresponding color electric current loops. These calculations suggest that the deconfined phase of Yang-Mills theory has the p...
Currents and anomalies in topological Yang-Mills theory
Dahmen, H. D.; Marculescu, S.; Szymanowski, L.
1992-09-01
The quantum properties of topological Yang-Mills theory are investigated in the light of the N = 2 supersymmetry observed in flat space. We construct a unique system of covariantly (partially) conserved currents which develop anomalies while preserving BRS invariance of the theory. In particular, the one-loop renormalized energy-momentum tensor is free of purely gravitational contributions and can be written as a BRS variation. We study the consequences of changing the renormalization prescriptions inherited from the N = 2 supersymmetry to those consistent with BRS. Most of our conclusions are verified by explicit calculations. As a byproduct we derive the formula of Atiyah, Hitchin and Singer for the dimension of the moduli space of self-dual Yang-Mills fields. Finally strong arguments are given that the full system of Donaldson polynomials and the quantum BRS current are not renormalized beyond one-loop.
A Curious Relation Between Gravity and Yang-Mills Theories
Baulieu, L
2000-01-01
We find that Euclidian or Minkowski gravity in d dimensions can be formally expressed as the restriction to a slice of a supersymmetric Yang-Mills theory in d+1 dimensions with SO(d+1), SO(d,1) or SO(d-1,2) internal symmetry. We suggest that renormalization effects in the bulk imply a contraction of the latter symmetry into the Poincare group ISO(d) or ISO(d-1,1).
Induced mass in N=2 super Yang-Mills theories
Araújo-Diniz, S; Diniz, Sortelano A.; Piguet, Olivier
2003-01-01
The masses of the matter fields of N=2 Super-Yang-Mills theories can be defined as parameters of deformed supersymmetry transformations. The formulation used involves central charges for the matter fields. The explicit form of the deformed supersymmetry transformations and of the invariant Lagrangian in presence of the gauge supermultiplet are constructed. This works generalizes a former one, due to the same authors, which presented the free matter case.
New Results on N=4 SuperYang-Mills Theory
Baulieu, L; Baulieu, Laurent; Bossard, Guillaume
2005-01-01
The N=4 SuperYang--Mills theory is covariantly determined by a U(1) \\times SU(2) \\subset SL(2,R) \\times SU(2) internal symmetry and two scalar and one vector BRST topological symmetry operators. This determines an off-shell closed sector of N=4 SuperYang-Mills, with 6 generators, which is big enough to fully determine the theory, in a Lorentz covariant way. This reduced algebra derives from horizontality conditions in four dimensions. The horizontality conditions only depend on the geometry of the Yang-Mills fields. They also descend from a genuine horizontality condition in eight dimensions. In fact, the SL(2,R) symmetry is induced by a dimensional reduction from eight to seven dimensions, which establishes a ghost-antighost symmetry, while the SU(2) symmetry occurs by dimensional reduction from seven to four dimensions. When the four dimensional manifold is hyperKahler, one can perform a twist operation that defines the N=4 supersymmetry and its SL(2,H)\\sim SU(4) R-symmetry in flat space. (For defining a TQ...
Super-Yang-Mills theories on S4 x R
Kim, Jungmin; Lee, Kimyeong; Park, Jaemo
2014-01-01
We construct super-Yang-Mills theories on S4 x R, S4 x S1 and S4 x interval with the field content of maximal SYM, coupled to boundary degrees in the last case. These theories provide building blocks of the `5d uplifts' of gauge theories on S4, obtained by compactifying the 6d (2,0) theory. We pay special attention to the N=2* theory on S4. We also explain how to construct maximal SYM on S5 x R, and clarify when SYM theories can be put on S^n x R.
Directory of Open Access Journals (Sweden)
A. G. Sergeev
1986-01-01
Full Text Available We describe briefly the basic ideas and results of the twistor theory. The main points: twistor representation of Minkowsky space, Penrose correspondence and its geometrical properties, twistor interpretation of linear massless fields, Yang-Mills fields (including instantons and monopoles and Einstein-Hilbert equations.
Nonperturbative Results for Yang-Mills Theories
DEFF Research Database (Denmark)
Sannino, Francesco; Schechter, Joseph
2010-01-01
of the coupling constant, g. First it is noted, using dimensional analysis, that physical quantities behave smoothly as one travels from one side of the pole to the other. Then it is argued that the form of the integrated beta function g(μ), where μ is the mass scale, determines the mass gap of the theory...
Ward identity implies recursion relations in Yang-Mills theory
Chen, Gang
2012-07-01
The Ward identity in gauge theory constrains the behavior of the amplitudes. We discuss the Ward identity for amplitudes with a pair of shifted lines with complex momenta. This will induce a recursion relation identical to Britto-Cachazo-Feng-Witten recursion relations at the finite poles of the complexified amplitudes. Furthermore, according to the Ward identity, it is also possible to transform the boundary term into a simple form, which can be obtained by a new recursion relation. For the amplitude with one off-shell line in pure Yang-Mills theory, we find this technique is effective for obtaining the amplitude even when there are boundary contributions.
Yang-Mills Theories at High-Energy Accelerators
Sterman, George
2016-01-01
I'll begin with a brief review of the triumph of Yang-Mills theory at particle accelerators, a development that began some years after their historic paper. This story reached a culmination, or at least local extremum, with the discovery at the Large Hadron Collider of a Higgs-like scalar boson in 2012. The talk then proceeds to a slightly more technical level, discussing how we derive predictions from the gauge field theories of the Standard Model and its extensions for use at high energy accelerators.
N=1 supersymmetric Yang-Mills theory on the lattice
Energy Technology Data Exchange (ETDEWEB)
Piemonte, Stefano
2015-04-08
Supersymmetry (SUSY) relates two classes of particles of our universe, bosons and fermions. SUSY is considered nowadays a fundamental development to explain many open questions about high energy physics. The N=1 super Yang-Mills (SYM) theory is a SUSY model that describes the interaction between gluons and their fermion superpartners called ''gluinos''. Monte Carlo simulations on the lattice are a powerful tool to explore the non-perturbative dynamics of this theory and to understand how supersymmetry emerges at low energy. This thesis presents new results and new simulations about the properties of N=1 SYM, in particular about the phase diagram at finite temperature.
Integrability in N=4 super Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Eden, B. [ITF and Spinoza Institute, University of Utrecht, Minnaertgebouw, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2008-10-15
We use the Bethe ansatz to calculate the cusp anomalous dimension in planar N=4 super Yang-Mills theory as an exact function of the coupling constant. The calculation allows us to fix the remaining ambiguities in the integrable system describing the spectrum of operators/string energy levels in the AdS/CFT correspondence. The cusp anomalous dimension is not affected by finite size effects, which in general remain ill-understood. We suggest a method for computing the lowest example of an anomalous dimension modified by such corrections.
Width of the confining string in Yang-Mills theory.
Gliozzi, F; Pepe, M; Wiese, U-J
2010-06-11
We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)D SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multilevel algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher-order terms in the effective string action are calculated analytically. They accurately fit the numerical data.
Branes from Moyal Deformation Quantization of Generalized Yang Mills Theories
Castro, C
1999-01-01
It is shown that a Moyal deformation quantization of the SO(4k) Generalized Yang-Mills (GYM) theory action in D=4k dimensions, for spacetime independent field configurations, in the $\\hbar \\to 0$ limit, yields the Dolan-Tchrakian p-brane action after fixing the conformal and world volume reparametrization invariance, associated with the p-brane world volume dimension p+1=4k, embedded in a D=4k target spacetime background. The gauge fields/target spacetime coordinates correspondence is required but no large N limit is necessary.
Callan-Symanzik approach to infrared Yang-Mills theory
Directory of Open Access Journals (Sweden)
Weber Axel
2014-01-01
Full Text Available Dyson-Schwinger equations are the most common tool for the determination of the correlation functions of Landau gauge Yang-Mills theory in the continuum, in particular in the infrared regime. We shall argue that the use of Callan-Symanzik renormalization group equations has distinctive advantages over the Dyson-Schwinger equations, in particular for the vertex functions. We present a generalization of the infrared safe renormalization scheme proposed by Tissier and Wschebor in 2011. The comparison with the existing lattice data for the gluon and ghost propagators can be used to determine the most appropriate renormalization scheme.
Transport coefficients in Yang-Mills theory and QCD
Energy Technology Data Exchange (ETDEWEB)
Strodthoff, Nils; Christiansen, Nicolai; Haas, Michael [Institut fuer Theoretische Physik, Heidelberg (Germany); Pawlowski, Jan M. [Institut fuer Theoretische Physik, Heidelberg (Germany); ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2015-07-01
We calculate the shear viscosity over entropy density ratio η/s in Yang-Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of η/s over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently we provide a first estimate for η/s in QCD.
Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems
D'Hoker, Eric; Phong, D. H.
Introduction Supersymmetry and the Standard Model Supersymmetry and Unification of Forces Supersymmetric Yang-Mills Dynamics Supersymmetric Yang-Mills in 4 Dimensions Supersymmetry Algebra Massless Particle Representations Massive Particle Representations Field Contents of Supersymmetric Field Theories N = 1 Supersymmetric Lagrangians N = 1 Superfield Methods Irreducible Superfields of N = 1 General N = 1 Susy Lagrangians via Superfields Renormalizable N = 2,4 Susy Lagrangians N = 2 Superfield Methods: Unconstrained Superspace N = 2 Superfield Methods: Harmonic/Analytic Superspaces Seiberg-Witten Theory Wilson Effective Couplings and Actions Holomorphicity and Nonrenormalization Low Energy Dynamics of N = 2 Super-Yang-Mills Particle and Field Contents Form of the N = 2 Low Energy Effective Lagrangian Physical Properties of the Prepotential Electric-Magnetic Duality Monodromy via Elliptic Curves for SU(2) Gauge Group Physical Interpretation of Singularities Hypergeometric Function Representation More General Gauge Groups, Hypermultiplets Model of Riemann Surfaces Identifying Seiberg-Witten and Riemann Surface Data SU(N) Gauge Algebras, Fundamental Hypermultiplets Classical Gauge Algebras, Fundamental Hypermultiplets Mechanical Integrable Systems Lax Pairs with Spectral Parameter-Spectral Curves The Toda Systems The Calogero-Moser Systems for SU(N) Relation between Calogero-Moser and Toda for SU(N) Relations with KdV and KP Systems Calogero-Moser Systems for General Lie Algebras Scaling of Calogero-Moser to Toda for General Lie Algebras Calogero-Moser Lax Pairs for General Lie Algebras Lax Pairs with Spectral Parameter for Classical Lie Algebras The General Ansatz Lax Pairs for Untwisted Calogero-Moser Systems Lax Pairs for Twisted Calogero-Moser Systems Scaling Limits of Lax Pairs Super-Yang-Mills and Calogero-Moser Systems Correspondence of Seiberg-Witten and Integrable Systems Calogero-Moser and Seiberg-Witten Theory for SU(N) Four Fundamental Theorems Partial
Topological susceptibility for the SU(3) Yang--Mills theory
Del Debbio, L; Pica, C; Debbio, Luigi Del; Giusti, Leonardo; Pica, Claudio
2005-01-01
We present the results of a computation of the topological susceptibility in the SU(3) Yang--Mills theory performed by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi=(191 \\pm 5 MeV)^4 if F_K is used to set the scale. Our result supports the Witten--Veneziano explanation for the large mass of the eta'.
Emergent Yang-Mills theories from universal extra dimensions
Chkareuli, J. L.; Kepuladze, Z.
2017-02-01
We study emergent Yang-Mills theories which could origin from universal extra dimensions. Particularly, some vector field potential terms or polynomial vector field constraints introduced into five-dimensional (5D) non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional four-dimensional (4D) gauge boson candidates. As a special signature, apart from conventional gauge couplings, there appear an infinite number of the properly suppressed direct multi-boson (multi-photon in particular) interaction couplings in emergent Yang-Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in these theories, an internal symmetry also appeared spontaneously broken to its diagonal subgroups. This breaking originates from the extra vector field components playing the role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar field multiplet. Remarkably, when applied to Grand Unified Theories (GUTs), this results in an automatic breakdown of emergent GUTs down to the Standard Model (SM) just at the 5D Lorentz violation scale M.
Lifting the Gribov ambiguity in Yang-Mills theories
Serreau, Julien
2013-01-01
We report on the work presented in Phys. Lett. B712 (2012) 97, where a new one-parameter family of Landau gauges has been proposed for Yang-Mills theories, inspired by an analogy with disordered systems in condensed matter physics. This is based on a particular average over Gribov copies which avoids the Neuberger zero problem of the standard Fadeev-Popov construction. The proposed gauge fixing can be formulated as a local renormalizable field theory in four dimensions and is well-suited for analytical calculations. A remarkable feature is that, for what concerns the calculation of ghost and gauge field correlators, the gauged-fixed action is perturbatively equivalent to a simple massive extension of the Faddeev-Popov action. The renormalization group flow of the theory admits infrared safe trajectories, with no Landau pole. The one-loop calculations of Yang-Mills two-point correlators show remarkable agreement with lattice simulations all the way to the deep infrared.
Confinement in a three-dimensional Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Frasca, Marco
2017-04-15
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in the literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group. (orig.)
Confinement in a three-dimensional Yang-Mills theory
Frasca, Marco
2017-04-01
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in the literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group.
Confinement in a three-dimensional Yang-Mills theory
Frasca, Marco
2016-01-01
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a confining theory. The potential we obtain agrees fairly well with preceding findings in literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depends on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory.
Effective Lagrangian of SU(2) Yang-Mills Theory in the Presence of Fermions
Institute of Scientific and Technical Information of China (English)
FAN Ji-Yang; JIANG Ying; ZHU Zhong-Yuan
2002-01-01
We derive the one-loop effective action of SU(2) Yang Mills theory in the presence of fermions in the lowenergy limit. This result is presented by separating the topological degrees, which describe the non-Abelian monopolesfrom the dynamical degrees of the gauge potential and integrate out all the dynamical degrees and fermions in SU(2)Yang-Mills theory.
Lifting the Gribov ambiguity in Yang-Mills theories
Energy Technology Data Exchange (ETDEWEB)
Serreau, J., E-mail: serreau@apc.univ-paris7.fr [APC, AstroParticule et Cosmologie, Universite Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris, Sorbonne Paris Cite, 10, rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13 (France); Tissier, M. [LPTMC, Laboratoire de Physique Theorique de la Matiere Condensee, CNRS UMR 7600, Universite Pierre et Marie Curie, boite 121, 4 pl. Jussieu, 75252 Paris Cedex 05 (France)
2012-05-30
We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Faddeev-Popov construction. The resulting gauge-fixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Faddeev-Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some - including physically relevant - range of values of the renormalized parameters.
Lifting the Gribov ambiguity in Yang-Mills theories
Serreau, Julien
2012-01-01
We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Fadeev-Popov construction. The resulting gauge-fixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Fadeev-Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some - including physically relevant - range of values of the renormalized parameters.
Lifting the Gribov ambiguity in Yang-Mills theories
Serreau, J.; Tissier, M.
2012-05-01
We propose a new one-parameter family of Landau gauges for Yang-Mills theories which can be formulated by means of functional integral methods and are thus well suited for analytic calculations, but which are free of Gribov ambiguities and avoid the Neuberger zero problem of the standard Faddeev-Popov construction. The resulting gauge-fixed theory is perturbatively renormalizable in four dimensions and, for what concerns the calculation of ghost and gauge field correlators, it reduces to a massive extension of the Faddeev-Popov action. We study the renormalization group flow of this theory at one-loop and show that it has no Landau pole in the infrared for some - including physically relevant - range of values of the renormalized parameters.
Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
DEFF Research Database (Denmark)
Caron-Huot, Simon; Henn, Johannes M.
2014-01-01
he classical Kepler problem, as well as its quantum mechanical version, the hydrogen atom, enjoys a well-known hidden symmetry, the conservation of the Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there a relativistic quantum field theory extension that preserves...... this symmetry? In this Letter we show that the answer is positive: in the nonrelativistic limit, we identify the dual conformal symmetry of planar N=4 super Yang-Mills theory with the well-known symmetries of the hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute...... the spectrum of bound states of massive W bosons in the theory. We perform nontrivial tests of this setup at weak and strong coupling and comment on the possible extension to arbitrary values of the coupling....
Perturbative study of Yang-Mills theory in the infrared
Siringo, Fabio
2015-01-01
Pure Yang-Mills SU(N) theory is studied in four dimensional space and Landau gauge by a double perturbative expansion based on a massive free-particle propagator. By dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the original Lagrangian. The emerging perturbation theory is safe in the infrared and shares the same behaviour of the standard perturbation theory in the UV. At one-loop, Gluon and ghost propagators are found in excellent agreement with the data of lattice simulations and an infrared-safe running coupling is derived. A natural scale m=0.5-0.6 GeV is extracted from the data for N=3.
Yang-Mills Theory and the ABC Conjecture
He, Yang-Hui; Probst, Malte; Read, James
2016-01-01
We establish a precise correspondence between the ABC Conjecture and N=4 super-Yang-Mills theory. This is achieved by combining three ingredients: (i) Elkies' method of mapping ABC-triples to elliptic curves in his demonstration that ABC implies Mordell/Faltings; (ii) an explicit pair of elliptic curve and associated Belyi map given by Khadjavi-Scharaschkin; and (iii) the fact that the bipartite brane-tiling/dimer model for a gauge theory with toric moduli space is a particular dessin d'enfant in the sense of Grothendieck. We explore this correspondence for the highest quality ABC-triples as well as large samples of random triples. The Conjecture itself is mapped to a statement about the fundamental domain of the toroidal compactification of the string realization of N=4 SYM.
Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
Anastasiou, C; Dixon, L; Kosower, D A
2003-01-01
The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N_c L-loop amplitudes should be simple enough to allow a resummation to all orders.
Lifshitz black holes in Einstein-Yang-Mills theory
Devecioglu, Deniz Olgu
2014-01-01
We find that the four dimensional cosmological Einstein-Yang-Mills theory with $SU(2)$ gauge group admits Lifshitz spacetime as a base solution for the dynamical exponent $z>1$. Motivated by this, we next demonstrate numerically that the field equations admit black hole solutions which behave regularly on the horizon and at spatial infinity for different horizon topologies. The solutions depend on one parameter, the strength of the gauge field at the horizon, which is fine-tuned to capture the Lifshitz asymptotics at infinity. We also discuss the behavior of solutions and the change in Hawking temperature for black holes that are large or small with respect to the length scale $L$, which is itself fixed by the value of the cosmological constant.
Function group approach to unconstrained Hamiltonian Yang-Mills theory
Salmela, A
2004-01-01
Starting from the temporal gauge Hamiltonian for classical pure Yang-Mills theory with the gauge group SU(2) a canonical transformation is initiated by parametrising the Gauss law generators with three new canonical variables. The construction of the remaining variables of the new set proceeds through a number of intermediate variables in several steps, which are suggested by the Poisson bracket relations and the gauge transformation properties of these variables. The unconstrained Hamiltonian is obtained from the original one by expressing it in the new variables and then setting the Gauss law generators to zero. This Hamiltonian turns out to be local and it decomposes into a finite Laurent series in powers of the coupling constant.
Residual Confinement in High-Temperature Yang-Mills Theory
Maas, A; Gruter, B; Alkofer, R; Maas, Axel; Wambach, Jochen; Gruter, Burghard; Alkofer, Reinhard
2004-01-01
The infrared behavior of Landau gauge gluon and ghost propagators are investigated in Yang-Mills theory at non-vanishing temperatures. Self-consistent solutions are presented for temperatures below the presumed phase transition and in the infinite temperature limit. Gluon confinement is manifest in the infrared behavior of these propagators. As expected confinement prevails below the phase transition. In the infinite-temperature limit a qualitative change is observed: the chromoelectric sector exhibits a near-perturbative behavior while long-range chromomagnetic interactions, mediated by soft ghost modes, are still present. The latter behavior is in agreement with corresponding lattice results. It furthermore implies that part of the gluons are still confined.
Residual Confinement in High-Temperature Yang-Mills Theory
Maas, A.; Wambach, J.; Grüter, B.; Alkofer, R.
2005-01-01
The infrared behavior of Landau gauge gluon and ghost propagators are investigated in Yang-Mills theory at non-vanishing temperatures. Self-consistent solutions are presented for temperatures below the presumed phase transition and in the infinite temperature limit. Gluon confinement is manifest in the infrared behavior of these propagators. As expected confinement prevails below the phase transition. In the infinite-temperature limit a qualitative change is observed: the chromoelectric sector exhibits a near-perturbative behavior while long-range chromomagnetic interactions, mediated by soft ghost modes, are still present. The latter behavior is in agreement with corresponding lattice results. It furthermore implies that part of the gluons are still confined.
Thermal Yang-Mills theory in the Einstein universe
Avramidi, Ivan G.; Collopy, Samuel
2012-09-01
We study the stability of a non-Abelian chromomagnetic vacuum in Yang-Mills theory in Euclidean Einstein universe S1 × S3. We assume that the gauge group is a simple compact group G containing the group SU(2) as a subgroup and consider static covariantly constant gauge fields on S3 taking values in the adjoint representation of the group G and forming a representation of the group SU(2). We compute the heat kernel for the Laplacian acting on fields on S3 in an arbitrary representation of SU(2) and use this result to compute the heat kernels for the gluon and the ghost operators and the one-loop effective action. We show that the only configuration of the covariantly constant Yang-Mills background that is stable is the one that contains only spinor (fundamental) representations of the group SU(2); all other configurations contain negative modes and are unstable. For the stable configuration we compute the asymptotics of the effective action, the energy density, the entropy and the heat capacity in the limits of low/high temperature and small/large volume and show that the energy density has a non-trivial minimum at a finite value of the radius of the sphere S3. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.
Infra-red structure of Yang-Mills theories
Cvitanovic, P
1976-01-01
An analysis of QCD magnetic moment shows that all infra-red divergences are contained in the coupling constant renormalization. They are controlled by the renormalization function beta for the pure Yang-Mills field. (21 refs).
Yang-Mills theory in terms of gauge invariant dual variables
Diakonov, D
2002-01-01
Quantum Yang-Mills theory and the Wilson loop can be rewritten identically in terms of local gauge-invariant variables being directly related to the metric of the dual space. In this formulation, one reveals a hidden high local symmetry of the Yang-Mills theory, which mixes up fields with spins up to J=N for the SU(N) gauge group. In the simplest case of the SU(2) group the dual space seems to tend to the de Sitter space in the infrared region. This observation suggests a new mechanism of gauge-invariant mass generation in the Yang-Mills theory.
Geometry and off-shell nilpotency for N = 1 supersymmetric Yang-Mills theory
Meziane, A
2015-01-01
We show that for N = 1 supersymmetric Yang-Mills theory it is possible to build an off-shell nilpotent BRST and anti-BRST algebra in terms of a BRST superspace formalism. This is based on the introduction of the basic fields of the quantized theory together with an auxiliary real field via the lowest components of the superfield components of a superYang-Mills connection. Here, the associated supercurvature is constrained by horizontality conditions as in ordinary Yang-Mills theory. We also show how the off-shell BRST-invariant quantum action can be constructed starting from a gauge-fixed superaction.
Non-perturbative Solutions to N=2 Supersymmetric Yang-Mills Theories Progress and Perspective
Ohta, Y
1999-01-01
This note reviews the progress on the low energy dynamics of N=2 supersymmetric Yang-Mills theories after the works of Seiberg and Witten. Specifically, the theory of prepotential for non-specialists is reviewed.
N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory
Chicherin, Dmitry
2017-02-10
We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N=2 gauge and hypermultiplet matter theories. In the twin paper \\cite{twin} we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N=4 stress-tensor supermultiplet.
N = 4 super-Yang-Mills in LHC superspace part I: classical and quantum theory
Chicherin, Dmitry; Sokatchev, Emery
2017-02-01
We present a formulation of the maximally supersymmetric N = 4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N =4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N = 4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N = 2 gauge and hypermultiplet matter theories. In the twin paper arXiv:1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N = 4 stress-tensor supermultiplet.
N=4 super-Yang-Mills in LHC superspace. Part I: Classical and quantum theory
Chicherin, Dmitry
2016-01-01
We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N=2 gauge and hypermultiplet matter theories. In the twin paper \\cite{twin} we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N=4 stress-tensor supermultiplet.
Stabilization of the Yang-Mills chaos in non-Abelian Born-Infeld theory
Galtsov, D V
2003-01-01
We investigate dynamics of the homogeneous time-dependent SU(2) Yang-Mills fields governed by the non-Abelian Born-Infeld lagrangian which arises in superstring theory as a result of summation of all orders in the string slope parameter $\\alpha'$. It is shown that generically the Born-Infeld dynamics is less chaotic than that in the ordinary Yang-Mills theory, and at high enough field strength the Yang-Mills chaos is stabilized. More generally, a smothering effect of the string non-locality on behavior of classical fields is conjectured.
Form Invariance, Topological Fluctuations and Mass Gap of Yang-Mills Theory
Qian, Yachao
2016-01-01
In order to have a new perspective on the long-standing problem of the mass gap in Yang-Mills theory, we study the quantum Yang-Mills theory in the presence of topologically nontrivial backgrounds in this paper. The topologically stable gauge fields are constrained by the form invariance condition and the topological properties. Obeying these constraints, the known classical solutions to the Yang-Mills equation in the 3- and 4-dimensional Euclidean spaces are recovered, and the other allowed configurations form the nontrivial topological fluctuations at quantum level. Together, they constitute the background configurations, upon which the quantum Yang-Mills theory can be constructed. We demonstrate that the theory mimics the Higgs mechanism in a certain limit and develops a mass gap at semi-classical level on a flat space with finite size or on a sphere.
A novel renormalizable representation of the Yang-Mills theory
Dubin, A Yu
2007-01-01
For a generic gauge-invariant correlator _{A}, we reformulate the standard D=4 Yang-Mills theory as a renormalizable system of two interacting fields a_{\\mu} and B_{\\mu} which faithfully represent high- and low-energy degrees of freedom of the single gauge field A_{\\mu} in the original formulation. It opens a possibility to synthesize an infrared-nonsingular weak-coupling series, employed to integrate over a_{\\mu} for a given background B_{\\mu}, with qualitatively different methods. These methods are to be applied to evaluate the resulting (after the a_{\\mu}-integration) representation of _{A} in terms of gauge-invariant generically non-local low-energy observables, like Wilson loops. The latter observables are averaged over B_{\\mu} with respect to a gauge-invariant Wilsonean effective action S_{eff}[B]. To avoid a destructive dissipation between the high- and low-energy excitations, we implement a specific fine-tuning of the interaction between the pair of the fields: prior to the integration over B_{\\mu}, t...
Model of Polyakov duality: String field theory Hamiltonians from Yang-Mills theories
Periwal, Vipul
2000-08-01
Polyakov has conjectured that Yang-Mills theory should be equivalent to a noncritical string theory. I point out, based on the work of Marchesini, Ishibashi, Kawai and collaborators, and Jevicki and Rodrigues, that the loop operator of the Yang-Mills theory is the temporal gauge string field theory Hamiltonian of a noncritical string theory. The consistency condition of the string interpretation is the zig-zag symmetry emphasized by Polyakov. I explicitly show how this works for the one-plaquette model, providing a consistent direct string interpretation of the unitary matrix model for the first time.
N=4 Super-Yang-Mills Theory, QCD and Collider Physics
Bern, Z; Kosower, D A
2004-01-01
We review how (dimensionally regulated) scattering amplitudes in N=4 super-Yang-Mills theory provide a useful testing ground for perturbative QCD calculations relevant to collider physics, as well as another avenue for investigating the AdS/CFT correspondence. We describe the iterative relation for two-loop scattering amplitudes in N=4 super-Yang-Mills theory found in C. Anastasiou et al., Phys. Rev. Lett. 91:251602 (2003), and discuss recent progress toward extending it to three loops.
One-dimensional structures behind twisted and untwisted super Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Baulieu, Laurent [CERN, Geneve (Switzerland). Theoretical Div.; Toppan, Francesco, E-mail: baulieu@lpthe.jussieu.f, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
2010-07-01
We give a one-dimensional interpretation of the four-dimensional twisted N = 1 super Yang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 super Yang-Mills theory. (author)
Park, J S
1992-01-01
We re-examine the geometry and algebraic structure of BRST's of Topological Yang-Mills theory based on the universal bundle formalism of Atiyah and Singer. This enables us to find a natural generalization of the {\\it Russian formula and descent equations\\/}, which can be used as algebraic method to find the non-Abelian anomalies counterparts in Topological Yang-Mills theory. We suggest that the presence of the non-Abelian anomaly obstructs the proper definition of Donaldson's invariants.
The deconfinement phase transition in Yang-Mills theory with general Lie group G
Holland, K; Wiese, U J
2004-01-01
We present numerical results for the deconfinement phase transition in Sp(2) and Sp(3) Yang-Mills theories in (2+1)-D and (3+1)-D. We then make a conjecture on the order of this phase transition in Yang-Mills theories with general Lie groups G = SU(N), SO(N), Sp(N) and with exceptional groups G = G(2), F(4), E(6), E(7), E(8).
Topological Quantization of Instantons in SU(2) Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
ZHONG Wo-Jun; DUAN Yi-Shi
2008-01-01
By decomposing SU(2) gauge potential in four-dimensional Euclidean SU(2) Yang-Mills theory in a new way,we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree.It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang-Mills theory.
Integrability in Yang-Mills theory on the light cone beyond leading order
Belitsky, A V; Müller, D
2004-01-01
The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that while integrability is broken for matter in the fundamental representation of the SU(3) gauge group, for the adjoint SU(N_c) matter it survives the conformal symmetry breaking and persists in supersymmetric N=1, N=2 and N=4 Yang-Mills theories.
A U(4) QCD Model Using Generalized Yang-Mills Theory
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; ZHONG Hai-Yang
2008-01-01
Generalized Yang-Mills theory has a covariant derivative which contains both vector and pseudoscalar gauge bosons.Based on this theory,we construct a U(4) strong interaction model By using this U(4) generalized Yang-Mills model,we obtain that mesons can be realized as the colorless pseudoscalar gauge bosons.We also obtain a gauge potential solution which can be used to explain the asymptotic behavior and color confinement.
One-dimensional structures behind twisted and untwisted superYang-Mills theory
Baulieu, Laurent
2011-01-01
We give a one-dimensional interpretation of the four-dimensional twisted N=1 superYang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N=1 superYang-Mills theory.
SU(2) Yang-Mills Theory: Waves, Particles, and Quantum Thermodynamics
Hofmann, Ralf
2016-01-01
We elucidate how Quantum Thermodynamics at temperature $T$ emerges from pure and classical SU(2) Yang-Mills theory on a four-dimensional Euclidean spacetime slice $S_1\\times {\\bf R}^3$. The concept of a (deconfining) thermal ground state, composed of certain solutions to the fundamental, classical Yang-Mills equation, allows for a unified addressation of both (classical) wave- and (quantum) particle-like excitations thereof.
A Unified Field Theory of Gravity, Electromagnetism, and the Yang-Mills Gauge Field
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold S4 via the connection, with the general- ized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.
Surface-Invariants in 2D Classical Yang-Mills Theory
Díaz, R; Leal, L; D\\'{\\i}az, Rafael; Leal, Lorenzo
2006-01-01
We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to non dynamical particles carrying chromo-electric charge, and by means of a perturbative scheme, we obtain the first two contributions to the on shell action, which are area-invariants. A geometrical interpretation of these invariants is given.
Observables in Topological Yang-Mills Theories With Extended Shift Supersymmetry
Constantinidis, C P; Spalenza, W; Constantinidis, Clisthenis P.; Piguet, Olivier; Spalenza, Wesley
2006-01-01
We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator.
Linear Broadening of the Confining String in Yang-Mills Theory at Low Temperature
Gliozzi, F; Wiese, U -J
2010-01-01
The logarithmic broadening predicted by the systematic low-energy effective field theory for the confining string has recently been verified in numerical simulations of (2+1)-d SU(2) lattice Yang-Mills theory at zero temperature. The same effective theory predicts linear broadening of the string at low non-zero temperature. In this paper, we verify this prediction by comparison with very precise Monte Carlo data. The comparison involves no additional adjustable parameters, because the low-energy constants of the effective theory have already been fixed at zero temperature. It yields very good agreement between the underlying Yang-Mills theory and the effective string theory.
Composite Operators in the Twistor Formulation of $\\mathcal{N}=4$ SYM Theory
Koster, Laura; Staudacher, Matthias; Wilhelm, Matthias
2016-01-01
We incorporate gauge-invariant local composite operators into the twistor-space formulation of $\\mathcal{N}=4$ Super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many interaction vertices and we argue that the same applies to composite operators. To test our definition of the local composite operators in twistor space, we compute several corresponding form factors, thereby also initiating the study of form factors using the position twistor-space framework. Throughout this letter, we use the composite operator built from two identical complex scalars as a pedagogical example; we treat the general case in a follow-up paper.
Fifty Years of Yang-Mills Theory and my Contribution to it
Jackiw, Roman W
2004-01-01
On the fiftieth anniversary of Yang-Mills theory, I review the contribution to its understanding by my collaborators and me. Contents: 1.Gauge Theories and Quantum Anomalies; 2.Mathematical Connections; 3. Gauge Field Dynamics other than Yang-Mills; 4. Gauge Formalism for General Relativity Variables; A. Christoffel connection as a gauge potential, B. Gravitational Chern-Simons term from gauge theory Chern-Simons term, C. Coordinate transformations in general relativity and gauge theory, (i) Response to changes in coordinates (ii) Invariant fields and constants of motion. References.
Nonsymmetric unified theory of gravitation, electromagnetism and Yang-Mills field
Energy Technology Data Exchange (ETDEWEB)
Ragusa, S [Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, 13560-970 Sao Carlos, SP (Brazil)
2002-12-07
The recently studied new variation of Einstein's metric nonsymmetric unified field theory of gravitation and electromagnetism is enlarged to include the Yang-Mills field theory. It is shown that the antisymmetric part of the metric tensor, now a 2x2 matrix, can be made to describe both a field obeying Maxwell's equations and a field obeying Yang-Mills's field equations in the flat space linear approximation, thereby making its identification with the sum of a generalized electromagnetic and isotopic field strength tensors a possibly consistent procedure. The theory is shown to be free of unphysical ghost-negative energy radiative modes even when expanded on a curved Riemannian background. The Einstein-Maxwell-Yang-Mills theory is contained in the first approximation of the field equations on a curved general relativity background.
Supersymmetric Yang-Mills theory as higher Chern-Simons theory
Sämann, Christian; Wolf, Martin
2017-07-01
We observe that the string field theory actions for the topological sigma models describe higher or categorified Chern-Simons theories. These theories yield dynamical equations for connective structures on higher principal bundles. As a special case, we consider holomorphic higher Chern-Simons theory on the ambitwistor space of four-dimensional space-time. In particular, we propose a higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory.
Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory
Lopez-Ruiz, Miguel Angel; Liao, Jinfeng
2016-01-01
The mechanism of confinement in Yang-Mills theories remains a challenge to our understanding of nonperturbative gauge dynamics. While it is widely perceived that confinement may arise from chromo-magnetically charged gauge configurations with nontrivial topology, it is not clear what types of configurations could do that and how, in pure Yang-Mills and QCD-like (non-supersymmetric) theories. Recently a promising approach has emerged, based on statistical ensembles of dyons/anti-dyons that are constituents of instanton/anti-instanton solutions with nontrivial holonomy where the holonomy plays a vital role as an effective "Higgsing" mechanism. We report a thorough numerical investigation of the confinement dynamics in SU(2) Yang-Mills theory by constructing such a statistical ensemble of correlated instanton-dyons.
Plane wave matrix theory vs. N=4 D=4 super Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Kim, N. [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Golm (Germany)
2004-06-01
A mass deformed, supersymmetric, Yang-Mills quantum mechanics has been introduced recently as the matrix model of M-theory on plane-wave backgrounds. Here we point out that the massive matrix model can be obtained as a dimensional reduction of N=4, D=4 Super Yang-Mills theory on S{sup 3}. The hamiltonian of the matrix model can be matched with the dilatation operator of the conformal field theory, and we discuss how they behave in the perturbative computations. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Quantum Metamorphosis of Conformal Transformation in D3-Brane Yang-Mills Theory
Jevicki, A; Yoneya, T
1998-01-01
We show how the linear special conformal transformation in four-dimensional N=4 super Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti-de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS supergravity and super conformal Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence.
Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice
Energy Technology Data Exchange (ETDEWEB)
Shibata, Akihiro [Computing Research Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 (Japan); Kondo, Kei-Ichi; Shinohara, Toru [Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522 (Japan); Kato, Seikou [Fukui National College of Technology, Sabae 916-8507 (Japan)
2016-01-22
In order to investigate quark confinement, we give a new reformulation of the SU (N) Yang-Mills theory on a lattice and present the results of the numerical simulations of the SU (3) Yang-Mills theory on a lattice. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the “Abelian” dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc.
Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
Caselle, Michele; Panero, Marco
2015-01-01
We present a high-precision lattice calculation of the equation of state in the confining phase of SU(2) Yang-Mills theory. We show that the results are described very well by a gas of massive, non-interacting glueballs, provided one assumes an exponentially growing Hagedorn spectrum. The latter can be derived within an effective bosonic closed-string model, leading to a parameter-free theoretical prediction, which is in perfect agreement with our lattice results. Furthermore, when applied to SU(3) Yang-Mills theory, this effective model accurately describes the lattice results reported by Bors\\'anyi et al. in JHEP 07 (2012) 056.
Hagedorn spectrum and equation of state of Yang-Mills theories
Caselle, Michele; Panero, Marco
2015-01-01
We present a novel lattice calculation of the equation of state of SU(2) Yang-Mills theory in the confining phase. We show that a gas of massive, non-interacting glueballs describes remarkably well the results, provided that a bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy glueball states with no free parameters. This effective model can be applied to SU(3) Yang-Mills theory and the theoretical prediction agrees nicely with the lattice results reported by Bors\\'anyi et al. in JHEP 07 (2012) 056.
Relating Gribov-Zwanziger theory and Yang-Mills theory in Batalin-Vilkovisky formalism
Upadhyay, Sudhaker
2011-01-01
We consider the BRST invariant Gribov-Zwanziger theory with appropriate horizon term in Batalin-Vilkovisky formalism. The usual infinitesimal BRST transformation is generalized by considering the parameter finite and field dependent. We show that such finite field dependent BRST transformation with suitable choice of finite parameter relates the generating functional of Gribov-Zwanziger theory to that of the Yang-Mills theory.
Nonlinear Schrodinger solitons in massive Yang-Mills theory and partial localization of Dirac matter
Maintas, X N; Diakonos, F K; Frantzeskakis, D J
2013-01-01
We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kink soliton, modulated by a plane wave, in a linear subspace transverse to the direction of free propagation. Subsequently, we explore how these solutions affect the dynamics of a Dirac field possessing an SU(2) charge. We find that this class of Yang-Mills configurations, when regarded as an external field, leads to the localization of the fermion along a line in the transverse space. Our analysis reveals a mechanism for trapping SU(2) charged fermions in the presence of an external Yang-Mills field indicating the non-abelian analogue of Landau localization in electrodynamics.
The Configuration Space of Low-dimensional Yang-Mills Theories
Pause, T
1998-01-01
We discuss the construction of the physical configuration space for Yang-Mills quantum mechanics and Yang-Mills theory on a cylinder. We explicitly eliminate the redundant degrees of freedom by either fixing a gauge or introducing gauge invariant variables. Both methods are shown to be equivalent if the Gribov problem is treated properly and the necessary boundary identifications on the Gribov horizon are performed. In addition, we analyze the significance of non-generic configurations and clarify the relation between the Gribov problem and coordinate singularities.
Gauge field spectrum in massive Yang-Mills theory with Lorentz violation
Santos, T R S; Tomaz, A A
2016-01-01
The spectrum of the massive CPT-odd Yang-Mills propagator with Lorentz violation is performed at tree-level. The modification is due to mass terms generated by the exigence of multiplicative renormalizability of Yang-Mills theory with Lorentz violation. The causality analysis is performed from group and front velocities for both, spacelike and timelike background tensors. It is show that, by demanding causality, it is always possible to define a physical sector for the gauge propagator. Hence, it is expected that the model is also unitary, if one takes the Faddeev-Popov ghost into account.
Freedom and confinement in lattice Yang-Mills theories. A case for divorce
Energy Technology Data Exchange (ETDEWEB)
Colangelo, P.; Cosmai, L.; Pellicoro, M.; Preparata, G.
1986-03-01
We present evidence that nonperturbative effects in lattice gauge theories do not obey at small coupling constant (large ..beta..) asymptotic scaling, but they rather behave as suggested by a recent result in continuum Yang-Mills theories. We also discuss the possible impact of these results on our understanding of QCD.
Classical and semi-classical solutions of the Yang--Mills theory. [Review
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R.; Nohl, C.; Rebbi, C.
1977-12-01
This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator.
Notes on equivalences and Higgs branches in N=2 supersymmetric Yang-Mills theory
Danielsson, U H; Danielsson, Ulf H; Stjernberg, Par
1996-01-01
In this paper we investigate how various equivalences between effective field theories of N=2 SUSY Yang-Mills theory with matter can be understood through Higgs breaking, i.e. by giving expectation values to squarks. We give explicit expressions for the flat directions for a wide class of examples.
Covariant gauges without Gribov ambiguities in Yang-Mills theories
Serreau, Julien; Tresmontant, Andréas
2013-01-01
We propose a formulation of a certain class of nonlinear covariant gauges as an extremization procedure that can be implemented on the lattice. At high energies, where the Gribov ambiguities can be ignored, this reduces to the Curci-Ferrari-Delbourgo-Jarvis gauges. We further propose a continuum formulation in terms of a local action which is free of Gribov ambiguities and avoids the Neuberger zero problem of the standard Faddeev-Popov construction. This involves an averaging over Gribov copies with a nonuniform weight, which introduces a new gauge-fixing parameter. We show that the proposed gauge-fixed action is perturbatively renormalizable in four dimensions and we provide explicit expressions of the renormalization factors at one loop. We discuss the possible implications of the present proposal for the calculation of Yang-Mills correlators.
Covariant gauges without Gribov ambiguities in Yang-Mills theories
Serreau, J.; Tissier, M.; Tresmontant, A.
2014-06-01
We propose a one-parameter family of nonlinear covariant gauges which can be formulated as an extremization procedure that may be amenable to lattice implementation. At high energies, where the Gribov ambiguities can be ignored, this reduces to the Curci-Ferrari-Delbourgo-Jarvis gauges. We further propose a continuum formulation in terms of a local action which is free of Gribov ambiguities and avoids the Neuberger zero problem of the standard Faddeev-Popov construction. This involves an averaging over Gribov copies with a nonuniform weight, which introduces a new gauge-fixing parameter. We show that the proposed gauge-fixed action is perturbatively renormalizable in four dimensions and we provide explicit expressions of the renormalization factors at one loop. We discuss the possible implications of the present proposal for the calculation of Yang-Mills correlators.
Cylindrically symmetric solitons in Einstein-Yang-Mills theory
Galtsov, D V; Davydov, Evgeny A.; Gal'tsov, Dmitri V.
2006-01-01
Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which describe superconducting strings with Kasner asymptotic (hep-th/0610183). Here we study the static cylindrically symmetric SU(2) EYM system in more detail. The ansatz for the gauge field corresponds to superposition of the azimuthal $B_\\phi$ and the longitudinal $B_z$ components of the color magnetic field. We derive sum rules relating data on the symmetry axis to asymptotic data and show that generic asymptotic structure of regular solutions is Kasner. Solutions starting with vacuum data on the axis generically are divergent. Regular solutions correspond to some bifurcation manifold in the space of parameters which has the low-energy limiting point corresponding to string solutions in flat space (with the divergent total energy) and the high-curvature point where gravity is crucial. Some analytical results are presented for the low energy limit, and numerical bifurcation curves are constructed in the gravitating case. Depending on ...
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
DEFF Research Database (Denmark)
Caron Huot, Simon; He, Song
2013-01-01
We study the S-matrix of planar = 4 supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics, in particular...
Existence of axially symmetric solutions in SU(2)-Yang-Mills and related theories
Hannibal, L; Hannibal, Ludger; Ossietzky, Carl von
1999-01-01
It is shown that the static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Dilaton theory constructed by Kleihaus and Kunz are gauge-equivalent to two-parameter families of embedded abelian solutions, characterized by mass and magnetic dipole moment. The existence of other particle-like solutions is excluded.
The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces
Driver, Bruce K; Hall, Brian C; Kemp, Todd
2016-01-01
We prove the Makeenko-Migdal equation for two-dimensional Euclidean Yang-Mills theory on an arbitrary compact surface, possibly with boundary. In particular, we show that two of the proofs given by the first, third, and fourth authors for the plane case extend essentially without change to compact surfaces.
Exact Solutions of the SU(2) Yang-Mills-Higgs Theory
Teh, R
2001-01-01
Some exact static solutions of the SU(2) Yang-Mills-Higgs theory are presented. These solutions do not satisfy the first order Bogomol'nyi equations, and do not possess finite energy. They are axially symmetric and could possibly represent monopoles and an antimonopole sitting on the z-axis.
The low-lying spectrum of N=1 supersymmetric Yang-Mills theory
Bergner, Georg; Montvay, Istvan; Muenster, Gernot; Piemonte, Stefano
2015-01-01
The spectrum of the lightest bound states in N=1 supersymmetric Yang-Mills theory with SU(2) gauge group, calculated on the lattice, is presented. The masses have first been extrapolated towards vanishing gluino mass and then to the continuum limit. The final picture is consistent with the formation of degenerate supermultiplets.
Monte Carlo simulation of SU(2) Yang-Mills theory with light gluinos
Campos, I; Kirchner, R; Luckmann, S; Montvay, István; Münster, G; Spanderen, K; Westphalen, J
1999-01-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with light dynamical gluinos the low energy features of the dynamics as confinement and bound state mass spectrum are investigated. The motivation is supersymmetry at vanishing gluino mass. The performance of the applied two-step multi-bosonic dynamical fermion algorithm is discussed.
Numerical simulations of dynamical gluinos in SU(3) Yang-Mills theory: first results
Energy Technology Data Exchange (ETDEWEB)
Feo, Alessandra; Kirchner, Robert; Luckmann, Silke; Montvay, Istvan; Muenster, Gernot
2000-03-01
In a numerical Monte Carlo simulation of SU(3) Yang-Mills theory with dynamical gluinos we have investigated the behaviour of the expectation value of the scalar and pseudoscalar gluino condensates in order to determine the phase structure. Preliminary results are presented as a function of the hopping parameter.
Monte Carlo simulation of SU(2) Yang-Mills theory with light gluinos
Energy Technology Data Exchange (ETDEWEB)
Campos, I.; Kirchner, R.; Montvay, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Feo, A.; Luckmann, S.; Muenster, G.; Spanderen, K. [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1
1999-12-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with light dynamical gluinos the low energy features of the dynamics as confinement and bound state mass spectrum are investigated. The motivation is supersymmetry at vanishing gluino mass. The performance of the applied two-step multi-bosonic dynamical fermion algorithm is discussed. (orig.)
Evidence for discrete chiral symmetry breaking in $N = 1$ supersymmetric Yang-Mills theory
Kirchner, R; Montvay, István; Spanderen, K; Westphalen, J
1999-01-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with dynamical gauginos we find evidence for two degenerate ground states at the supersymmetry point corresponding to zero gaugino mass. This is consistent with the expected pattern of spontaneous discrete chiral symmetry breaking $Z_4 \\to Z_2$ caused by gaugino condensation.
Numerical simulations of dynamical gluinos in SU(3) Yang-Mills theory first results
Feo, A; Luckmann, S; Montvay, István; Münster, G; Feo, Alessandra; Kirchner, Robert; Luckmann, Silke; Montvay, Istvan; Münster, Gernot
2000-01-01
In a numerical Monte Carlo simulation of SU(3) Yang-Mills theory with dynamical gluinos we have investigated the behaviour of the expectation value of the scalar and pseudoscalar gluino condensates in order to determine the phase structure. Preliminary results are presented as a function of the hopping parameter.
Evidence for discrete chiral symmetry breaking in N=1 supersymmetric Yang-Mills theory
Desy-Münster Collaboration; Kirchner, R.; Montvay, I.; Westphalen, J.; Luckmann, S.; Spanderen, K.
1999-01-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with dynamical gauginos we find evidence for two degenerate ground states at the supersymmetry point corresponding to zero gaugino mass. This is consistent with the expected pattern of spontaneous discrete chiral symmetry breaking Z4-->Z2 caused by gaugino condensation.
Numerical simulations of dynamical gluinos in SU (3) Yang-Mills theory: first results
Feo, Alessandra; Kirchner, Robert; Luckmann, Silke; Montvay, István; Münster, Gernot; DESY-Münster Collaboration
In a numerical Monte Carlo simulation of SU(3) Yang-Mills theory with dynamical gluinos we have investigated the behaviour of the expectation value of the scalar and pseudoscalar gluino condensates in order to determine the phase structure. Preliminary results are presented as a function of the hopping parameter.
Generalized WDVV equations for $F_4$ pure N=2 Super-Yang-Mills theory
Hoevenaars, L.K.; Kersten, P.H.M.; Martini, R.
2000-01-01
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 Super-Yang-Mills theory for the Lie algebra $F_4$ . Existence and associativity of this algebra, combined with the general arguments in the work of Marshakov, Mironov and Morozov, proves that the prepote
The Hamiltonian structure of Yang-Mills theories and instantons II
Bergvelt, M. J.; De Kerf, E. A.
1986-11-01
The formalism of constraints, reviewed in paper I, is applied to Yang-Mills theory to determine the physical phase space. This turns out to be the cotangent bundle of orbit space, the space of gauge inequivalent potentials. Self-dual configurations are not Hamiltonian with respect to the symplectic structure inherited from the general system.
The thermodynamics of quantum Yang-Mills theory theory and applications
Hofmann, Ralf
2016-01-01
This latest edition enhances the material of the first edition with a derivation of the value of the action for each of the Harrington-Shepard calorons/anticalorons that are relevant for the emergence of the thermal ground state. Also included are discussions of the caloron center versus its periphery, the role of the thermal ground state in U(1) wave propagation, photonic particle-wave duality, and calculational intricacies and book-keeping related to one-loop scattering of massless modes in the deconfining phase of an SU(2) Yang-Mills theory. Moreover, a derivation of the temperature-redshift relation of the CMB in deconfining SU(2) Yang-Mills thermodynamics and its application to explaining an apparent early re-ionization of the Universe are given. Finally, a mechanism of mass generation for cosmic neutrinos is proposed.
Two-loop Feynman Diagrams in Yang-Mills Theory from Bosonic String Amplitudes
Körs, B; Kors, Boris; Schmidt, Michael G.
2000-01-01
We present intermediate results of an ongoing investigation which attempts a generalization of the well known one-loop Bern Kosower rules of Yang-Mills theory to higher loop orders. We set up a general procedure to extract the field theoretical limit of bosonic open string diagrams, based on the sewing construction of higher loop world sheets. It is tested with one- and two-loop scalar field theory, as well as one-loop and two-loop vacuum Yang-Mills diagrams, reproducing earlier results. It is then applied to two-loop two-point Yang-Mills diagrams in order to extract universal renormalization coefficients that can be compared to field theory. While developing numerous technical tools to compute the relevant contributions, we hit upon important conceptual questions: Do string diagrams reproduce Yang-Mills Feynman diagrams in a certain preferred gauge? Do they employ a certain preferred renormalization scheme? Are four gluon vertices related to three gluon vertices? Unfortunately, our investigations remained in...
Isotropy theorem for cosmological Yang-Mills theories
Cembranos, J A R; Jareño, S J Núñez
2012-01-01
We consider homogeneous non-abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. We consider also the case in which a gauge-fixing term is introduced in the action and show that the average equation of state does not depend on such a term. Finally, we extend the results to arbitrary background geometries and show that the average energy-momentum tensor of a rapidly evolving Yang-Mills fields is always isotropic and has the perfect fluid form for any locally inertial observer.
Transport properties of N=4 supersymmetric Yang-Mills theory at finite coupling
Benincasa, P; Benincasa, Paolo; Buchel, Alex
2006-01-01
Gauge theory-string theory duality describes strongly coupled N=4 supersymmetric SU(n) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n N=4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation for the shear and the sound wave lowest quasinormal modes in the leading order alpha'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the alpha'-corrected nonextremal black branes in string theory.
A solution to the non-linear equations of D=10 super Yang-Mills theory
Mafra, Carlos R
2015-01-01
In this letter, we present a formal solution to the non-linear field equations of ten-dimensional super Yang--Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher mass dimensions are defined and their equations of motion spelled out.
Einstein and Yang-Mills theories in hyperbolic form without gauge-fixing
Abrahams, A M; Choquet-Bruhat, Y; York, J W
1995-01-01
The evolution of physical and gauge degrees of freedom in the Einstein and Yang-Mills theories are separated in a gauge-invariant manner. We show that the equations of motion of these theories can always be written in flux-conservative first-order symmetric hyperbolic form. This dynamical form is ideal for global analysis, analytic approximation methods such as gauge-invariant perturbation theory, and numerical solution.
Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
Kokenyesi, Zoltan; Szabo, Richard J
2016-01-01
We derive the analog of the large $N$ Gross-Taylor holomorphic string expansion for the refinement of $q$-deformed $U(N)$ Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of $q$-deformed Yang-Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit $q=1$, the expansion defines a new $\\beta$-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit $\\beta=1$ to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and $\\beta$-ensembles of matrix models arising in refined topological string theory.
Deconfinement in Yang-Mills theory through toroidal compactification with deformation
Simic, Dusan
2010-01-01
We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double- trace deformation of toroidally compactified Yang-Mills theory on R2 \\times S1_L \\times S1_{\\beta}. At large N, fixed-L, and arbitrary {\\beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {\\beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic comp...
Matsuura, So; Ohta, Kazutoshi
2014-01-01
We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of the generic lattice, the discretized theory becomes topologically twisted $\\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory on $\\Sigma_g$. If we adopt the usual square lattice as a special case of the discretization, our formulation is identical with Sugino's lattice model. Although the tuning of parameters is generally required while taking the continuum limit, the number of the necessary parameters is at most two because of the gauge symmetry and the supersymmetry. In particular, we do not need any fine-tuning if we arrange the theory so as to possess an extra global $U(1)$ symmetry ($U(1)_{R}$ symmetry) which rotates the scalar fields.
Universal aspects in the equation of state for Yang-Mills theories
Nada, Alessandro
2015-01-01
We present high-precision lattice calculations of the thermodynamics of Yang-Mills theories with different gauge groups. In the confining phase, we show that the equation of state is described remarkably well by a gas of massive, non-interacting glueballs, provided that an effective bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy states. In particular, this model describes very accurately the results for the SU(3) theory reported by Bors\\'anyi et al. in JHEP 07 (2012) 056, as well as a novel set of lattice data for the SU(2) theory. In addition, we also also show that the equation of state in the deconfined phase exhibits a near perfect proportionality to the number of gluon degrees of freedom, including for the Yang-Mills theory based on the exceptional, center-less gauge group $G_2$.
Superspace Formulation of N=4 Super Yang-Mills Theory with a Central Charge
Saito, J
2005-01-01
A superspace formulation using superconnections and supercurvatures is specifically constructed for N=4 extended super Yang-Mills theory with a central charge in four dimensions, first proposed by Sohnius, Stelle and West long ago. We find that the constraints, almost uniquely derived from the possible spin structure of the multiplet, can be algebraically solved which results in an off-shell supersymmetric formulation of the theory on the superspace.
Amplitude relations in heterotic string theory and Einstein-Yang-Mills
Schlotterer, Oliver
2016-11-01
We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension α' and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.
Dual-color decompositions at one-loop level in Yang-Mills theory
Du, Yi-Jian; Fu, Chih-Hao
2014-01-01
In this work, we extend the construction of dual color decomposition in Yang-Mills theory to one-loop level, i.e., we show how to write one-loop integrands in Yang-Mills theory to the dual DDM-form and the dual trace-form. In dual forms, integrands are decomposed in terms of color-ordered one-loop integrands for color scalar theory with proper dual color coefficients.In dual DDM decomposition, The dual color coefficients can be obtained directly from BCJ-form by applying Jacobi-like identities for kinematic factors. In dual trace decomposition, the dual trace factors can be obtained by imposing one-loop KK relations, reflection relation and their relation with the kinematic factors in dual DDM-form.
Amplitude relations in heterotic string theory and Einstein-Yang-Mills
Schlotterer, Oliver
2016-01-01
We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension alpha' and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.
On perturbative field theory and twistor string theory
Bedford, James
2007-01-01
It is well-known that perturbative calculations in field theory can lead to far simpler answers than the Feynman diagram approach might suggest. In some cases scattering amplitudes can be constructed for processes with any desired number of external legs yielding compact expressions which are inaccessible from the point of view of conventional perturbation theory. In this thesis we discuss some attempts to address the nature of this underlying simplicity and then use the results to calculate some previously unknown amplitudes of interest. Witten's twistor string theory is introduced and the CSW rules at tree-level and one-loop are described. We use these techniques to calculate the one-loop gluonic MHV amplitudes in N=1 super-Yang-Mills as a verification of their validity and then proceed to evaluate the general MHV amplitudes in pure Yang-Mills with a scalar running in the loop. This latter amplitude is a new result in QCD. In addition to this, we review some recent on-shell recursion relations for tree-leve...
Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
Caporaso, N; Griguolo, L; Pasquetti, S; Seminara, D; Szabó, R J
2006-01-01
We study the relations between two-dimensional Yang-Mills theory on the torus, topological string theory on a Calabi-Yau threefold whose local geometry is the sum of two line bundles over the torus, and Chern-Simons theory on torus bundles. The chiral partition function of the Yang-Mills gauge theory in the large N limit is shown to coincide with the topological string amplitude computed by topological vertex techniques. We use Yang-Mills theory as an efficient tool for the computation of Gromov-Witten invariants and derive explicitly their relation with Hurwitz numbers of the torus. We calculate the Gopakumar-Vafa invariants, whose integrality gives a non-trivial confirmation of the conjectured nonperturbative relation between two-dimensional Yang-Mills theory and topological string theory. We also demonstrate how the gauge theory leads to a simple combinatorial solution for the Donaldson-Thomas theory of the Calabi-Yau background. We match the instanton representation of Yang-Mills theory on the torus with ...
Renormalization aspects of N = 1 Super Yang-Mills theory in the Wess-Zumino gauge
Energy Technology Data Exchange (ETDEWEB)
Capri, M.A.L.; Granado, D.R.; Guimaraes, M.S.; Justo, I.F.; Sorella, S.P.; Vercauteren, D. [UERJ-Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Instituto de Fisica, Maracana, Rio de Janeiro (Brazil); Mihaila, L. [Karlsruhe Institute of Technology (KIT), Institut fuer Theoretische Teilchenphysik, Karlsruhe (Germany)
2014-04-15
The renormalization of N = 1 Super Yang-Mills theory is analyzed in the Wess-Zumino gauge, employing the Landau condition. An all-orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field, and gluino renormalization. The nonrenormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N = 1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three-loop calculation. (orig.)
Hedgehogs in Wilson loops and phase transition in SU(2) Yang-Mills theory
Belavin, V A; Kozlov, I E
2006-01-01
We suggest that the gauge-invariant hedgehogs-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang-Mills theory. The trajectories of these hedgehogs are closed curves which correspond to center-valued (untraced) Wilson loops and are characterized by the center charge and by the winding number. We show numerically in SU(2) Yang-Mills theory that the density of the hedgehogs in the thermal Wilson-Polyakov line is very sensitive to the finite temperature phase transition. The (additively normalized) hedgehog density behaves as an order parameter: the density is almost independent of the temperature in the confinement phase and changes substantially as the system gets into the deconfinement phase. Our results suggest in particular that the (static) hedgehogs may be relevant degrees of freedom around the deconfinement transition, and thus affect evolution of the quark-gluon plasma in high-energy heavy ion collisions.
Excluded-volume effects for a hadron gas in Yang-Mills theory
Alba, Paolo; Nada, Alessandro; Panero, Marco; Stöcker, Horst
2016-01-01
When the multiplicities of particles produced in heavy-ion collisions are fitted to the hadron-resonance-gas model, excluded-volume effects play a significant role. In this work, we study the impact of such effects onto the equation of state of pure Yang-Mills theory at low temperatures, comparing the predictions of the statistical model with lattice results. In particular, we present a detailed analysis of the SU(2) and SU(3) Yang-Mills theories: we find that, for both of them, the best fits to the equilibrium thermodynamic quantities are obtained when one assumes that the volume of different glueball states is inversely proportional to their mass. The implications of these findings for QCD are discussed.
Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
Energy Technology Data Exchange (ETDEWEB)
Caselle, Michele; Nada, Alessandro; Panero, Marco [Department of Physics, University of Turin & INFN,Via Pietro Giuria 1, I-10125 Turin (Italy)
2015-07-27
We present a high-precision lattice calculation of the equation of state in the confining phase of SU(2) Yang-Mills theory. We show that the results are described very well by a gas of massive, non-interacting glueballs, provided one assumes an exponentially growing Hagedorn spectrum. The latter can be derived within an effective bosonic closed-string model, leading to a parameter-free theoretical prediction, which is in perfect agreement with our lattice results. Furthermore, when applied to SU(3) Yang-Mills theory, this effective model accurately describes the lattice results reported by Borsányi et al. in http://dx.doi.org/10.1007/JHEP07(2012)056.
Tree amplitudes of noncommutative U(N) Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Huang Jiahui [Center of Mathematical Science, Zhejiang University, Hangzhou (China); Huang Rijun; Jia Yin, E-mail: huangjh19@gmail.com [Physics Department, Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou (China)
2011-10-21
Following the spirit of the S-matrix program, we propose a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified BCFW recursion relation to compute or analyze color-ordered tree amplitudes without relying on any detailed information of noncommutative Yang-Mills theory. After clarifying the color structure of noncommutative tree amplitudes, we write down the noncommutative analogies of Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered tree amplitudes and prove them using the modified BCFW recursion relation. This checks the consistency of the relation. (paper)
Tree amplitudes of noncommutative U(N) Yang-Mills theory
Huang, Jia-Hui; Huang, Rijun; Jia, Yin
2011-10-01
Following the spirit of the S-matrix program, we propose a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified BCFW recursion relation to compute or analyze color-ordered tree amplitudes without relying on any detailed information of noncommutative Yang-Mills theory. After clarifying the color structure of noncommutative tree amplitudes, we write down the noncommutative analogies of Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered tree amplitudes and prove them using the modified BCFW recursion relation. This checks the consistency of the relation.
Hedgehogs in Wilson loops and phase transition in SU(2) Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Belavin, V.A. [Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RU-117259 Moscow (Russian Federation); Chernodub, M.N. [Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RU-117259 Moscow (Russian Federation) and Department of Theoretical Physics, Uppsala University, P.O. Box 803, S-75108 Uppsala (Sweden)]. E-mail: maxim.chernodub@itep.ru; Kozlov, I.E. [Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RU-117259 Moscow (Russian Federation); Faculty of Physics, Moscow State University, RU-119992 Moscow (Russian Federation)
2006-08-07
We suggest that the gauge-invariant hedgehog-like structures in the Wilson loops are physically interesting degrees of freedom in the Yang-Mills theory. The trajectories of these 'hedgehog loops' are closed curves corresponding to center-valued (untraced) Wilson loops and are characterized by the center charge and winding number. We show numerically in the SU(2) Yang-Mills theory that the density of hedgehog structures in the thermal Wilson-Polyakov line is very sensitive to the finite-temperature phase transition. The (additively normalized) hedgehog line density behaves like an order parameter: The density is almost independent of the temperature in the confinement phase and changes substantially as the system enters the deconfinement phase. In particular, our results suggest that the (static) hedgehog lines may be relevant degrees of freedom around the deconfinement transition and thus affect evolution of the quark-gluon plasma in high-energy heavy-ion collisions.
Infrared Behaviour of Landau Gauge Yang-Mills Theory with a Fundamentally Charged Scalar Field
Fister, Leonard
2010-01-01
The infrared behaviour of the n-point functions of a Yang-Mills theory with a charged scalar field in the fundamental representation of SU(N) is studied in the formalism of Dyson-Schwinger equations. Assuming a stable skeleton expansion solutions in form of power laws for the Green functions are obtained. For a massless scalar field the uniform limit is sufficient to describe the infrared scaling behaviour of vertices. Not taking into account a possible Higgs-phase it turns out that kinematic singularities play an important role for the scaling solutions of massive scalars. On a qualitative level scalar Yang-Mills theory yields similar scaling solutions as recently obtained for QCD.
Some Comments on the String Singularity of the Yang-Mills-Higgs Theory
Lim, Kok-Geng; Teh, Rosy
2010-07-01
We are going to make use of the regulated polar angle which had been introduced by Boulware et al.. to show that in the SU(2) Yang-Mills-Higgs theory when the magnetic monopole is carried by the gauge field, the Higgs field does not carry the monopole and vice versa. In the Yang-Mills-Higgs theory, our solution shows that when the parameter ɛ ≠ 0, the monopole is carried by the gauge field and there is a string singularity in the gauge field. When the parameter ɛ → 0, the monopole is transferred from the gauge field to the Higgs field and the string singularity disappeared. The solution is only singular at the origin, that is at r = 0 as it becomes the Wu-Yang monopole.
Spontaneous breaking of color in N=1 Super Yang-Mills theory without matter
Diakonov, D; Diakonov, Dmitri; Petrov, Victor
2002-01-01
We argue that in the pure N=1 Super Yang-Mills theory gauge symmetry is spontaneously broken to the maximal Abelian subgroup. In particular, colored gluino condensate is nonzero. It invalidates, in a subtle way, the so-called strong-coupling instanton calculation of the (normal) gluino condensate and resolves the long-standing paradox why its value does not agree with that obtained by other methods.
Bassetto, A; Torrielli, A; Vian, F
2005-01-01
We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.
On the string actions for the generalized two-dimensional Yang-Mills theories
Sugawara, Y
1996-01-01
We study the structures of partition functions of the large N generalized two-dimensional Yang-Mills theories (gYM_2) by recasting the higher Casimirs. We clarify the appropriate interpretations of them and try to extend the Cordes-Moore-Ramgoolam's topological string model describing the ordinary YM_2 \\cite{CMR} to those describing gYM_2. The concept of ''deformed gravitational descendants'' will be introduced for this purpose.
Emergence of Yang Mills theory from the Non-Abelian Nambu Model
Escobar, C A
2016-01-01
The equivalence between the Non-Abelian Nambu model (NANM) and Yang Mills theory is proved, after demanding the Gauss laws at some initial time to the first one. Thereby, the Lorentz violation encoded into the constraint that defines the NANM is physically unobservable. As result, the Goldstone bosons in the NANM arising from the spontaneous symmetry breaking can be identified as the standard gauge fields.
Statistical mechanics for dilatations in N=4 super Yang--Mills theory
Sochichiu, C
2006-01-01
Matrix model describing the anomalous dimensions of composite operators in $\\mathcal{N}=4$ super Yang--Mills up to one-loop level theory is considered at finite temperature. We compute the thermal effective action for this model, which we define as the log of the partition function restricted to the states of given length and spin. The result is obtained in the limits of high and low temperature.
Topological susceptibility in lattice Yang-Mills theory with open boundary condition
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, Abhishek; Harindranath, A. [Theory Division, Saha Institute of Nuclear Physics,1/AF Bidhan Nagar, Kolkata 700064 (India); Maiti, Jyotirmoy [Department of Physics, Barasat Government College,10 KNC Road, Barasat, Kolkata 700124 (India); Majumdar, Pushan [Department of Theoretical Physics, Indian Association for the Cultivation of Science,Kolkata 700032 (India)
2014-02-11
We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum extrapolation at a lower computational cost.
Geometry of the gauge algebra in noncommutative Yang-Mills theory
Lizzi, Fedele; Zampini, Alessandro; Szabo, Richard J.
2001-08-01
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in non-commutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra u(∞), and of the C*-algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.
Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
Lizzi, F; Zampini, A
2001-01-01
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra, and of the algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.
Supersymmetry algebra and BPS states of super Yang-Mills theories on noncommutative tori
Konechny, Anatoly; Schwarz, Albert
1999-04-01
We consider 10-dimensional super Yang-Mills theory with topological terms compactified on a noncommutative torus. We calculate supersymmetry algebra and derive BPS energy spectra from it. The cases of d-dimensional tori with d=2,3,4 are considered in full detail. SO(d,d,Z)-invariance of the BPS spectrum and relation of new results to the previous work in this direction are discussed.
A new sphaleron in SU(3) Yang-Mills-Higgs theory
Energy Technology Data Exchange (ETDEWEB)
Nagel, Pascal; Klinkhamer, Frans [Karlsruher Institut fuer Technologie (KIT), Karlsruhe (Germany)
2016-07-01
The sphaleron solution S is known to contribute to baryon-number violation within the electroweak Standard Model. To gain further insight into the nonperturbative dynamics of QCD (and GUTs), we study a new sphaleron solution of SU(3) Yang-Mills-Higgs theory, the solution S. Two independent numerical approaches yield solutions of the reduced field equations and a surprising structure of the energy barrier in configuration space.
Infrared Safe Observables in ${\\cal N}=4$ Super Yang-Mills Theory
Bork, L V; Vartanov, G S; Zhiboedov, A V
2009-01-01
The infrared structure of MHV gluon amplitudes in ${\\cal N}=4$ super Yang-Mills theory is considered in the next-to-leading order of PT. Explicit cancelation of the infrared divergencies in properly defined cross-sections is demonstrated. The remaining finite parts for some inclusive differential cross-sections are calculated analytically. In general, contrary to the virtual corrections, they do not reveal any simple structure.
Black Hole Solution of Einstein-Born-Infeld-Yang-Mills Theory
Directory of Open Access Journals (Sweden)
Kun Meng
2017-01-01
Full Text Available A new four-dimensional black hole solution of Einstein-Born-Infeld-Yang-Mills theory is constructed; several degenerated forms of the black hole solution are presented. The related thermodynamical quantities are calculated, with which the first law of thermodynamics is checked to be satisfied. Identifying the cosmological constant as pressure of the system, the phase transition behaviors of the black hole in the extended phase space are studied.
Instanton Calculus, Topological Field Theories and N = 2 Super Yang-Mills Theories
Bellisai, D; Tanzini, A; Travaglini, G; Bellisai, Diego; Fucito, Francesco; Tanzini, Alessandro; Travaglini, Gabriele
2000-01-01
The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N=2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This suggests that the instanton saddle point saturates the non-perturbative contribution to the functional integral. A natural framework in which corrections to this approximation are absent is given by the topological field theory built out of the N=2 Super Yang-Mills theory. After extending the standard construction of the Topological Yang-Mills theory to encompass the case of a non-vanishing vacuum expectation value for the scalar field, a BRST transformation is defined (as a supersymmetry plus a gauge variation), which on the instanton moduli space is the exterior derivative. The topological field theory approach makes the so-called "constrained instanton" configurations and the instanton measure arise in a natural way. As a consequence, instanton-dominated Green's functions...
Reformulations of the Yang-Mills theory toward quark confinement and mass gap
Kondo, Kei-Ichi; Shibata, Akihiro; Shinohara, Toru
2014-01-01
We propose the reformulations of the $SU(N)$ Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the $SU(N)$ Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the $SU(N)$ extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the $SU(N)$ Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole ...
The gluino-glue particle and relevant scales for the simulations of supersymmetric Yang-Mills theory
Bergner, Georg; Münster, Gernot; Sandbrink, Dirk; Özugurel, Umut D
2012-01-01
Supersymmetric Yang-Mills theory is in several respects different from QCD and pure Yang-Mills theory. Therefore, a reinvestigation of the scales, at which finite size effects and lattice artifacts become relevant, is necessary. Both, finite size effects and lattice artifacts, induce a breaking of supersymmetry. In view of the unexpected mass gap between bosonic and fermionic particles an estimation of these effects is essential.
Boundary behaviors for general off-shell amplitudes in Yang-Mills theory
Zhang, Yun; Chen, Gang
2013-07-01
The boundary behavior of amplitudes—the amplitudes’ behavior under a large Britto-Cachazo-Feng-Witten (BCFW) momenta deformation for a pair of legs—in Yang-Mills theory is of great interest recently. In this article we analyze the boundary behavior of off-shell Yang-Mills amplitudes in Feynman gauge. The deformed legs can be either adjacent or nonadjacent. We find that a set of reduced vertices can be used to simplify the analysis and calculation of the boundary behavior of amplitudes. Boundary behavior for amplitudes with adjacent BCFW deformation is read off from the reduced vertices. Then we discover a relationship between a permutation sum with fixed color ordering of the legs and the improved boundary behavior for the off-shell amplitudes with a nonadjacent BCFW momenta deformation. Based on the boundary behavior, we generalize the BCFW recursion relation to calculate general tree-level off-shell amplitudes and analyze the relations between them.
Studies In Field Theories: Mhv Vertices, Twistor Space, Recursion Relations And Chiral Rings
Svrcek, P
2005-01-01
In this thesis we study different aspects of four dimensional field theories. In the first chapter we give introduction and overview of the thesis. In the second chapter we review the connection between perturbative Yang-Mills and twistor string theory. Inspired by this, we propose a new way of constructing Yang-Mills scattering amplitudes from Feynman graphs in which the vertices are off-shell continuations of the tree level MHV amplitudes. The MHV diagrams lead to simple formulas for tree-level amplitudes. We then give a heuristic derivation of the diagrams from twistor string theory. In the third chapter, we explore the twistor structure of scattering amplitudes in theories for which a twistor string theory analogous to the one for N = 4 gauge theory has not yet been proposed. We study the differential equations of one-loop amplitudes of gluons in gauge theories with reduced supersymmetry and of tree level and one-loop amplitudes of gravitons in general relativity and supergravity. We find that the scat...
All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
Bern, Z; Dixon, L J; Kosower, D A; Bern, Zvi; Duca, Vittorio Del; Dixon, Lance J.; Kosower, David A.
2004-01-01
We compute the non-MHV one-loop seven-gluon amplitudes in N=4 super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes, (- - - + + + +), (- - + - + + +), (- - + + -+ +) and (- + - + - + +). The MHV amplitudes containing two negative-helicity and five positive-helicity gluons were computed previously, so all independent one-loop seven-gluon helicity amplitudes are now known for this theory. We present partial information about an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three negative-helicity and n-3 positive-helicity gluons, and the color ordering (- - - + + ... + +); we give a new coefficient of one class of integral functions entering this amplitude. We discuss the twistor-space properties of the box-integral-function coefficients in the amplitudes, which are quite simple and suggestive.
The Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
Energy Technology Data Exchange (ETDEWEB)
Bern, Z.
2004-10-22
We compute the non-MHV one-loop seven-gluon amplitudes in N = 4 super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes, (---++++), (--+-+++), (--++-++) and (-+-+-++). The MHV amplitudes containing two negative-helicity and five positive-helicity gluons were computed previously, so all independent one-loop seven-gluon helicity amplitudes are now known for this theory. We present partial information about an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three negative-helicity and n - 3 positive-helicity gluons, and the color ordering (---+{center_dot}{center_dot}{center_dot}++); we give a new coefficient of one class of integral functions entering this amplitude. We discuss the twistor-space properties of the box-integral-function coefficients in the amplitudes, which are quite simple and suggestive.
Yang-Mills theory as bimetrical gravity: Polarization effects and finite-energy gluon clusters
Energy Technology Data Exchange (ETDEWEB)
Pavlovsky, Oleg V
2002-01-01
In this report a gravity representation of Yang-Mills theory is given. Using this approach, one obtains new information on solutions of classical YM theory. Singular solutions (black-hole-like solutions) of the YM equations are discussed in connection with bimetrical gravity. The behaviour of these solutions in a theory with a 'cosmological' Lambda-part is also investigated. A physical interpretation of such solutions is given. Using an effective field theory approach we try to show that quantum fluctuations and vacuum polarization effects lead to the generation of finite-energy objects in QCD.
Cohomological Yang-Mills Theories on Kahler 3-Folds
Hofman, C.; Park, J.S
2001-01-01
We study topological gauge theories with N-c = (2, 0) supersymmetry based on stable bundles on general Kahler 3-folds. In order to have a theory that is well defined and well behaved, we consider a model based on an extension of the usual holomorphic bundle by including a holomorphic 3-form. The cor
N=4 Supersymmetric Yang-Mills Theory on a Kaehler Surface
Dijkgraaf, R; Schroers, B J
1998-01-01
We study N=4 supersymmetric Yang-Mills theory on a Kaehler manifold with $b_2^+ \\geq 3$. Adding suitable perturbations we show that the partition function of the N=4 theory is the sum of contributions from two branches: (i) instantons, (ii) a special class of Seiberg-Witten monopoles. We determine the partition function for the theories with gauge group SU(2) and SO(3), using S-duality. This leads us to a formula for the Euler characteristic of the moduli space of instantons.
Wilson punctured network defects in 2D q-deformed Yang-Mills theory
Watanabe, Noriaki
2016-01-01
In the context of class S theories and 4D/2D duality relations there, we discuss the skein relations of general topological defects on the 2D side which are expected to be counterparts of composite surface-line operators in 4D class S theory. Such defects are geometrically interpreted as networks in a three dimensional space. We also propose a conjectural computational procedure for such defects in two dimensional SU(N) topological q-deformed Yang-Mills theory by interpreting it as a statistical mechanical system associated with ideal triangulations.
Wilson punctured network defects in 2D q-deformed Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Watanabe, Noriaki [Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa, Chiba 277-8583 (Japan)
2016-12-14
In the context of class S theories and 4D/2D duality relations there, we discuss the skein relations of general topological defects on the 2D side which are expected to be counterparts of composite surface-line operators in 4D class S theory. Such defects are geometrically interpreted as networks in a three dimensional space. We also propose a conjectural computational procedure for such defects in two dimensional SU(N) topological q-deformed Yang-Mills theory by interpreting it as a statistical mechanical system associated with ideal triangulations.
Domain Walls in Supersymmetric Yang-Mills Theories
Kaplunovsky, V S; Yankielowicz, Shimon; Kaplunovsky, Vadim S.; Sonnenschein, Jacob; Yankielowicz, Shimon
1999-01-01
We study BPS saturated domain walls in the supersymmetric SU(2) gauge theory. For a theory with a very light adjoint scalar (mass <~ Lambda/400) we use the perturbed N=2 Seiberg-Witten theory to calculate the actual field configuration of the domain wall. The wall has a sandwich-like five-layer structure of three distinct phases -- electric confinement, Coulomb and oblique confinement -- separated by two separate transition regions. For larger scalar masses, the three-phase structure disappears and the Seiberg-Witten theory becomes inadequate because of two major problems: First, the higher-derivative interactions between the light fields become relevant and second, both the magnetic monopole condensate and the dyon condensate show up in the same region of space, a phenomenon indescribable in terms of a local field theory. Nevertheless, we argue that the BPS saturated domain wall continues to exist in this regime and give a qualitative description of the scalar and gaugino condensates. Finally, we discuss ...
Quantization of Yang-Mills Theories without the Gribov Ambiguity
Zhou, Gao-Liang
2016-01-01
A gauge condition is presented here to quantize non-Abelian gauge theory on the manifold $R\\otimes S^{1}\\otimes S^{1}\\otimes S^{1}$, which is free from the Gribov ambiguity. Perturbative calculations in the new gauge behave like the axial gauge in ultraviolet region, while infrared behaviours of the perturbative series are quite nontrivial. The new gauge condition, which reads $n\\cdot\\partial n\\cdot A=0$, may not satisfy the requirement that $A^{\\mu}(\\infty)=0$ in conventional perturbative calculations. However, such contradiction is not harmful for gauge theories constructed on the manifold $R\\otimes S^{1}\\otimes S^{1}\\otimes S^{1}$.
Classical Solutions of SU(3) Pure Yang-Mills Theory
2002-01-01
Regular classical solutions of pure SU(3) gauge theories, in Minkowsky spacetime, are computed in the Landau gauge. The classical fields have an intrinsic energy scale and produce quark confinement if interpreted in the sense of a nonrelativistic potential. Moreover, the quark propagator in the background of these fields vanishes at large positive and negative time and space separations.
Amplitudes in N = 4 Super-Yang-Mills Theory
Spradlin, Marcus
These lecture notes provide a lightning introduction to some aspects of scattering amplitudes in maximally supersymmetric theory, aimed at the audience of students attending the 2014 TASI summer school "Journeys Through the Precision Frontier: Amplitudes for Colliders". Emphasis is placed on explaining modern terminology so that students needing to delve further may more easily access the available literature.
Chiral anomalies in N=1 supersymmetric Yang-Mills theories
Energy Technology Data Exchange (ETDEWEB)
Girardi, G.; Grimm, R.; Stora, R. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)
1985-06-20
We establish a manifestly supersymmetric, compact, formula for the chiral anomalies of supersymmetric gauge theories. This result is obtained by combining superspace geometry with the usual algebra of anomalies. Except for a Wess-Zumino type term, we obtain an expression which is polynomial in the coefficients of the superconnection form.
Intermediate distance correlators in hot Yang-Mills theory
Laine, M; Vuorinen, A
2010-01-01
Lattice measurements of spatial correlation functions of the operators FF and FF-dual in thermal SU(3) gauge theory have revealed a clear difference between the two channels at "intermediate" distances, x ~ 1/(pi T). This is at odds with the AdS/CFT limit which predicts the results to coincide. On the other hand, an OPE analysis at short distances (x 1/(pi T)) as well as effective theory methods at long distances (x 1/(pi T)) suggest differences. Here we study the situation at intermediate distances by determining the time-averaged spatial correlators through a 2-loop computation. We do find unequal results, however the numerical disparity is small. Apart from theoretical issues, a future comparison of our results with time-averaged lattice measurements might also be of phenomenological interest in that understanding the convergence of the weak-coupling series at intermediate distances may bear on studies of the thermal broadening of heavy quarkonium resonances.
Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge
Capri, M A L; Guimaraes, M S; Justo, I F; Mihaila, L; Sorella, S P; Vercauteren, D
2014-01-01
The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino, as explicitly shown through a three loop calculation.
Let's Twist Again: N=2 Super Yang Mills Theory Coupled To Matter
Maggiore, Nicola
2010-01-01
We give the twisted version of N=2 Super Yang Mills theory coupled to matter, including quantum fields, supersymmetry transformations, action and algebraic structure. We show that the whole action, coupled to matter, can be written as the variation of a nilpotent operator, modulo field equations. An extended Slavnov-Taylor identity, collecting gauge symmetry and supersymmetry, is written, which allows to define the web of algebraic constraints, in view of the algebraic renormalization and of the extension of the non-renormalization theorems holding for N=2 SYM theory without matter.
Reformulations of the Yang-Mills theory toward quark confinement and mass gap
Energy Technology Data Exchange (ETDEWEB)
Kondo, Kei-Ichi; Shinohara, Toru [Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522 (Japan); Kato, Seikou [Fukui National College of Technology, Sabae 916-8507 (Japan); Shibata, Akihiro [Computing Research Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 (Japan)
2016-01-22
We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N− 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1){sup N−1}, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
DEFF Research Database (Denmark)
Caron Huot, Simon; He, Song
2013-01-01
, the higher-point amplitudes we consider can be obtained from those with lowest-points by a collinear uplifting. Based on a compact formula for one-loop N(2)MHV amplitudes, we use an equation proposed previously to compute, for the first time, the complete two-loop NMHV and three-loop MHV octagons, which we......We study the S-matrix of planar = 4 supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics, in particular...
N=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\\bf Z}_2$
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$. In classical geometry, K3 surface is constructed from the orbifold-$T^4/{\\bf Z}_2$. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-$T^4/{\\bf Z}_2$. The partition function is given by the product of the contribution of the untwisted sector of $T^4/{\\bf Z}_2$, and that of the twisted sector of $T^4/{\\bf Z}_2$ i.e., ${\\cal O}(-2)$ curve blow-up formula.
Towards a precise determination of the topological susceptibility in the SU(3) Yang-Mills theory
Giusti, Leonardo; Petrarca, Silvano
2009-01-01
An ongoing effort to compute the topological susceptibility for the SU(3) Yang-Mills theory in the continuum limit with a precison of about 2% is reported. The susceptibility is computed by using the definition of the charge suggested by Neuberger fermions for two values of the negative mass parameter s. Finite volume and discretization effects are estimated to meet this level of precision. The large statistics required has been obtained by using PCs of the INFN-GRID. Simulations with larger lattice volumes are necessary in order to better understanding the continuum limit at small lattice spacing values.
A novel computation of the thermodynamics of the SU(3) Yang-Mills theory
Giusti, Leonardo
2015-01-01
We present an accurate computation of the Equation of State of the SU(3) Yang-Mills theory using shifted boundary conditions in the temporal direction. In this framework, the entropy density s can be obtained in a simple way from the expectation value of the space-time components T0k of the energy-momentum tensor. At each given value of the temperature, s is measured in an independent way at several values of the lattice spacing. The extrapolation to the continuum limit shows small discretization effects with respect to the statistical errors of approximatively 0.5%.
From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.
Pepe, M; Wiese, U-J
2009-05-15
We study {2Q+1} strings connecting two static charges Q in (2+1)D SU(2) Yang-Mills theory. While the fundamental {2} string between two charges Q=1/2 is unbreakable, the adjoint {3} string connecting two charges Q=1 can break. When a {4} string is stretched beyond a critical length, it decays into a {2} string by gluon pair creation. When a {5} string is stretched, it first decays into a {3} string, which eventually breaks completely. The energy of the screened charges at the ends of a string is well described by a phenomenological constituent gluon model.
The Width of the Confining String in Yang-Mills Theory
Gliozzi, F; Wiese, U -J
2010-01-01
We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)-d SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multi-level algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher order terms in the effective string action are calculated analytically. They accurately fit the numerical data.
Fifty years of Yang-Mills Theories: a phenomenological point of view
De Rújula, Alvaro
2005-01-01
On the occasion of the celebration of the first half-century of Yang--Mills theories, I am contributing a personal recollection of how the subject, in its early times, confronted physical reality, that is, its "phenomenology". There is nothing original in this work, except, perhaps, my own points of view. But I hope that the older practitioners of the field will find here grounds for nostalgia, or good reasons to disagree with me. Younger addicts may learn that history does not resemble at all what is reflected in current textbooks: it was orders of magnitude more fascinating.
BPS Equations in Omega-deformed N=4 Super Yang-Mills Theory
Ito, Katsushi; Nakajima, Hiroaki; Sasaki, Shin
2015-01-01
We study supersymmetry of N=4 super Yang-Mills theory in four dimensions deformed in the Omega-background. We take the Nekrasov-Shatashvili limit of the background so that two-dimensional super Poincare symmetry is recovered. We compute the deformed central charge of the superalgebra and study the 1/2 and 1/4 BPS states. We obtain the Omega-deformed 1/2 and 1/4 BPS dyon equations from the deformed supersymmetry transformation and the Bogomol'nyi completion of the energy.
Twisted N=4 Super Yang-Mills Theory in Omega-background
Ito, Katsushi; Sasaki, Shin
2013-01-01
We study the twisted N=4 super Yang-Mills theories in the Omega-background with the constant R-symmetry Wilson line gauge field. Based on the classification of topological twists of N=4 supersymmetry (the half, the Vafa-Witten and the Marcus twists), we construct the deformed off-shell supersymmetry associated with the scalar supercharges for these twists. We find that the Omega-deformed action is written in the exact form with respect to the scalar supercharges as in the undeformed case.
Gluon scattering in N=4 super-Yang-Mills theory fromweak to strong coupling
Energy Technology Data Exchange (ETDEWEB)
Dixon, Lance J.; /SLAC
2008-03-25
I describe some recent developments in the understanding of gluon scattering amplitudes in N = 4 super-Yang-Mills theory in the large-N{sub c} limit. These amplitudes can be computed to high orders in the weak coupling expansion, and also now at strong coupling using the AdS/CFT correspondence. They hold the promise of being solvable to all orders in the gauge coupling, with the help of techniques based on integrability. They are intimately related to expectation values for polygonal Wilson loops composed of light-like segments.
't Hooft Loops, Electric Flux Sectors and Confinement in SU(2) Yang-Mills Theory
De Forcrand, Philippe; Forcrand, Philippe de; Smekal, Lorenz von
2002-01-01
We use 't Hooft loops of maximal size on finite lattices to calculate the free energy in the sectors of SU(2) Yang-Mills theory with fixed electric flux as a function of temperature and (spatial) volume. Our results provide evidence for the mass gap. The confinement of electric fluxes in the low temperature phase and their condensation in the high temperature phase are demonstrated. In a surprisingly large scaling window around criticality, the transition is quantitatively well described by universal exponents and amplitude ratios relating the properties of the two phases.
Transport properties of N = 4 supersymmetric Yang-Mills theory at finite coupling
Energy Technology Data Exchange (ETDEWEB)
Benincasa, Paolo [Department of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON, N6A 5B7 (Canada); Buchel, Alex [Department of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON, N6A 5B7 (Canada); Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada)
2006-01-15
Gauge theory-string theory duality describes strongly coupled N = 4 supersymmetric SU(n{sub c}) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in the inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n{sub c} N = 4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation of the shear and the sound wave lowest quasinormal modes in the leading order {alpha}'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the {alpha}'-corrected nonextremal black branes in string theory.
Transport properties of Script N = 4 supersymmetric Yang-Mills theory at finite coupling
Benincasa, Paolo; Buchel, Alex
2006-01-01
Gauge theory-string theory duality describes strongly coupled Script N = 4 supersymmetric SU(nc) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in the inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-nc Script N = 4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation of the shear and the sound wave lowest quasinormal modes in the leading order α'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the α'-corrected nonextremal black branes in string theory.
Mass Deformations of Super Yang-Mills Theories in D= 2+1, and Super-Membranes: A Note
Agarwal, Abhishek
2008-01-01
Mass deformations of supersymmetric Yang-Mills theories in three spacetime dimensions are considered. The gluons of the theories are made massive by the inclusion of a non-local gauge and Poincare invariant mass term due to Alexanian and Nair, while the matter fields are given standard Gaussian mass-terms. It is shown that the dimensional reduction of such mass deformed gauge theories defined on $R^3$ or $R\\times T^2$ produces matrix quantum mechanics with massive spectra. In particular, all known massive matrix quantum mechanical models obtained by the deformations of dimensional reductions of minimal super Yang-Mills theories in diverse dimensions are shown also to arise from the dimensional reductions of appropriate massive Yang-Mills theories in three spacetime dimensions. Explicit formulae for the gauge theory actions are provided.
Aspects Of Yang-mills Theory: Solitons, Dualities And Spin Chains
Freyhult, L K
2004-01-01
One of the still big problems in the Standard Model of particle physics is the problem of confinement. Quarks or other coloured particles have never been observed in isolation. Quarks are only observed in colour neutral bound states. The strong interactions are described using a Yang-Mills theory. These type of theories exhibits asymptotic freedom, i.e. the coupling is weak at high energies. This means that the theory is perturbative at high energies only. Understanding quark confinement requires knowledge of the non perturbative regime. One attempt has been to identify the proper order parameters for describing the low energy limit and then to write down effective actions in terms of these order parameters. We discuss one possible scenario for confinement and the effective models constructed with this as inspiration. Further we discuss solitons in these models and their properties. Yang-Mills theory has also become important in the context of string theory. According to the AdS/CFT correspondence string theo...
Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Koekenyesi, Zoltan; Sinkovics, Annamaria [Institute of Theoretical Physics, MTA-ELTE Theoretical Research Group, Eoetvoes Lorand University, 1117, Budapest, Pazmany, s. 1/A (Hungary); Szabo, Richard J. [Heriot-Watt Univ., Edinburgh (United Kingdom). Dept. of Mathematics; Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); The Higgs Centre for Theoretical Physics, Edinburgh (United Kingdom)
2016-11-15
We derive the analog of the large N Gross-Taylor holomorphic string expansion for the refinement of q-deformed U(N) Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of q-deformed Yang-Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit q = 1, the expansion defines a new β-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit β = 1 to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and β-ensembles of matrix models arising in refined topological string theory. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Analytical approach to the D3-brane gravity dual for 3d Yang-Mills theory
Forkel, Hilmar
2015-01-01
The complexity of "top-down" string-dual candidates for strongly-coupled Yang-Mills theories and in particular for QCD almost always prohibits their exact analytical or even comprehensive numerical treatment. This impedes both a thorough quantitative analysis and the development of more realistic gravity duals. To mitigate these impediments, we devise an analytical approach to top-down duals on the basis of controlled, uniformly converging high-accuracy approximations for the normalizable string modes corresponding to gauge-theory states. We demonstrate the potential of this approach in Witten's dual for $3d$ Yang-Mills theory, i.e. in the near-horizon limit of non-extremal $D\\text{3}$-branes, compactified on $S^{1}$. We obtain accurate analytical approximations to the bulk modes which satisfy the boundary conditions exactly. On their basis, analytical results for masses, sizes, pole residues and correlation functions of glueball excitations are derived by spectral methods. These approximations can be systema...
D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
Bern, Zvi; Dixon, Lance J.; Douglas, Michael R.; von Hippel, Matt; Johansson, Henrik
2013-01-01
The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large $N_c$) maximally supersymmetric Yang-Mills theory in D = 5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences through five loops. This formula predicts the approximate values of the ultraviolet divergence at loop orders L > 6 in the critical dimension D = 4 + 6/L. To obtain the six-loop divergence we first construct the planar six-loop four-point amplitude integrand using generalized unitarity. The ultraviolet divergence follows from a set of vacuum integrals, which are obtained by expanding the integrand in the external momenta. T...
Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
Anber, Mohamed M; Teeple, Brett
2014-01-01
We study the phase structure of N=1 supersymmetric Yang-Mills theory on R^3XS^1, with massive gauginos, periodic around the S^1, with Sp(2N) (N>=2), Spin(N) (N>=5), G_2, F_4, E_6, E_7, E_8 gauge groups. As the gaugino mass m is increased, with S^1 size and strong coupling scale fixed, we find a first-order phase transition both for theories with and without a center. This semiclassically calculable transition is driven, as in SU(N) and G_2, arxiv.org/abs/1205.0290 and arxiv.org/abs/1212.1238, by a competition between monopole-instantons and exotic topological "molecules"---"neutral" or "magnetic" bions. We compute the trace of the Polyakov loop and its two-point correlator near the transition. We find a behavior similar to the one observed near the thermal deconfinement transition in the corresponding pure Yang-Mills (YM) theory in lattice studies (whenever available). Our results lend further support to the conjectured continuity, as a function of m, between the quantum phase transition studied here and the ...
Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery
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Mansfield, P. (Dept. of Mathematical Sciences, Univ. of Durham (United Kingdom))
1994-04-25
We solve Schroedinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero. (orig.)
Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
Cé, Marco; Engel, Georg P; Giusti, Leonardo
2015-01-01
We study the topological charge distribution of the SU(3) Yang--Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang--Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t_0^2*chi=6.67(7)*10^-4, where t_0 is a standard reference scale, while for the...
Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies
Hofmann, Ralf
2013-01-01
A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field $\\phi$, based on non-propagating (anti)selfdual field configurations of topological charge unity. We explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planc...
Solving the Ghost-Gluon System of Yang-Mills Theory on GPUs
Hopfer, Markus; Haase, Gundolf
2012-01-01
We solve the ghost-gluon system of Yang-Mills theory using Graphics Processing Units (GPUs). Working in Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description as this approach is well-suited to directly benefit from the computing power of the GPUs. With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method, the non-linear system of coupled integral equations is linearized. The resulting Newton matrix is generated in parallel using OpenMPI and CUDA(TM). Our results show, that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code. This makes the proposed techniques well-suited for Dyson-Schwinger calculations on more complicated systems where the Yang-Mills sector of QCD serves as a starting point. In addition, the computation of Schwinger functions using GPU devices is studied.
Geometrodynamics of gauge fields on the geometry of Yang-Mills and gravitational gauge theories
Mielke, Eckehard W
2016-01-01
This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter t...
Kajantie, K; Vepsalainen, M; Vuorinen, Aleksi
2011-01-01
We use AdS/QCD duality to compute the finite temperature Green's function G(omega,k;T) of the shear operator T_12 for all omega,k in hot Yang-Mills theory. The goal is to assess how the existence of scales like the transition temperature and glueball masses affects the correlator computed in the scalefree conformal N=4 supersymmetric Yang-Mills theory. We observe sizeable effects for T close to T_c which rapidly disappear with increasing T. Quantitative agreement of these predictions with future lattice Monte Carlo data would suggest that QCD matter in this temperature range is strongly interacting.
High energy behavior of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory
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Bartels, Jochen; Hentschinski, Martin; Mischler, Anna-Maria [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Ewerz, Carlo [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; GSI Helmholtzzentrum fuer Schwerionenforschung, Darmstadt (Germany). ExtreMe Matter Institute EMMI; Bielefeld Univ. (Germany). Fakultaet fuer Physik; European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), Villazzano (Italy)
2009-12-15
We study the high energy limit of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory for finite N{sub c}. We make use of the framework of perturbative resummation of large logarithms of the energy. More specifically, we apply the (extended) generalized leading logarithmic approximation. We find that the same conformally invariant two-to-four gluon vertex occurs as in non-supersymmetric Yang-Mills theory. As a new feature we find a direct coupling of the four-gluon t-channel state to the R-current impact factor. (orig.)
Zhu, Yan
2013-01-01
In this PhD thesis, I will review recent progress in perturbative studies of energy momentum tensor correlators in high-temperature Yang-Mills theory. After briefly introducing the necessary tools and physical motivation, I proceed to discuss the machinery developed for the extraction of next-to-leading order Operator Product Expansions and thermal spectral functions and to introduce the results obtained in the bulk and shear channels of Yang-Mills theory. Particular emphasis is placed on the comparison of the results with recent lattice and gauge/gravity calculations, as well as on discussing their use in extracting the corresponding transport coefficients from Euclidean lattice data.
The Stringy Representation of the D>=3 Yang-Mills Theory
Dubin, A Yu
2001-01-01
I put forward the stringy representation of the 1/N strong coupling (SC) expansion for the regularized Wilson's loop-averages in the continuous D>=3 Yang-Mills theory (YM_{D}) with a sufficiently large bare coupling constant \\lambda>\\lambda_{cr} and a fixed ultraviolet cut off \\Lambda. The proposed representation is proved to provide with the confining solution of the Dyson-Schwinger chain of the judiciously regularized U(N) Loop equations. Building on the results obtained, we suggest the stringy pattern of the low-energy theory associated to the D=4 U(\\infty)=SU(\\infty) gauge theory in the standard \\lambda=>0 phase with the asymptotic freedom in the UV domain. A nontrivial test, to clarify whether the AdS/CFT correspondence conjecture may be indeed applicable to the large N pure YM_{4} theory in the \\lambda=>\\infty limit, is also discussed.
Effective lattice Polyakov loop theory vs. full SU(3) Yang-Mills at finite temperature
Bergner, Georg; Philipsen, Owe
2013-01-01
A three-dimensional effective theory of Polyakov loops has recently been derived from Wilson's Yang-Mills lattice action by means of a strong coupling expansion. It is valid in the confined phase up to the deconfinement phase transition, for which it predicts the correct order and gives quantitative estimates for the critical coupling. In this work we study its predictive power for further observables like correlation functions and the equation of state. We find that the effective theory correctly reproduces qualitative features and symmetries of the full theory as the continuum is approached. Regarding quantitative predictions, we identify two classes of observables by numerical comparison as well as analytic calculations: correlation functions and their associated mass scales cannot be described accurately from a truncated effective theory, due to its inherently non-local nature involving long-range couplings. On the other hand, phase transitions and bulk thermodynamic quantities are accurately reproduced b...
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
Ruiz, F Ruiz
2015-01-01
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary.
Perturbative quantization of Yang-Mills theory with classical double as gauge algebra
Energy Technology Data Exchange (ETDEWEB)
Ruiz Ruiz, F. [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2016-02-15
Perturbative quantization of Yang-Mills theory with a gauge algebra given by the classical double of a semisimple Lie algebra is considered. The classical double of a real Lie algebra is a nonsemisimple real Lie algebra that admits a nonpositive definite invariant metric, the indefiniteness of the metric suggesting an apparent lack of unitarity. It is shown that the theory is UV divergent at one loop and that there are no radiative corrections at higher loops. One-loop UV divergences are removed through renormalization of the coupling constant, thus introducing a renormalization scale. The terms in the classical action that would spoil unitarity are proved to be cohomologically trivial with respect to the Slavnov-Taylor operator that controls gauge invariance for the quantum theory. Hence they do not contribute gauge invariant radiative corrections to the quantum effective action and the theory is unitary. (orig.)
The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter
Cremonesi, Stefano
2015-01-01
This paper presents a formula for the Hilbert series that counts gauge invariant chiral operators in 3d N=2 Yang-Mills theories with vectorlike matter and no Chern-Simons interactions. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background, which is determined by the Higgs mechanism. The sum over magnetic charges is restricted due to instanton effects that partially lift the classical Coulomb branch. The formalism is applied to unitary and symplectic gauge theories with fundamental matter, reproducing old results for the moduli space of vacua and the chiral ring, without resorting to any further effective superpotential on the moduli space.
`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories
Raptis, Ioannis
2007-05-01
Certain pivotal results from various applications of Abstract Differential Geometry (ADG) to gravity and gauge theories are presently collected and used to argue that we already possess a geometrically (pre)quantized, second quantized and manifestly background spacetime manifold independent vacuum Einstein gravitational field dynamics. The arguments carry also mutatis mutandis to the case of free Yang-Mills theories, since from the ADG-theoretic perspective gravity is regarded as another gauge field theory. The powerful algebraico-categorical, sheaf cohomological conceptual and technical machinery of ADG is then employed, based on the fundamental ADG-theoretic conception of a field as a pair ({mathcal{E}},{mathcal{D}}) consisting of a vector sheaf {mathcal{E}} and an algebraic connection {mathcal{D}} acting categorically as a sheaf morphism on {mathcal{E}}'s local sections, to introduce a ‘universal’, because expressly functorial, field quantization scenario coined third quantization. Although third quantization is fully covariant, on intuitive and heuristic grounds alone it formally appears to follow a canonical route; albeit, in a purely algebraic and, in contradistinction to geometric (pre)quantization and (canonical) second quantization, manifestly background geometrical spacetime manifold independent fashion, as befits ADG. All in all, from the ADG-theoretic vantage, vacuum Einstein gravity and free Yang-Mills theories are regarded as external spacetime manifold unconstrained, third quantized, pure gauge field theories. The paper abounds with philosophical smatterings and speculative remarks about the potential import and significance of our results to current and future Quantum Gravity research. A postscript gives a brief account of this author's personal encounters with Rafael Sorkin and his work.
Itoh, K; Sawanaka, H; So, H; Ukita, N
2003-01-01
We present a lattice theory with an exact fermionic symmetry, which mixes the link and the fermionic variables. The staggered fermionic variables may be reconstructed into a Majorana fermion in the continuum limit. The gauge action has a novel structure. Though it is the ordinary plaquette action, two different couplings are assigned in the ``Ichimatsu pattern'' or the checkered pattern. In the naive continuum limit, the fermionic symmetry survives as a continuum (or an $O(a^0)$) symmetry. The transformation of the fermion is proportional to the field strength multiplied by the difference of the two gauge couplings in this limit. This work is an extension of our recently proposed cell model toward the realization of supersymmetric Yang-Mills theory on lattice.
Energy-momentum tensor on the lattice: non-perturbative renormalization in Yang--Mills theory
Giusti, Leonardo
2015-01-01
We construct an energy-momentum tensor on the lattice which satisfies the appropriate Ward Identities (WIs) and has the right trace anomaly in the continuum limit. It is defined by imposing suitable WIs associated to the Poincare` invariance of the continuum theory. These relations come forth when the length of the box in the temporal direction is finite, and they take a particularly simple form if the coordinate and the periodicity axes are not aligned. We implement the method for the SU(3) Yang--Mills theory discretized with the standard Wilson action in presence of shifted boundary conditions in the (short) temporal direction. By carrying out extensive numerical simulations, the renormalization constants of the traceless components of the tensor are determined with a precision of roughly half a percent for values of the bare coupling constant in the range 0<= g^2_0<=1.
Confinement interpretation in a Yang-Mills + Higgs theory when considering Gribov's ambiguity
Justo, I F; Dudal, D; Gómez, A J; Guimaraes, M S; Sorella, S P; Vercauteren, D
2015-01-01
This work presents concisely the results obtained from the analysis of the two-point function of the gauge field in the $SU(2)$ and $SU(2)\\times U(1)$ gauge theories, in the Landau gauge, coupled to a scalar Higgs field in the fundamental or adjoint representation. Non-perturbative effects are considered by taking into account the Gribov ambiguity. In general, in both Yang-Mills models the gluon propagator has non-trivial contributions of physical and non-physical modes, which clearly depends on the group representation of the Higgs field. These results were presented during the Fourth Winter Workshop on Non-perturbative Quantum Field Theory, which took place in Sophia-Antipolis - France.
Supersymmetric Yang Mills Fields and Black Holes ; In Ten Dimensional Unified Field Theory
Patwardhan, Ajay
2007-01-01
The Ten dimensional Unified field theory has a 4 dimensional Riemannian spacetime and six dimensional Calabi Yau space structure. The supersymmetric Yang Mills fields and black holes are solutions in these theories. The formation of primordial black holes in early universe, the collapse to singularity of stellar black holes, the Hawking evaporation of microscopic black holes in LHC are topics of observational and theoretical interest. The observation of gamma ray bursts and creation of spectrum of particles and radiation of dark and normal matter occur due to primordial and microscopic black holes. The approach to singularity in black hole interior solutions, require the Bogoliubov transforms of SUSY YM fields in black hole geometries; both during formation and in evaporation. The Hawking effect of radiating black holes is applicable for all the fields. Invariants can be defined to give the conditions for these processes.
The five-loop beta function of Yang-Mills theory with fermions
Herzog, F.; Ruijl, B.; Ueda, T.; Vermaseren, J. A. M.; Vogt, A.
2017-02-01
We have computed the five-loop corrections to the scale dependence of the renormalized coupling constant for Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum Electrodynamics (QED). Our analytical result, obtained using the background field method, infrared rearrangement via a new diagram-by-diagram implementation of the R* operation and the Forcer program for massless four-loop propagators, confirms the QCD and QED results obtained by only one group before. The numerical size of the five-loop corrections is briefly discussed in the standard overline{MS} scheme for QCD with n f flavours and for pure SU( N) Yang-Mills theory. Their effect in QCD is much smaller than the four-loop contributions, even at rather low scales.
Lattice simulation of a center symmetric three dimensional effective theory for SU(2) Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Smith, Dominik
2010-11-17
We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for theWilson line which includes a ''fuzzy'' bag term to generate non-perturbative fluctuations between Z(2) degenerate ground states. The model is studied in the limit where the gauge fields are set to zero as well as the full model with gauge fields. We confirm that, at moderately weak coupling, the ''fuzzy'' bag term leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase. The effective potential for the Polyakov loop in the theory with gauge fields is extracted from the simulations including all modes of the loop as well as for cooled configurations where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram. Other results include the exact location of the phase boundary in the plane spanned by the coupling parameters, correlation lengths of several operators in the magnetic and electric sectors and the spatial string tension. We also present results from simulations of the full 4D Yang-Mills theory and attempt to make a qualitative comparison to the 3D effective theory. (orig.)
Thermodynamics of SU(2 quantum Yang-Mills theory and CMB anomalies
Directory of Open Access Journals (Sweden)
Hofmann Ralf
2014-04-01
Full Text Available A brief review of effective SU(2 Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field φ, based on non-propagating (antiselfdual field configurations of topological charge unity. We also discuss kinematic constraints on interacting propagating gauge fields implied by the according spatial coarse-graining, and we explain why the screening physics of an SU(2 photon is subject to an electric-magnetically dual interpretation. This argument relies on the fact that only (anticalorons of scale parameter ρ ∼ |φ|−1 contribute to the coarse-graining required for thermal-ground-state emergence at temperature T. Thus, use of the effective gauge coupling e in the (anticaloron action is justified, yielding the value ħ for the latter at almost all temperatures. As a consequence, the indeterministic transition of initial to final plane waves caused by an effective, pointlike vertex is fundamentally mediated in Euclidean time by a single (anticaloron being part of the thermal ground state. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2 Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2 photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2 vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck which would disqualify the latter as radiation. Indeed, if interpreted as single center
Kleihaus, B
1999-01-01
We point out that the statements in [hep-th/9903063] concerning the regularity of static axially symmetric solutions in Yang-Mills-dilaton (YMD) [1] and Einstein-Yang-Mills(-dilaton) (EYMD) theory [2,3] are incorrect, and that the non-singular local gauge potential of the YMD solutions [4] is twice differentiable.
Kleihaus, B; Kunz, Jutta
1999-01-01
In [hep-th/9907222] Hannibal claims to exclude the existence of particle-like static axially symmetric non-abelian solutions in SU(2) Einstein-Yang-Mills-dilaton theory. His argument is based on the asymptotic behaviour of such solutions. Here we disprove his claim by giving explicitly the asymptotic form of non-abelian solutions with winding number n=2.
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
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Pereira, A.D. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Potsdam (Germany); UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Sobreiro, R.F. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Sorella, S.P. [UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)
2016-10-15
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
Equal-time two-point correlation functions in Coulomb gauge Yang-Mills theory
Campagnari, D; Reinhardt, H; Astorga, F; Schleifenbaum, W
2009-01-01
We apply a new functional perturbative approach to the calculation of the equal-time two-point correlation functions and the potential between static color charges to one-loop order in Coulomb gauge Yang-Mills theory. The functional approach proceeds through a solution of the Schroedinger equation for the vacuum wave functional to order g^2 and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders.
Stochastic Feynman Rules for Yang-Mills Theory on the Plane
Nguyen, Timothy
2016-01-01
We analyze quantum Yang-Mills theory on $\\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is indefinite rather than positive definite. Specifically, we work with Lie-algebra valued fields on a lattice and exploit an approximate gauge-invariance that is restored when taking the continuum limit. This analysis is applied to show the equivalence between Wilson loop expectations computed using partial axial-gauge, complete axial-gauge, and the Migdal-Witten lattice formulation. As a consequence, we obtain intriguing Lie-theoretic identities involving heat kernels and iterated integrals.
The large $N$ limit of the topological susceptibility of Yang-Mills gauge theory
Cè, Marco; Giusti, Leonardo; Schaefer, Stefan
2016-01-01
We present a precise computation of the topological susceptibility $\\chi_{_\\mathrm{YM}}$ of SU$(N)$ Yang-Mills theory in the large $N$ limit. The computation is done on the lattice, using high-statistics Monte Carlo simulations with $N=3, 4, 5, 6$ and three different lattice spacings. Two major improvements make it possible to go to finer lattice spacing and larger $N$ compared to previous works. First, the topological charge is implemented through the gradient flow definition; and second, open boundary conditions in the time direction are employed in order to avoid the freezing of the topological charge. The results allow us to extrapolate the dimensionless quantity $t_0^2\\chi_{_\\mathrm{YM}}$ to the continuum and large $N$ limits with confidence. The accuracy of the final result represents a new quality in the verification of large $N$ scaling.
Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory
Bergner, Georg; Münster, Gernot; Özugurel, Umut D; Sandbrink, Dirk
2013-01-01
We present the current results of our simulations of N=1 supersymmetric Yang-Mills theory on a lattice. The masses of the gluino-glue particle, the a-eta-prime, the a-f0 meson, and the scalar glueball are obtained at finer lattice spacing than before, and extrapolations towards vanishing gluino mass are made. The calculations employ different levels of stout smearing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are better than in previous investigations. Taking the statistical and systematic uncertainties into account, the extrapolations towards vanishing gluino mass of the masses of the fermionic and bosonic states in our present calculations are consistent with the formation of degenerate supermultiplets.
A local and BRST-invariant Yang-Mills theory within the Gribov horizon
Capri, M A L; Fiorentini, D; Guimaraes, M S; Justo, I F; Pereira, A D; Mintz, B W; Palhares, L F; Sobreiro, R F; Sorella, S P
2016-01-01
We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies \\`a la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter independence of all correlation functions of local BRST-invariant operators.
Bassetto, A.; Nardelli, G.; Torrielli, A.
2002-10-01
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with n windings a nontrivial scaling intertwines n and N. In the noncommutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger gauge group U(∞). We perform an explicit perturbative calculation of such a loop up to O(g6) rather surprisingly, we find that in the contribution from the crossed graphs (the genuine noncommutative terms) the scaling we mentioned occurs for large n and N in the limit of maximal noncommutativity θ=∞. We present arguments in favor of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.
Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Bergner, G. [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Montvay, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Muenster, G.; Oezugurel, U.D.; Sandbrink, D. [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1
2013-04-15
We present the current results of our simulations of N=1 supersymmetric Yang-Mills theory on a lattice. The masses of the gluino-glue particle, the a-{eta}', the a-f{sub 0} meson, and the scalar glueball are obtained at finer lattice spacing than before, and extrapolations towards vanishing gluino mass are made. The calculations employ different levels of stout smearing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are better than in previous investigations. Taking the statistical and systematic uncertainties into account, the extrapolations towards vanishing gluino mass of the masses of the fermionic and bosonic states in our present calculations are consistent with the formation of degenerate supermultiplets.
Finite temperature and the Polyakov loop in the covariant variational approach to Yang-Mills Theory
Quandt, Markus; Reinhardt, Hugo
2017-03-01
We extend the covariant variational approach for Yang-Mills theory in Landau gauge to non-zero temperatures. Numerical solutions for the thermal propagators are presented and compared to high-precision lattice data. To study the deconfinement phase transition, we adapt the formalism to background gauge and compute the effective action of the Polyakov loop for the colour groups SU(2) and SU(3). Using the zero-temperature propagators as input, all parameters are fixed at T = 0 and we find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for SU(2) and first order for SU(3). The critical temperatures obtained are in reasonable agreement with lattice data.
Covariant variational approach to Yang-Mills theory: Effective potential of the Polyakov loop
Quandt, M.; Reinhardt, H.
2016-09-01
We compute the effective action of the Polyakov loop in S U (2 ) and S U (3 ) Yang-Mills theory using a previously developed covariant variational approach. The formalism is extended to background gauge and it is shown how to relate the low-order Green's functions to the ones in Landau gauge studied earlier. The renormalization procedure is discussed. The self-consistent effective action is derived and evaluated using the numerical solution of the gap equation. We find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for S U (2 ) and first order for S U (3 ). The critical temperatures obtained are in reasonable agreement with high-precision lattice data.
Covariant variational approach to Yang-Mills Theory: effective potential of the Polyakov loop
Quandt, Markus
2016-01-01
We compute the effective action of the Polyakov loop in SU(2) and SU(3) Yang-Mills theory using a previously developed covariant variational approach. The formalism is extended to background gauge and it is shown how to relate the low order Green's functions to the ones in Landau gauge studied earlier. The renormalization procedure is discussed. The self-consistent effective action is derived and evaluated using the numerical solution of the gap equation. We find a clear signal for a deconfinement phase transition at finite temperatures, which is second order for SU(2) and first order for SU(3). The critical temperatures obtained are in reasonable agreement with high precision lattice data.
Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory
Koloğlu, Murat
2016-01-01
We analyze the classical and quantum vacua of 2d $\\mathcal{N}=(8,8)$ supersymmetric Yang-Mills theory with $SU(N)$ and $U(N)$ gauge group, describing the worldvolume interactions of $N$ parallel D1-branes with flat transverse directions $\\mathbb{R}^8$. We claim that the IR limit of the $SU(N)$ theory in the superselection sector labeled $M \\pmod{N}$ --- identified with the internal dynamics of $(M,N)$-string bound states of Type IIB string theory --- is described by the symmetric orbifold $\\mathcal{N}=(8,8)$ sigma model into $(\\mathbb{R}^8)^{D-1}/\\mathbb{S}_D$ when $D=\\gcd(M,N)>1$, and by a single massive vacuum when $D=1$, generalizing the conjectures of E. Witten and others. The full worldvolume theory of the D1-branes is the $U(N)$ theory with an additional $U(1)$ 2-form gauge field $B$ coming from the string theory Kalb-Ramond field. This $U(N)+B$ theory has generalized field configurations, labeled by the $\\mathbb{Z}$-valued generalized electric flux and an independent $\\mathbb{Z}_N$-valued 't Hooft flux...
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold $S_4$ via the connection, with the generalized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.
Balakin, Alexander B; Zayats, Alexei E
2016-01-01
Alternative theories of gravity and their solutions are of considerable importance as at some fundamental level the world can reveal new features. Indeed, it is suspected that the gravitational field might be nonminimally coupled to the other fields at scales not yet probed, bringing into the forefront nonminimally coupled theories. In this mode, we consider a nonminimal Einstein-Yang-Mills theory with a cosmological constant. Imposing spherical symmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for the Yang-Mills field, we find expressions for the solutions of the theory. Further imposing constraints on the nonminimal parameters we find a family of exact solutions of the theory depending on five parameters, namely, two nonminimal parameters, the cosmological constant, the magnetic charge, and the mass. These solutions represent magnetic monopoles and black holes in magnetic monopoles with de Sitter, Minkowskian, and anti-de Sitter asymptotics, depending on the sign and value of the cosmol...
On Yang--Mills Theories with Chiral Matter at Strong Coupling
Energy Technology Data Exchange (ETDEWEB)
Shifman, M.; /Minnesota U., Theor. Phys. Inst. /Saclay, SPhT; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2008-08-20
Strong coupling dynamics of Yang-Mills theories with chiral fermion content remained largely elusive despite much effort over the years. In this work, we propose a dynamical framework in which we can address non-perturbative properties of chiral, non-supersymmetric gauge theories, in particular, chiral quiver theories on S{sub 1} x R{sub 3}. Double-trace deformations are used to stabilize the center-symmetric vacuum. This allows one to smoothly connect smaller(S{sub 1}) to larger(S{sub 1}) physics (R{sub 4} is the limiting case) where the double-trace deformations are switched off. In particular, occurrence of the mass gap in the gauge sector and linear confinement due to bions are analytically demonstrated. We find the pattern of the chiral symmetry realization which depends on the structure of the ring operators, a novel class of topological excitations. The deformed chiral theory, unlike the undeformed one, satisfies volume independence down to arbitrarily small volumes (a working Eguchi-Kawai reduction) in the large N limit. This equivalence, may open new perspectives on strong coupling chiral gauge theories on R{sub 4}.
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...
Lattice Study of the Extent of the Conformal Window in Two-Color Yang-Mills Theory
Voronov, Gennady
2013-01-01
We perform a lattice calculation of the Schr\\"odinger functional running coupling in SU(2) Yang-Mills theory with six massless Wilson fermions in the fundamental representation. The aim of this work is to determine whether the above theory has an infrared fixed point. Due to sensitivity of the $SF$ renormalized coupling to the tuning of the fermion bare mass we were unable to reliably extract the running coupling for stronger bare couplings.
Deconfinement transition in SU(2) Yang-Mills theory: a two-loop study
Reinosa, U; Tissier, M; Wschebor, N
2014-01-01
In a recent work we have proposed a perturbative approach for the study of the phase transition of pure Yang-Mills theories at finite temperature. This is based on a simple massive extension of background field methods in the Landau-DeWitt gauge, where the gluon mass term is related to the existence of Gribov ambiguities. We have shown that a one-loop calculation of the background field effective potential describes well the phase structure of the SU(2) and SU(3) theories. Here, we present the calculation of the next-to-leading order contribution in perturbation theory for the SU(2) case. In particular, we compute the background field effective potential at two-loop order and the corresponding Polyakov loop, a gauge invariant order parameter of the transition, at one-loop order. We show that the two-loop correction brings the critical temperature closer to its actual value as compared to the previous one-loop result. We also compute the thermodynamic pressure as a function of the temperature and show that two...
Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
Bork, L V; Vartanov, G S; Zhiboedov, A V
2009-01-01
In this paper we give all the details of the calculation that we presented in our previous paper ArXiv:0908.0387 where the infrared structure of the MHV gluon amplitudes in the planar limit for ${\\cal N}=4$ super Yang-Mills theory was considered in the next-to-leading order of perturbation theory. Explicit cancellation of the infrared divergencies in properly defined inclusive cross-sections is demonstrated first in a toy model example of "conformal QED" and then in the real ${\\cal N}=4$ SYM theory. We give the full-length details both for the calculation of the real emission and for the diagrams with splitting in initial and final states. The finite parts for some inclusive differential cross-sections are presented in an analytical form. In general, contrary to the virtual corrections, they do not reveal any simple structure. An example of the finite part containing just the log functions is presented. The dependence of inclusive cross-section on the external scale related to the definition of asymptotic sta...
Analytical study of Yang-Mills theory in the infrared from first principles
Siringo, Fabio
2015-01-01
Pure Yang-Mills SU(N) theory is studied in the Landau gauge and four dimensional space. While leaving the original Lagrangian unmodified, a double perturbative expansion is devised, based on a massive free-particle propagator. In dimensional regularization, all diverging mass terms cancel exactly in the double expansion, without the need to include mass counterterms that would spoil the symmetry of the Lagrangian. No free parameters are included that were not in the original theory, yielding a fully analytical approach from first principles. The expansion is safe in the infrared and is equivalent to the standard perturbation theory in the UV. At one-loop, explicit analytical expressions are given for the propagators and the running coupling and are found in excellent agreement with the data of lattice simulations. A universal scaling property is predicted for the inverse propagators and shown to be satisfied by the lattice data. Higher loops are found to be negligible in the infrared below 300 MeV where the c...
Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories
Golterman, M F L; Golterman, Maarten; Shamir, Yigal
2006-01-01
In equivariantly gauge-fixed SU(N) Yang--Mills theories, the gauge symmetry is only partially fixed, leaving a subgroup $H\\subset SU(N)$ unfixed. Such theories avoid Neuberger's nogo theorem if the subgroup $H$ contains at least the Cartan subgroup $U(1)^{N-1}$, and they are thus non-perturbatively well defined if regulated on a finite lattice. We calculate the one-loop beta function for the coupling $\\tilde{g}^2=\\xi g^2$, where $g$ is the gauge coupling and $\\xi$ is the gauge parameter, for a class of subgroups including the cases that $H=U(1)^{N-1}$ or $H=SU(M)\\times SU(N-M)\\times U(1)$. The coupling $\\tilde{g}$ represents the strength of the interaction of the gauge degrees of freedom associated with the coset $SU(N)/H$. We find that $\\tilde{g}$, like $g$, is asymptotically free. We solve the renormalization-group equations for the running of the couplings $g$ and $\\tilde{g}$, and find that dimensional transmutation takes place also for the coupling $\\tilde{g}$, generating a scale $\\tilde{\\Lambda}$ which c...
Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function
Tsukiji, Hidekazu; Kunihiro, Teiji; Ohnishi, Akira; Takahashi, Toru T
2016-01-01
We investigate possible entropy production in Yang-Mills (YM) field theory by using a quantum distribution function called Husimi function $f_{\\rm H}(A, E, t)$ for YM field, which is given by a coarse graining of Wigner function and non-negative. We calculate the Husimi-Wehrl (HW) entropy $S_{\\rm HW}(t)=-{\\rm Tr}f_H \\log f_H$ defined as an integral over the phase-space, for which two adaptations of the test-particle method are used combined with Monte-Carlo method. We utilize the semiclassical approximation to obtain the time evolution of the distribution functions of the YM field, which is known to show a chaotic behavior in the classical limit. We also make a simplification of the multi-dimensional phase-space integrals by making a product ansatz for the Husimi function, which is found to give a 10-20 per cent over estimate of the HW entropy for a quantum system with a few degrees of freedom. We show that the quantum YM theory does exhibit the entropy production, and that the entropy production rate agrees ...
Picard-Fuchs Ordinary Differential Systems in $N = 2$ Supersymmetric Yang-Mills Theories
Ohta, Y
1999-01-01
In general, Picard-Fuchs systems in N=2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independent periods. This paper discusses some properties of these Picard-Fuchs ODEs. In contrast with the usual Picard-Fuchs systems written in terms of moduli derivatives, there exists a Wronskian for this ordinary differential system and this Wronskian produces a new relation among periods, moduli and QCD scale parameter, which in the case of SU(2) is reminiscent of scaling relation of prepotential. On the other hand, in the case of the SU(3) theory, there are two kinds of ordinary differential equations, one of which is the equation directly constructed from periods and the other is derived from the SU(3) Picard-Fuchs equation...
Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
Ferrari, Frank
2003-04-01
We study the physics of N=1 super Yang-Mills theory with the gauge group U(N) and one adjoint Higgs field, by using the recently derived exact effective superpotentials. Interesting phenomena occur for some special values of the Higgs potential couplings. We find critical points with massless glueballs and/or massless monopoles, confinement without a mass gap, and tensionless domain walls. We describe the transitions between regimes with different patterns of gauge symmetry breaking, or, in the matrix model language, between solutions with a different number of cuts. The standard large N expansion is singular near the critical points, with domain wall tensions scaling as a fractional power of N. We argue that the critical points are four-dimensional analogues of the Kazakov critical points that are commonly found in low dimensional matrix integrals. We define a double scaling limit that yields the exact tension of BPS two-branes in the resulting N=1, four-dimensional noncritical string theory. D-brane states can be deformed continuously into closed string solitonic states, and vice versa, along paths that go over regions where the string coupling is strong.
Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
Ferrari, F
2003-01-01
We study the physics of N=1 super Yang-Mills theory with gauge group U(Nc) and one adjoint Higgs field, by using the recently derived exact effective superpotentials. Interesting phenomena occur for some special values of the Higgs potential couplings. We find critical points with massless glueballs and/or massless monopoles, confinement without a mass gap, and tensionless domain walls. We describe the transitions between regimes with different patterns of gauge symmetry breaking, or, in the matrix model language, between solutions with a different number of cuts. The standard large Nc expansion is singular near the critical points, with domain walls tensions scaling as a fractional power of Nc. We argue that the critical points are four dimensional analogues of the Kazakov critical points that are commonly found in low dimensional matrix integrals. We define a double scaling limit that yields the exact tension of BPS two-branes in the resulting N=1, four dimensional non-critical string theory. D-brane states...
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...
Yang-Mills theory for semidirect products G x g{sup *} and its instantons
Energy Technology Data Exchange (ETDEWEB)
Ruiz Ruiz, F. [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2015-07-15
Yang-Mills theory with a symmetry algebra that is the semidirect product h x h* defined by the coadjoint action of a Lie algebra h on its dual h* is studied. The gauge group is the semidirect product G{sub h} x h*, a noncompact group given by the coadjoint action on h* of the Lie group G{sub h} of h* For h simple, a method to construct the self-antiself dual instantons of the theory and their gauge nonequivalent deformations is presented. Every G{sub h} x h* instanton has an embedded G{sub h} instanton with the same instanton charge, in terms of which the construction is realized. As an example, h = su(2) and instanton charge one is considered. The gauge group is in this case SU(2) x R{sup 3}. Explicit expressions for the selfdual connection, the zero modes and the metric and complex structures of the moduli space are given. (orig.)
Tachyonic instabilities in 2+1 dimensional Yang-Mills theory and its connection to Number Theory
Chamizo, Fernando
2016-01-01
We consider the $2+1$ dimensional Yang-Mills theory with gauge group $\\text{SU}(N)$ on a flat 2-torus under twisted boundary conditions. We study the possibility of phase transitions (tachyonic instabilities) when $N$ and the volume vary and certain chromomagnetic flux associated to the topology of the bundle can be adjusted. Under natural assumptions about how to match the perturbative regime and the expected confinement, we prove that the absence of tachyonic instabilities is related to some problems in number theory, namely the Diophantine approximation of irreducible fractions by other fractions of smaller denominator.
Energy Technology Data Exchange (ETDEWEB)
Bergner, G. [Universität Bern, Institut für Theoretische Physik,Länggasse, 3012 Bern (Switzerland); Langelage, J.; Philipsen, O. [Institut für Theoretische Physik, Goethe-Universität Frankfurt,Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany)
2015-11-04
We consider a three-dimensional effective theory of Polyakov lines derived previously from lattice Yang-Mills theory and QCD by means of a resummed strong coupling expansion. The effective theory is useful for investigations of the phase structure, with a sign problem mild enough to allow simulations also at finite density. In this work we present a numerical method to determine improved values for the effective couplings directly from correlators of 4d Yang-Mills theory. For values of the gauge coupling up to the vicinity of the phase transition, the dominant short range effective coupling are well described by their corresponding strong coupling series. We provide numerical results also for the longer range interactions, Polyakov lines in higher representations as well as four-point interactions, and discuss the growing significance of non-local contributions as the lattice gets finer. Within this approach the critical Yang-Mills coupling β{sub c} is reproduced to better than one percent from a one-coupling effective theory on N{sub τ}=4 lattices while up to five couplings are needed on N{sub τ}=8 for the same accuracy.
Plane-wave matrix theory from N=4 super-Yang-Mills on RxS{sup 3}
Energy Technology Data Exchange (ETDEWEB)
Kim, Nakwoo E-mail: kim@aei.mpg.de; Klose, Thomas E-mail: thklose@aei.mpg.de; Plefka, Jan E-mail: plefka@aei.mpg.de
2003-11-03
Recently a mass deformation of the maximally supersymmetric Yang-Mills quantum mechanics has been constructed from the supermembrane action in eleven-dimensional plane-wave backgrounds. However, the origin of this plane-wave matrix theory in terms of a compactification of a higher-dimensional super-Yang-Mills model has remained obscure. In this paper we study the Kaluza-Klein reduction of D=4, N=4 super-Yang-Mills theory on a round three-sphere, and demonstrate that the plane-wave matrix theory arises through a consistent truncation to the lowest lying modes. We further explore the relation between the dilatation operator of the conformal field theory and the Hamiltonian of the quantum mechanics through perturbative calculations up to two-loop order. In particular, we find that the one-loop anomalous dimensions of pure scalar operators are completely captured by the plane-wave matrix theory. At two-loop level this property ceases to exist.
Directory of Open Access Journals (Sweden)
Trunev A. P.
2015-10-01
Full Text Available The article presents a project of the capacitor in the Yang-Mills theory. Model capacitor represents the equipotential surfaces separated by a space. To describe the mechanism of condensation chromodynamics field used numerical models developed based on an average of the Yang-Mills theory. In the present study, we used eight-scalar component model that in the linear case is divided into two groups containing three or five fields respectively. In contrast to classical electrodynamics, a static model of the Yang-Mills is not divided into independent equations because of the nonlinearity of the model itself. However, in the case of a linear theory separation is possible. It is shown that in this particular case, the Yang-Mills theory is reduced to Poisson theory, which describes the electrostatic and magnetostatic phenomena. In the present work it is shown that in a certain region of the parameters of the capacitor of the Yang-Mills theory on the functional properties of the charge accumulation and retention of the field is similar to the capacitor of the electrostatic field or a magnet in magnetostatics. This means that in nature there are two types of charges, which are sources of macroscopic Yang-Mills field, which are similar to the properties of electric and magnetic charges in the Poisson theory. It is shown that in Yang-Mills only one type of charge may be associated with the distribution density of the substance, while another type of charge depends on the charge distribution of the first type. This allows us to provide an explanation for the lack of symmetry between electric and magnetic charges
${\\cal N}=4$ Supersymmetric Yang-Mills Theory on Orbifold-$T^4\\/{\\bf Z}_$2 Higher Rank Case
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of ${\\cal N}=4$ supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$ for SU(N). We generalize our previous work for SU(2) to the SU(N) case. These partition functions can be factorized into product of bulk contribution of quotient space $T^4/{\\bf Z}_2$ and of blow-up formula including $A_{N-1}$ theta functions with level N.
Non-perturbative renormalization of the energy-momentum tensor in SU(3) Yang-Mills theory
Giusti, Leonardo
2014-01-01
We present a strategy for a non-perturbative determination of the finite renormalization constants of the energy-momentum tensor in the SU(3) Yang-Mills theory. The computation is performed by imposing on the lattice suitable Ward Identites at finite temperature in presence of shifted boundary conditions. We show accurate preliminary numerical data for values of the bare coupling g_0^2 ranging for 0 to 1.
The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
Bern, Z; Kosower, D A; Roiban, R; Spradlin, M; Vergu, C; Volovich, A
2008-01-01
We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N=4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal...
The decay of unstable strings in SU(2) Yang-Mills theory
Pepé, M
2009-01-01
We investigate the stability of strings connecting charges Q in the representation {2Q+1} of SU(2) Yang-Mills theory in (2+1) dimensions. While the fundamental {2}-string between two charges Q=1/2 is unbreakable and stable, the string connecting static charges transforming under any other representation Q>1/2 is unstable and decays. A charge Q=1 can be completely screened by gluons and so the adjoint {3}-string ultimately breaks. A charge Q=3/2 can be only partially screened to a fundamental charge Q=1/2. Thus, stretching a {4}-string beyond a critical length, it decays into the stable {2}-string by gluon pair creation. The complete breaking of a {5}-string happens in two steps, it first decays into a {3}-string and then breaks completely. A phenomenological constituent gluon model provides a good quantitative description of the energy of the screened charges at the ends of an unstable string.
Konishi form factor at three loops in N =4 supersymmetric Yang-Mills theory
Ahmed, Taushif; Banerjee, Pulak; Dhani, Prasanna K.; Rana, Narayan; Ravindran, V.; Seth, Satyajit
2017-04-01
We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in N =4 supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction (D R ¯ ) scheme. We show that it satisfies the KG equation in D R ¯ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality of the infrared (IR) structures of on-shell form factors. In addition, the highest transcendental terms of the FF of the Konishi operator are identical to those of half-BPS operator indicating the probable existence of deeper structure of the on-shell FF. We also confirm the UV anomalous dimensions of the Konishi operator up to third order providing a consistency check on the both UV and universal IR structures in N =4 .
Hamiltonian Approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge
Reinhardt, H
2008-01-01
We study the Hamiltonian approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss' law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schroedinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the ...
On spinors, strings, integrable models and decomposed Yang-Mills theory
Ioannidou, Theodora; Niemi, Antti J
2014-01-01
This paper deals with various interrelations between strings and surfaces in three dimensional ambient space, two dimensional integrable models and two dimensional and four dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three dimensional string-like structures. Then its relation to the structure of the su(2) Lie algebra valued Maurer-Cartan one-form is presented; while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is show how the Lax pair of the integrable nonlinear Schroedinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation and it is described how a spinor based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schroedinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to ...
Spatially compact solutions and stabilization in Einstein-Yang-Mills-Higgs theories.
Forgács, Péter; Reuillon, Sébastien
2005-08-01
New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs equations with the Higgs field in the triplet (doublet) representation are presented. They form continuous families parametrized by alpha = M(W)/M(Pl) [M(W) (M(Pl)) denoting the W boson (the Planck) mass]. The corresponding space-times are regular and have spatially compact sections. A particularly interesting class with the Yang-Mills amplitude being nodeless is exhibited and is shown to be linearly stable with respect to spherically symmetric perturbations. For some solutions with nodes of the Yang-Mills amplitude a new stabilization phenomenon is found, according to which their unstable modes disappear as alpha increases (for the triplet) or decreases (for the doublet).
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.
Baker, M; Brambilla, Nora; Prosperi, G M; Zachariasen, F
1995-01-01
In this paper we express the velocity dependent, spin dependent heavy quark potential V_{q\\bar q} in QCD in terms of a Wilson Loop W(\\Gamma) determined by pure Yang Mills theory. We use an effective dual theory of long-distance Yang Mills theory to calculate W(\\Gamma) for large loops; i.e. for loops of size R > R_{FT}. (R_{FT} is the flux tube radius, fixed by the value of the Higgs (monopole) mass of the dual theory, which is a concrete realization of the Mandelstam 't Hooft dual superconductor mechanism of confinement). We replace W(\\Gamma) by W_{eff}(\\Gamma), given by a functional integral over the dual variables, which for R > R_{FT} can be evaluated by a semiclassical expansion, since the dual theory is weakly coupled at these distances. The classical approximation gives the leading contribution to W_{eff}(\\Gamma) and yields a velocity dependent heavy quark potential which for large R becomes linear in R, and which for small R approaches lowest order perturbative QCD. This latter fact means that these re...
Non-Gaussianity of the topological charge distribution in $\\mathrm{SU}(3)$ Yang-Mills theory
Cè, Marco
2015-01-01
In Yang-Mills theory, the cumulants of the na\\"ive lattice discretization of the topological charge evolved with the Yang-Mills gradient flow coincide, in the continuum limit, with those of the universal definition. We sketch in these proceedings the main points of the proof. By implementing the gradient-flow definition in numerical simulations, we report the results of a precise computation of the second and the fourth cumulant of the $\\mathrm{SU}(3)$ Yang-Mills theory topological charge distribution, in order to measure the deviation from Gaussianity. A range of high-statistics Monte Carlo simulations with different lattice volumes and spacings is used to extrapolate the results to the continuum limit with confidence by keeping finite-volume effects negligible with respect to the statistical errors. Our best result for the topological susceptibility is $t_0^2\\chi=6.67(7)\\times 10^{-4}$, while for the ratio between the fourth and the second cumulant we obtain $R=0.233(45)$.
Generating functional and large N limit of nonlocal 2D generalized Yang-Mills theories (nlgYM 2's)
Saaidi, K.; Sajadi, H. M.
2001-01-01
Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) on nonlocal generalized 2D Yang Mills theories (nlgYM_2's), which are nonlocal in the auxiliary field. This has been considered before by Saaidi and Khorrami. Our calculations are done for general surfaces. We find a general expression for the free energy of W(φ) =φ^{2k} in nlgYM_2 theories at the strong coupling phase (SCP) regime (A > A_c) for large groups. In the specific φ^4 model, we show that the theory has a third order phase transition.
Caporaso, Nicola; Cirafici, Michele; Griguolo, Luca; Pasquetti, Sara; Seminara, Domenico; Szabo, Richard J.
2006-01-01
We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of q-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite N, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large N limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point all non-trivial vacua contribute, instantons are enhanced and the theory appears to undergo a phase transition into a strong coupling regime. We rederive these results by performing a saddle-point approximation to the exact partition function. We obtain a q-deformed version of the Douglas-Kazakov equation for two-dimensional Yang-Mills theory on the sphere, whose one-cut solution below the transition point reproduces the resolved conifold geometry. Above the critical point we propose a two-cut solution that should reproduce the chiral-antichiral dynamics found for black holes on the Calabi-Yau threefold and the Gross-Taylor string in the undeformed limit. The transition from the strong coupling phase to the weak coupling phase appears to be of third order.
Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories
Anderson, Lara B.; Braun, Volker; Karp, Robert L.; Ovrut, Burt A.
2010-06-01
A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.
Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories
Anderson, Lara B; Karp, Robert L; Ovrut, Burt A
2010-01-01
A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.
Scattering amplitudes and Wilson loops in twistor space
Energy Technology Data Exchange (ETDEWEB)
Adamo, Tim; Mason, Lionel [Mathematical Institute, 24-29 St. Giles' , Oxford OX1 3LB (United Kingdom); Bullimore, Mathew [Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP (United Kingdom); Skinner, David, E-mail: adamo@maths.ox.ac.uk [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2 L 2Y5 (Canada)
2011-11-11
This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for N=4 super-Yang-Mills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally supersymmetric Yang-Mills theory. We start by deriving the MHV rules for gauge theory amplitudes from the twistor action in an axial gauge in twistor space, and show that this gives rise to the original momentum space version given by Cachazo, Svrcek and Witten. We then go on to obtain from these the construction of the momentum twistor space loop integrand using (planar) MHV rules and show how it arises as the expectation value of a holomorphic Wilson loop in twistor space. We explain the connection between the holomorphic Wilson loop and certain light-cone limits of correlation functions. We give a brief review of other ideas in connection with amplitudes in twistor space: twistor-strings, recursion in twistor space, the Grassmannian residue formula for leading singularities and amplitudes as polytopes. This paper is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Scattering amplitudes in gauge theories'. (review)
Energy Technology Data Exchange (ETDEWEB)
Sandbrink, Dirk
2015-01-26
One of the most promising candidates to describe the physics beyond the standard model is the so-called supersymmetry. This work was created in the context of the DESY-Muenster-Collaboration, which studies in particular the N=1 supersymmetric Yang-Mills theory (SYM). SYM is a comparatively simple theory, which is therefore well-suited to study the expected properties of a supersymmetric theory with the help of Monte Carlo simulations on the lattice. This thesis is focused on the numerical determination of the quarkpotential, the glueball masses and the phase structur of the N=1 supersymmetric Yang-Mills theory. The quarkpotential is used to calculate the Sommer scale, which in turn is needed to convert the dimensionless lattice spacing into physical units. Glueballs are hypothetical particles built out of gluons, their masses are relatively hard to determine in lattice simulations due to their pure gluonic nature. For this reason, various methods are studied to reduce the uncertainties of the mass determination. The focus lies on smearing methods and their use in variational smearing as well as on the use of different glueball operators. Lastly, a first look is taken at the phase diagram of the model at finite temperature. Various simulations have been performed at finite temperature in parallel to those performed at temperature zero to analyse the behaviour of the Polyakov loop and the gluino condensate in greater detail.
Directory of Open Access Journals (Sweden)
Trunev A. P.
2015-09-01
Full Text Available The article presents a project of the Yang-Mills amplifier. Amplifier model is a multilayer spherical shell with increasing density towards the center. In the center of the amplifier is the core of high-density material. It is shown that in such a system, the amplitude of the Yang-Mills waves rises from the periphery to the center of several orders of magnitude. The role of the Yang-Mills field in the processes occurring in the nuclei of galaxies, stars and planets is discussed. The data modeling to strengthen the Yang-Mills field in the bowels of the planet, with an atomic explosion, and in some special devices such as the voltaic pile. To describe the mechanism of amplification chromodynamics field used as accurate results in Yang-Mills theory and numerical models developed based on an average and the exact equations as well. Among the exact solutions of the special role played by the centralsymmetric metric describing the contribution of the Yang-Mills field in the speed of recession of galaxies. Among the approximate numerical models can be noted the eight-scalar model we have developed for the simulation of non-linear color oscillations and chaos in the Yang-Mills theory. Earlier models were investigated spatio-temporal oscillations of the YangMills theory in the case of three and eight colors. The results of numerical simulation show that the nonlinear interaction does not lead to a spatial mixing of colors as it might be in the case of turbulent diffusion. Depending on the system parameters there is a suppression of the amplitude of the oscillations the first three by five colors or vice versa. The kinetic energy fluctuations or shared equally between the color components, or dominated by the kinetic energy of repressed groups of colors. In the present study, we found that amplification chromodynamic field leads to a sharp increase in the amplitude of the suppressed color, which can lead to an increase in entropy, excitation of nuclear
Revisiting the deconfinement phase transition in SU(4) Yang-Mills theory in 2+1 dimensions
Holland, Kieran; Wiese, Uwe-Jens
2008-01-01
In order to deepen our understanding of the nature of the deconfinement phase transition for various gauge groups, we investigate SU(4) Yang-Mills theory in 2+1 dimensions. We find that the transition is weakly first order. We perform extensive Monte Carlo simulations on lattices with temporal extent N_t = 3, 4 and 5, and spatial sizes up to N_s = 20 N_t. We observe coexistence of confined and deconfined phases at the critical temperature, and finite-size scaling shows consistency with first order exponents. The continuum extrapolation of the latent heat yields L_h/T_c^3=0.187(9).
The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
Cè, Marco; García Vera, Miguel; Giusti, Leonardo; Schaefer, Stefan
2016-11-01
We compute the topological susceptibility of the SU (N) Yang-Mills theory in the large-N limit with a percent level accuracy. This is achieved by measuring the gradient-flow definition of the susceptibility at three values of the lattice spacing for N = 3 , 4 , 5 , 6. Thanks to this coverage of parameter space, we can extrapolate the results to the large-N and continuum limits with confidence. Open boundary conditions are instrumental to make simulations feasible on the finer lattices at the larger N.
A non-perturbative study of the correlation functions of three-dimensional Yang-Mills theory
Huber, Markus Q
2016-01-01
Yang-Mills theory is studied in three dimensions using the equations of motion of the $1$PI and $3$PI effective actions. The employed self-contained truncation includes the propagators, the three-point functions and the four-gluon vertex dynamically. In the gluon propagator also two-loop diagrams are taken into account. The higher gluonic correlation functions show sizable deviations from the tree-level only at low momenta. Also the couplings derived from the vertices agree well down to a few GeV. In addition, different methods to subtract spurious divergences are explored.
Predicting Planck scale and Newton constant from a Yang-Mills gauge theory: 1 and 2-loops estimates
Sobreiro, Rodrigo F
2016-01-01
Recently, a model for an emergent gravity based on $SO(5)$ Yang-Mills action in Euclidian four-dimensional spacetime was proposed. In this work we provide some 1 and 2-loop computations and show that the model can accomodate suitable predicting values for the Newton's gravitational constant. Moreover, it is shown that the typical scale of the expected phase transition between the quantum theory and the geometrodynamical phase is consistent with Planck scale. We also provide a discussion on the cosmological constant problem.
Yang-Mills theory in 2+1 dimensions: Coupling of matter fields and string-breaking effects
Energy Technology Data Exchange (ETDEWEB)
Agarwal, Abhishek [Physics Department, City College of the CUNY, New York, NY 10031 (United States)], E-mail: abhishek@sci.ccny.cuny.edu; Karabali, Dimitra [Department of Physics and Astronomy, Lehman College of the CUNY, Bronx, NY 10468 (United States)], E-mail: dimitra.karabali@lehman.cuny.edu; Nair, V.P. [Physics Department, City College of the CUNY, New York, NY 10031 (United States)], E-mail: vpn@sci.ccny.cuny.edu
2008-02-11
We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of gauge-invariant matrix variables. Coupling to scalar matter fields is discussed in terms of gauge-invariant fields. We analyze how the screening of adjoint (and other screenable) representations can arise in this formalism. A Schroedinger equation is then derived for the gluelump states which are the daughter states when an adjoint string breaks. A variational solution of this Schroedinger equation leads to an analytic estimate of the string-breaking energy which is within 8.8% of the latest lattice estimates.
The Deconfinement Phase Transition of Sp(2) and Sp(3) Yang-Mills Theories in 2+1 and 3+1 Dimensions
Holland, K; Wiese, U J
2003-01-01
Some time ago, Svetitsky and Yaffe have argued that -- if the deconfinement phase transition of a (d+1)-dimensional Yang-Mills theory with gauge group G is second order -- it should be in the universality class of a d-dimensional spin model symmetric under the center of G. For d=3 these arguments have been confirmed numerically only in the SU(2) case with center Z(2), simply because all SU(N) Yang-Mills theories with N>=3 seem to have non-universal first order phase transitions. The symplectic groups Sp(N) also have the center Z(2) and provide another extension of SU(2) = Sp(1) to general N. Using lattice simulations, we find that the deconfinement phase transition of Sp(2) Yang-Mills theory is first order in 3+1 dimensions, while in 2+1 dimensions stronger fluctuations induce a second order transition. In agreement with the Svetitsky-Yaffe conjecture, for (2+1)-d Sp(2) Yang-Mills theory we find the universal critical behavior of the 2-d Ising model. For Sp(3) Yang-Mills theory the transition is first order b...
Caporaso, N; Griguolo, L; Pasquetti, S; Seminara, D; Szabó, R J; Caporaso, Nicola; Cirafici, Michele; Griguolo, Luca; Pasquetti, Sara; Seminara, Domenico; Szabo, Richard J.
2006-01-01
We examine the problem of counting bound states of BPS black holes on local Calabi-Yau threefolds which are fibrations over a Riemann surface by computing the partition function of $q$-deformed Yang-Mills theory on the Riemann surface. We study in detail the genus zero case and obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for $U(N)$ Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. The correspondence between two and three dimensional gauge theories is elucidated by an explicit mapping between two-dimensional Yang-Mills instantons and flat connections on the Lens space. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces exactly to the trivial flat connection sector with instanton contributions exponentially suppressed, and the topological string partition function on the resolved conifold ...
Quantum fields in the non-perturbative regime. Yang-Mills theory and gravity
Energy Technology Data Exchange (ETDEWEB)
Eichhorn, Astrid
2011-09-06
In this thesis we study candidates for fundamental quantum field theories, namely non-Abelian gauge theories and asymptotically safe quantum gravity. Whereas the first ones have a stronglyinteracting low-energy limit, the second one enters a non-perturbative regime at high energies. Thus, we apply a tool suited to the study of quantum field theories beyond the perturbative regime, namely the Functional Renormalisation Group. In a first part, we concentrate on the physical properties of non-Abelian gauge theories at low energies. Focussing on the vacuum properties of the theory, we present an evaluation of the full effective potential for the field strength invariant F{sub {mu}}{sub {nu}}F{sup {mu}}{sup {nu}} from non-perturbative gauge correlation functions and find a non-trivial minimum corresponding to the existence of a dimension four gluon condensate in the vacuum. We also relate the infrared asymptotic form of the {beta} function of the running background-gauge coupling to the asymptotic behavior of Landau-gauge gluon and ghost propagators and derive an upper bound on their scaling exponents. We then consider the theory at finite temperature and study the nature of the confinement phase transition in d = 3+1 dimensions in various non-Abelian gauge theories. For SU(N) with N= 3,..,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. Our studies shed light on the question which property of a gauge group determines the order of the phase transition. In a second part we consider asymptotically safe quantum gravity. Here, we focus on the Faddeev-Popov ghost sector of the theory, to study its properties in the context of an interacting UV regime. We investigate several truncations, which all lend support to the conjecture that gravity may be asymptotically safe. In a first truncation, we study the ghost anomalous dimension
Wilhelm, Matthias
2016-01-01
In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in $\\mathcal{N}=4$ super Yang-Mills theory at various loop orders and for various numbers of external legs. We show how to use on-shell methods for their calculation and in particular extract the dilatation operator from the result. We also investigate the properties of the corresponding remainder functions. Moreover, we extend on-shell diagrams, a Gra{\\ss}mannian integral formulation and an integrability-based construction via R-operators to form factors, focussing on the chiral part of the stress-tensor supermultiplet as an example. In the second part, we study the $\\beta$- and the $\\gamma_i$-deformation, which were respectively shown to be the most general supersymmetric and non-supersymmetric field-theory deformations of $\\mathcal{N}=4$ super Yang-Mills theory that are integrable at the level of the asymptotic Bethe ansatz. For these theories, a new kind of finite-size effect occurs, which we call ...
Della Morte, Michele
2011-01-01
We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z_N^3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang--Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum ...
Della Morte, Michele; Giusti, Leonardo
2011-05-01
We make use of the global symmetries of the Yang-Mills theory on the lattice to design a new computational strategy for extracting glueball masses and matrix elements which achieves an exponential reduction of the statistical error with respect to standard techniques. By generalizing our previous work on the parity symmetry, the partition function of the theory is decomposed into a sum of path integrals each giving the contribution from multiplets of states with fixed quantum numbers associated to parity, charge conjugation, translations, rotations and central conjugations Z N 3. Ratios of path integrals and correlation functions can then be computed with a multi-level Monte Carlo integration scheme whose numerical cost, at a fixed statistical precision and at asymptotically large times, increases power-like with the time extent of the lattice. The strategy is implemented for the SU(3) Yang-Mills theory, and a full-fledged computation of the mass and multiplicity of the lightest glueball with vacuum quantum numbers is carried out at a lattice spacing of 0.17 fm.
Spacetime foam in twistor string theory
Hartnoll, S A; Hartnoll, Sean A.; Policastro, Giuseppe
2004-01-01
We show how a Kahler spacetime foam in four dimensional conformal (super)gravity may be mapped to twistor spaces carrying the D1 brane charge of the B model topological string theory. The spacetime foam is obtained by blowing up an arbitrary number of points in $\\C^2$ and can be interpreted as a sum over gravitational instantons. Some twistor spaces for blowups of $\\C^2$ are known explicitly. In these cases we write down a meromorphic volume form and suggest a relation to a holomorphic superform on a corresponding super Calabi-Yau manifold.
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).
Towards the large N limit of pure Nu = 1 super Yang-Mills theory.
Maldacena, J; Nuñez, C
2001-01-22
We find the gravity solution corresponding to a large number of Neveu-Schwarz or D5-branes wrapped on a two sphere so that we have pure Nu = 1 super Yang-Mills in the IR. The supergravity solution is smooth, it shows confinement, and it breaks the U(1)(R) chiral symmetry in the appropriate way. When the gravity approximation is valid the masses of glueballs are comparable to the masses of Kaluza-Klein (KK) states on the 5-brane, but if we could quantize strings on this background it looks like we should be able to decouple the KK states.
Fröb, Markus B
2016-01-01
We prove the existence of the operator product expansion (OPE) in Euclidean Yang-Mills theories as a short-distance expansion, to all orders in perturbation theory. We furthermore show that the Ward identities of the underlying gauge theory are reflected in the OPE; especially, the OPE of an arbitrary number of gauge-invariant composite operators only involves gauge-invariant composite operators. Moreover, we derive recursion relations which allow to construct the OPE coefficients, the quantum BRST differential and the quantum antibracket order by order in perturbation theory, starting from the known free-theory objects. These relations are completely finite from the start, and do not need any further renormalisation as is usually the case in other approaches. Our results underline the importance of the OPE as a general structure underlying quantum field theories. The proofs are obtained within the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisation group flow equations, and generalise similar...
A unified field theory II: Gravity interacting with a Yang-Mills and Higgs field
Gerhardt, Claus
2016-01-01
We quantize the interaction of gravity with a Yang-Mills and Higgs field using canonical quantization. Similar to the approach in a previous paper we discard the Wheeler-DeWitt equation and express the Hamilton constraint by the evolution equation of the mean curvature of the hypersurfaces in the foliation defined by the Hamiltonian setting. Expressing the time derivative of the mean curvature with the help of the Poisson brackets the canonical quantization of this equation leads to a wave equation in $Q=(0,\\infty)\\times \\cal{S}_o$, where $\\cal{S}_o$ is one of the Cauchy hypersurfaces in the Hamiltonian setting. The wave equation describes the interaction of an arbitrary Riemannian metric in $\\cal{S}_o$ and a given Yang-Mills and Higgs field. If the metric is complete $Q$ is globally hyperbolic. In case $\\cal{S}_o$ is compact we also prove a spectral resolution of the wave equation and establish sufficient conditions guaranteeing a mass gap.
Cho Abelian decomposition to the exact A-M-A solutions of the SU(2) Yang-Mills-Higgs theory
Wong, Khai-Ming; Teh, Rosy; Tie, Timothy
2015-04-01
We consider Cho Abelian decomposition to the exact A-M-A configurations in the SU(2) Yang-Mills-Higgs theory. The non-Abelian Yang-Mills gauge potential is decomposed into the restricted and the valence part. With the decomposition, the complete Abelian picture that draws to the various monopoles configurations can be seen clearly. The singularities for the two accompanying antimonopoles and the vortex ring are removed by the corresponding valence potential. However the singularity of the composite monopole at the origin is not removed, but strengthened. Hence the composite monopole is a different kind of monopole entity. Elsewhere, the plane singularity in the solution is not readily be removed by the valence potential. On the other hand, we also solve the decomposed equations to study the solutions that lead to the spatial infinity boundary conditions of the various numerical monopoles configurations. The decomposed equations are also solved in the near-origin region for exact solutions and their properties such as the magnetic field are plotted, which confirms the correspondence with their properties at the near infinity region.
Institute of Scientific and Technical Information of China (English)
寇谡鹏
2002-01-01
Used the dimensional reduction in the sense of Parisi and Sourlas, the gauge fixing term of the four-dimensionalYang-Mills field without the theta term is reduced to a two-dimensional principal chiral model. By adding the θ term(θ = π), the two-dimensional principal chiral model changes into the two-dimensional level 1 Wess-Zumino-Novikov-Witten model. The non-trivial fixed point indicates that Yang-Mills theory at θ = π is a critical theory without massgap and confinement.
Field-dependent BRST-antiBRST transformations in Yang-Mills and Gribov-Zwanziger theories
Moshin, Pavel Yu.; Reshetnyak, Alexander A.
2014-11-01
We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet λa, a=1,2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang-Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang-Mills vacuum functional, special field-dependent BRST-antiBRST transformations, with sa-potential parameters λa=saΛ induced by a finite even-valued functional Λ and by the anticommuting generators sa of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary Rξ-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the Yang-Mills action by the Gribov horizon functional in the Gribov-Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST-antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations. introduction of finite BRST-antiBRST transformations, being polynomial in powers of a constant Sp(2)-doublet of Grassmann-odd parameters λa and leaving the quantum action of the Yang-Mills theory invariant to all orders in λa; definition of finite field-dependent BRST-antiBRST transformations, being polynomial in powers of an Sp(2)-doublet of Grassmann-odd functionals λa(ϕ) depending on the classical Yang-Mills fields, the ghost
Wilson Loops in Noncommutative Yang Mills
Ishibashi, N; Kawai, H; Kitazawa, Y; Ishibashi, Nobuyuki; Iso, Satoshi; Kawai, Hikaru; Kitazawa, Yoshihisa
2000-01-01
We study the correlation functions of the Wilson loops in noncommutative Yang-Mills theory based upon its equivalence to twisted reduced models. We point out that there is a crossover at the noncommutativity scale. At large momentum scale, the Wilson loops in noncommmutative Yang-Mills represent extended objects. They coincide with those in ordinary Yang-Mills theory in low energy limit. The correlation functions on D-branes in IIB matrix model exhibit the identical crossover behavior. It is observed to be consistent with the supergravity description with running string coupling. We also explain that the results of Seiberg and Witten can be simply understood in our formalism.
Gürdoǧan, Ömer; Kazakov, Vladimir
2016-11-01
We introduce a family of new integrable quantum field theories in four dimensions by considering the γ -deformed N =4 supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the `t Hooft limit, these 4D theories are integrable, and contain a wealth of conformal correlators such that the whole arsenal of AdS /CFT integrability remains applicable. As a special case of these models, we obtain a quantum field theory of two complex scalars with a chiral, quartic interaction. The Berenstein-Maldacena-Nastase vacuum anomalous dimension is dominated in each loop order by a single "wheel" graph, whose bulk represents an integrable "fishnet" graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar N =4 SYM theory, at least in our limit. Using this feature and integrability results we provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.
A non-perturbative formulation of N=4 super Yang-Mills theory based on the large-N reduction
Ishiki, Goro; Tsuchiya, Asato
2011-01-01
We study a non-perturbative formulation of N=4 super Yang-Mills theory (SYM) on RxS^3 proposed in arXiv:0807.2352. This formulation is based on the large-N reduction, and the theory can be described as a particular large-N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S^3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.
Note on Nonlinear Schr\\"odinger Equation, KdV Equation and 2D Topological Yang-Mills-Higgs Theory
Nian, Jun
2016-01-01
In this paper we discuss the relation between the (1+1)D nonlinear Schr\\"odinger equation and the KdV equation. By applying the boson/vortex duality, we can map the classical nonlinear Schr\\"odinger equation into the classical KdV equation in the small coupling limit, which corresponds to the UV regime of the theory. At quantum level, the two theories satisfy the Bethe Ansatz equations of the spin-$\\frac{1}{2}$ XXX chain and the XXZ chain in the continuous limit respectively. Combining these relations with the dualities discussed previously in the literature, we propose a duality web in the UV regime among the nonlinear Schr\\"odinger equation, the KdV equation and the 2D $\\mathcal{N}=(2,2)^*$ topological Yang-Mills-Higgs theory.
Hebecker, A
2002-01-01
A manifestly gauge invariant formulation of 5-dimensional supersymmetric Yang-Mills theories in terms of 4d superfields is derived. It relies on a supersymmetry and gauge-covariant derivative operator in the $x^5$ direction. This formulation allows for a systematic study of higher-derivative operators by combining invariant 4d superfield expressions under the additional restriction of 5d Lorentz symmetry. In cases where the 5d theory is compactified on a gauge-symmetry-breaking orbifold, the formalism can be used for a simple discussion of possible brane operators invariant under the restricted symmetry of the fixed points. This is particularly relevant to recently constructed grand unified theories in higher dimensions (orbifold GUTs). Several applications, including proton decay operators and brane-localized mass terms, are discussed.
All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory
Fröb, Markus B; Hollands, Stefan
2015-01-01
We give a complete, self-contained, and mathematically rigorous proof that Euclidean Yang-Mills theories are perturbatively renormalisable, in the sense that all correlation functions of arbitrary composite local operators fulfil suitable Ward identities. Our proof treats rigorously both all ultraviolet and infrared problems of the theory and provides, in the end, detailed analytical bounds on the correlation functions of an arbitrary number of composite local operators. These bounds are formulated in terms of certain weighted spanning trees extending between the insertion points of these operators. Our proofs are obtained within the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisation group flow equations, combined with estimation techniques based on tree structures. Compared with previous mathematical treatments of massless theories without local gauge invariance [R. Guida and Ch. Kopper, arXiv:1103.5692; J. Holland, S. Hollands, and Ch. Kopper, arXiv:1411.1785] our constructions require seve...
Unconstrained Hamiltonian formulation of low energy SU(3) Yang-Mills quantum theory
Pavel, Hans-Peter
2012-01-01
An unconstrained Hamiltonian formulation of the SU(3) Yang-Mills quantum mechanics of spatially constant fields is given using the method of minimal embedding of SU(2) into SU(3) by Kihlberg and Marnelius. Using a canonical transformation of the gluon fields to a new set of adapted coordinates (a non-standard type polar decomposition), which Abelianizes the Non-Abelian Gauss law constraints to be implemented, the corresponding unconstrained Hamiltonian and total angular momentum are derived. This reduces the colored spin-1 gluons to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields. The obtained unconstrained Hamiltonian is then rewritten into a form, which separates the rotational from the scalar degrees of freedom. It is shown that the chromomagnetic potential has classical zero-energy valleys for two arbitrarily large classical glueball fields, which are the unconstrained analogs of the well-known "constant Abelian fields". On the quantum level, practically all glueball excitation e...
Balakin, Alexander B.; Lemos, José P. S.; Zayats, Alexei E.
2016-04-01
Alternative theories of gravity and their solutions are of considerable importance since, at some fundamental level, the world can reveal new features. Indeed, it is suspected that the gravitational field might be nonminimally coupled to the other fields at scales not yet probed, bringing into the forefront nonminimally coupled theories. In this mode, we consider a nonminimal Einstein-Yang-Mills theory with a cosmological constant. Imposing spherical symmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for the Yang-Mills field, we find expressions for the solutions of the theory. Further imposing constraints on the nonminimal parameters, we find a family of exact solutions of the theory depending on five parameters—two nonminimal parameters, the cosmological constant, the magnetic charge, and the mass. These solutions represent magnetic monopoles and black holes in magnetic monopoles with de Sitter, Minkowskian, and anti-de Sitter asymptotics, depending on the sign and value of the cosmological constant Λ . We classify completely the family of solutions with respect to the number and the type of horizons and show that the spacetime solutions can have, at most, four horizons. For particular sets of the parameters, these horizons can become double, triple, and quadruple. For instance, for a positive cosmological constant Λ , there is a critical Λc for which the solution admits a quadruple horizon, evocative of the Λc that appears for a given energy density in both the Einstein static and Eddington-Lemaître dynamical universes. As an example of our classification, we analyze solutions in the Drummond-Hathrell nonminimal theory that describe nonminimal black holes. Another application is with a set of regular black holes previously treated.
Form factors and the dilatation operator in N= 4 super Yang-Mills theory and its deformations
Energy Technology Data Exchange (ETDEWEB)
Wilhelm, Matthias Oliver
2016-02-12
In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in N=4 super Yang-Mills theory at various loop orders and for various numbers of external legs. We show how to use on-shell methods for their calculation and in particular extract the dilatation operator from the result. We also investigate the properties of the corresponding remainder functions. Moreover, we extend on-shell diagrams, a Grassmannian integral formulation and an integrability-based construction via R-operators to form factors, focussing on the chiral part of the stress-tensor supermultiplet as an example. In the second part, we study the β- and the γ{sub i}-deformation, which were respectively shown to be the most general supersymmetric and non-supersymmetric field-theory deformations of N=4 super Yang-Mills theory that are integrable at the level of the asymptotic Bethe ansatz. For these theories, a new kind of finite-size effect occurs, which we call prewrapping and which emerges from double-trace structures that are required in the deformed Lagrangians. While the β-deformation is conformal when the double-trace couplings are at their non-trivial IR fixed points, the γ{sub i}-deformation has running double-trace couplings without fixed points, which break conformal invariance even in the planar theory. Nevertheless, the γ{sub i}-deformation allows for highly non-trivial field-theoretic tests of integrability at arbitrarily high loop orders.
Yang-Mills origin of gravitational symmetries
Anastasiou, A; Duff, M J; Hughes, L J; Nagy, S
2014-01-01
By regarding gravity as the convolution of left and right Yang-Mills theories, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincar\\'e. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4 + 4, N_L = 1) and (3 + 0, N_R = 0).
Linde problem in Yang-Mills theory compactified on $\\mathbb{R}^2 \\times \\mathbb{T}^2$
Fraga, Eduardo S; Noronha, Jorge
2016-01-01
We investigate the perturbative expansion in $SU(3)$ Yang-Mills theory compactified on $\\mathbb{R}^2\\times \\mathbb{T}^2$ where the compact space is a torus $\\mathbb{T}^2= S^1_{\\beta}\\times S^1_{L}$, with $S^1_{\\beta}$ being a thermal circle with period $\\beta=1/T$ ($T$ is the temperature) while $S^1_L$ is a circle with length $L=1/\\Lambda$ where $\\Lambda$ is an energy scale. A Linde-type analysis indicates that perturbative calculations for the pressure in this theory break down already at order $\\mathcal{O}(g^2)$ due to the presence of a non-perturbative scale $\\sim g \\sqrt{T\\Lambda}$. We conjecture that a similar result should hold if the torus is replaced by any compact surface of genus one.
Large-N reduction of SU(N) Yang-Mills theory with massive adjoint overlap fermions
Hietanen, A
2010-01-01
We study four dimensional large-N SU(N) Yang-Mills theory coupled to adjoint overlap fermions on a single site lattice. Lattice simulations along with perturbation theory show that the bare quark mass has to be taken to zero as one takes the continuum limit in order to be in the physically relevant center-symmetric phase. But, it seems that it is possible to take the continuum limit with any renormalized quark mass and still be in the center-symmetric physics. We have also conducted a study of the correlations between Polyakov loop operators in different directions and obtained the range for the Wilson mass parameter that enters the overlap Dirac operator.
Baxter, J Erik
2015-01-01
We investigate the phase space of topological black hole solutions of ${\\mathfrak {su}}(N)$ Einstein-Yang-Mills theory in anti-de Sitter space with a purely magnetic gauge potential. The gauge field is described by $N-1$ magnetic gauge field functions $\\omega _{j}$, $j=1,\\ldots , N-1$. For ${\\mathfrak {su}}(2)$ gauge group, the function $\\omega _{1}$ has no zeros. This is no longer the case when we consider a larger gauge group. The phase space of topological black holes is considerably simpler than for the corresponding spherically symmetric black holes, but for $N>2$ and a flat event horizon, there exist solutions where at least one of the $\\omega _{j}$ functions has one or more zeros. For most of the solutions, all the $\\omega _{j}$ functions have no zeros, and at least some of these are linearly stable.
On the correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations
Huber, Markus Q
2016-01-01
The two- and three-point functions and the four-gluon vertex of three-dimensional Yang-Mills theory are calculated from their Dyson-Schwinger equations and the 3PI effective action. Within a self-contained truncation various effects of truncating Dyson-Schwinger equations are studied. Estimates for the errors induced by truncations are derived from comparisons between results from different equations, comparisons with lattice results and varying higher Green functions. The results indicate that the two-loop diagrams are important in the gluon propagator, where they are explicitly calculated, but not for the vertices. Furthermore, the influence of the four-gluon vertex on lower Green functions is found to be small.
Bassetto, A; Torrielli, A
2002-01-01
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with $n$ windings a non trivial scaling intertwines $n$ and $N$. In the non-commutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger group $U(\\infty)$. We perform an explicit perturbative calculation of such a loop up to ${\\cal O}(g^6)$; rather surprisingly, we find that in the contribution from the crossed graphs (the genuine non-commutative terms) the scaling we mentioned occurs for large $n$ and $N$ in the limit of maximal non-commutativity $\\theta=\\infty$. We present arguments in favour of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.
Guimaraes, M S; Sorella, S P
2016-01-01
In this paper, we discuss non-perturbative infrared features of Yang-Mills theory in Euclidean space-time dimensions greater than four in the Landau gauge and within the Refined Gribov-Zwanziger framework, which enables us to take into account the existence of gauge copies by restricting the domain of integration in the path integral to the Gribov region. Evidences for a decoupling/massive solution for the gluon propagator in higher dimensions are provided. This behavior is strengthened the bigger the dimension is. Further, we show that, by a dimensional reduction of the Refined Gribov-Zwanziger action from five to four dimensions, a non-perturbative coupling between the inverse of the Faddeev-Popov operator and the scalar field corresponding to the fifth component of the gauge field naturally arises, being in agreement with the recently proposed mechanism \\cite{Capri:2014bsa} to generalize the Refined Gribov-Zwanziger construction to the matter sector.
Spacetime and flux tube S-matrices at finite coupling for N=4 supersymmetric Yang-Mills theory.
Basso, Benjamin; Sever, Amit; Vieira, Pedro
2013-08-30
We propose a nonperturbative formulation of planar scattering amplitudes in N=4 supersymmetric Yang-Mills theory, or, equivalently, polygonal Wilson loops. The construction is based on the operator product expansion approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named pentagon transitions. These transitions satisfy a simple relation to the worldsheet S matrix on top of the so-called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this Letter we present a subsector of the full solution which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature.
Black p-branes versus black holes in non-asymptotically flat Einstein-Yang-Mills theory
Habib Mazharimousavi, S.; Halilsoy, M.
2016-09-01
We present a class of non-asymptotically flat (NAF) charged black p-branes (BpB) with p-compact dimensions in higher-dimensional Einstein-Yang-Mills theory. Asymptotically the NAF structure manifests itself as an anti-de sitter spacetime. We determine the total mass/energy enclosed in a thin shell located outside the event horizon. By comparing the entropies of BpB with those of black holes in the same dimensions we derive transition criteria between the two types of black objects. Given certain conditions satisfied, our analysis shows that BpB can be considered excited states of black holes. An event horizon r+ versus charge square Q2 plot for the BpB reveals such a transition where r+ is related to the horizon radius rh of the black hole (BH) both with the common charge Q.
Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
Kamata, Norihiko
2016-01-01
We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with a reference [Fodor et al., arXiv:1406.0827]. The tree-level $\\mathcal{O}(a^2)$ improvement can be achieved in a simple manner, where an appropriate weighted average is computed between two definitions of the action density $\\langle E(t)\\rangle$ measured at every flow time $t$. We further develop the idea of achieving the tree-level $\\mathcal{O}(a^4)$ improvement. For testing our proposal, we present numerical results of $\\langle E(t)\\rangle$ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings ($a\\approx 0.1, 0.07$ and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections in the relatively small-$t$ regime. To demonstrate the feasibility of our proposal, we also study the scaling behavior of the dimensionless combinations of the $\\Lambda_{\\ove...
On the absence of black hole event horizons: a test of De Sitter Yang-Mills Theory
Andersen, Timothy D
2014-01-01
De Sitter Quantum Gravity is a Yang-Mills theory based on the de Sitter or SO(4,1) group and a promising candidate for a quantum theory of gravity. In this paper, an exact, static, spherically symmetric solution of the classical equations is derived. I show that when the Schwarzchild radius to distance ratio is at post-Newtonian order the theory agrees with general relativity for all parameters but that, once the ratio becomes closer to unity, they differ. At the Schwarzchild radius from a black hole singularity, general relativity predicts an event horizon, which has become a controversial topic in quantum gravity because of information preservation issues. In the De Sitter theory I show, however, that time-like escape paths exist for any mass black hole until the singularity itself is reached. Since an event horizon has never been directly observed and there is currently no observation on which the two theories disagree, this provides a powerful test of the De Sitter theory.
Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
Kamata, Norihiko; Sasaki, Shoichi
2017-03-01
We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with Fodor et al. [J. High Energy Phys. 09 (2014) 018., 10.1007/JHEP09(2014)018]. The tree-level O (a2) improvement can be achieved in a simple manner, where an appropriate weighted average is computed between the plaquette and clover-leaf definitions of the action density ⟨E (t )⟩ measured at every flow time t . We further develop the idea of achieving the tree-level O (a4) improvement within a usage of actions consisting of the 1 ×1 plaquette and 1 ×2 planar loop for both the flow and gauge actions. For testing our proposal, we present numerical results for ⟨E (t )⟩ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings (a ≈0.1 ,0.07 , and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections on t2⟨E (t )⟩ in the relatively small-t regime for up to t ≳a2 . To demonstrate the feasibility of our tree-level improvement proposal, we also study the scaling behavior of the dimensionless combinations of the ΛMS ¯ parameter and the new reference scale tX, which is defined through tX2⟨E (tX)⟩=X for the smaller X , e.g., X =0.15 . It is found that √{t0.15 }ΛMS ¯ shows a nearly perfect scaling behavior as a function of a2 regardless of the types of gauge action and flow, after tree-level improvement is achieved up to O (a4) . Further detailed study of the scaling behavior exposes the presence of the remnant O (g2 na2) corrections, which are beyond the tree level. Although our proposal is not enough to eliminate all O (a2) effects, we show that the O (g2 na2) corrections can be well under control even by the simplest tree-level O (a2) improved flow.
On the Global Structure of Deformed Yang-Mills Theory and QCD(adj) on R^3XS^1
Anber, Mohamed M
2015-01-01
Spatial compactification on R^{3}XS^1_L at small S^1-size L often leads to a calculable vacuum structure, where various "topological molecules" are responsible for confinement and the realization of the center and discrete chiral symmetries. Within this semiclassically calculable framework, we study how distinct theories with the same SU(N_c)/Z_k gauge group (labeled by "discrete theta-angles") arise upon gauging of appropriate Z_k subgroups of the one-form global center symmetry of an SU(N_c) gauge theory. We determine the possible Z_k actions on the local electric and magnetic effective degrees of freedom, find the ground states, and use domain walls and confining strings to give a physical picture of the vacuum structure of the different SU(N_c)/Z_k theories. Some of our results reproduce ones from earlier supersymmetric studies, but most are new and do not invoke supersymmetry. We also study a further finite-temperature compactification to R^{2}XS^1_betaXS^1_L. We argue that, in deformed Yang-Mills theory...
A two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
Reinosa, U; Tissier, M; Wschebor, N
2015-01-01
We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature within a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first order transition temperature as compared to the one-loop result. We show that certain one-loop artifacts of thermodynamical observables disappear at two-loop order, as was already the case for the SU(2) theory. In particular, the entropy and the pressure are positive for all temperatures. We also discuss the groups SU(4) and Sp(2) which shed interesting light, respectively, on the relation between the (de)confinement of static matter sources in the various representations of the gauge group and on the use...
Equation of state of the SU($3$) Yang-Mills theory: a precise determination from a moving frame
Giusti, Leonardo
2017-01-01
The equation of state of the SU($3$) Yang-Mills theory is determined in the deconfined phase with a precision of about 0.5%. The calculation is carried out by numerical simulations of lattice gauge theory with shifted boundary conditions in the time direction. At each given temperature, up to $230\\, T_c$ with $T_c$ being the critical temperature, the entropy density is computed at several lattice spacings so to be able to extrapolate the results to the continuum limit with confidence. Taken at face value, above a few $T_c$ the results exhibit a striking linear behaviour in $\\ln(T/T_c)^{-1}$ over almost 2 orders of magnitude. Within errors, data point straight to the Stefan-Boltzmann value but with a slope grossly different from the leading-order perturbative prediction. The pressure is determined by integrating the entropy in the temperature, while the energy density is extracted from $T s=(\\epsilon + p )$. The continuum values of the potentials are well represented by Pad\\'e interpolating formulas, which als...
Bern, Z; Dixon, L J; Kosower, D A; Smirnov, V A; Bern, Zvi; Czakon, Michael; Dixon, Lance J.; Kosower, David A.; Smirnov, Vladimir A.
2006-01-01
We present an expression for the leading-color (planar) four-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2 e dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around e=0, and obtain analytic expressions for the poles from 1/e^8 through 1/e^4. We give numerical results for the coefficients of the 1/e^3 and 1/e^2 poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/e^2 coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing zeta_3^2, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimat...
Bondarenko, S
2015-01-01
We revisit the next-to-leading order~(NLO) correction to the eigenvalue of the BFKL equation in the adjoint representation and investigate its properties in analogy with the singlet BFKL in planar $\\mathcal{N}=4$ super Yang-Mills Theory~(SYM). We show that the adjoint NLO BFKL eigenvalue is needed to be slightly modified in order to have a property of hermitian separability present for the singlet BFKL. After this modification the adjoint NLO BFKL eigenvalue is expressed through holomorphic and antiholomophic parts of the leading order eigenvalue and their derivatives. The proposed choice of the modified NLO expression is supported by the fact that it is possible to obtain the same result in a relatively straightforward way directly from the singlet NLO BFKL eigenvalue replacing alternating series by series of constant sign. This transformation corresponds to changing cylindrical topology of the singlet BFKL to the planar topology of the adjoint BFKL. We believe that the original NLO calculation of Fadin and ...
García-Jiménez, I.; Novales-Sánchez, H.; Toscano, J. J.
2016-05-01
One-loop Standard Model observables produced by virtual heavy Kaluza-Klein fields play a prominent role in the minimal model of universal extra dimensions. Motivated by this aspect, we integrate out all the Kaluza-Klein heavy modes coming from the Yang-Mills theory set on a spacetime with an arbitrary number, n , of compact extra dimensions. After fixing the gauge with respect to the Kaluza-Klein heavy gauge modes in a covariant manner, we calculate a gauge-independent effective Lagrangian expansion containing multiple Kaluza-Klein sums that entail a bad divergent behavior. We use the Epstein-zeta function to regularize and characterize discrete divergences within such multiple sums, and then we discuss the interplay between the number of extra dimensions and the degree of accuracy of effective Lagrangians to generate or not divergent terms of discrete origin. We find that nonrenormalizable terms with mass dimension k are finite as long as k >4 +n . Multiple Kaluza-Klein sums of nondecoupling logarithmic terms, not treatable by Epstein-zeta regularization, are produced by four-dimensional momentum integration. On the grounds of standard renormalization, we argue that such effects are unobservable.
García-Jiménez, I; Toscano, J J
2016-01-01
One-loop Standard Model observables produced by virtual heavy Kaluza-Klein fields play a prominent role in the minimal model of universal extra dimensions. Motivated by this aspect, we integrate out all the Kaluza-Klein heavy modes coming from the Yang-Mills theory set on a spacetime with an arbitrary number, $n$, of compact extra dimensions. After fixing the gauge with respect to the Kaluza-Klein heavy gauge modes in a covariant manner, we calculate a gauge independent effective Lagrangian expansion containing multiple Kaluza-Klein sums that entail a bad divergent behavior. We use the Epstein-zeta function to regularize and characterize discrete divergences within such multiple sums, and then we discuss the interplay between the number of extra dimensions and the degree of accuracy of effective Lagrangians to generate or not divergent terms of discrete origin. We find that nonrenormalizable terms with mass dimension $k$ are finite as long as $k>4+n$. Multiple Kaluza-Klein sums of nondecoupling logarithmic te...
Large-N limit of the non-local 2D Yang-Mills and generalized Yang-Mills theories on a cylinder
Saaidi, K; Saaidi, Khaled; Khorrami, Mohammad
2002-01-01
The large-group behavior of the nonlocal YM$_2$'s and gYM$_2$'s on a cylinder or a disk is investigated. It is shown that this behavior is similar to that of the corresponding local theory, but with the area of the cylinder replaced by an effective area depending on the dominant representation. The critical areas for nonlocal YM$_2$'s on a cylinder with some special bounary conditions are also obtained.
Non-relativistic twistor theory and Newton--Cartan geometry
Dunajski, Maciej
2015-01-01
We develop a non-relativistic twistor theory, in which Newton--Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle ${\\mathcal O}\\oplus{\\mathcal O}(2)$. We show that the Newton--Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton--Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non--trivial on twistor lines. The resulting geometries agree with non--relativistic limits of anti-self-dual gravitational instantons.
Energy Technology Data Exchange (ETDEWEB)
Epple, Mark Dominik
2008-12-03
time, which produces a lineary rising static quark potential. We also obtain a running coupling which shows the correct infrared fixpoint with very high precision. Further numerical studies were made for the fully coupled system without horizon condition. We confirm the analytically predicted result that the system cannot be solved using the horizon condition. But it is a noval result that we can obtain solutions which show for a certain range (but not for arbitrarily large distances) a linearly rising static quark potential. In the last large part of this work we use the newly obtained results to calculate the 't Hoof loop which is a (dis-)order parameter of the confinement phase transition of Yang-Mills theory. We examine analytically and compute numerically a continuum representation for the 't Hooft loop operator that has been given recently. We can show that the 't Hooft loop shows a perimeter law and thus indicates confinement if the relevant renormalization parameter is set to the value representing the minimal vacuum energy. Thus we further reduce the number of renormalization parameters in the Dyson-Schwinger-equations by one. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Bern, Zvi; Czakon, Michael; Dixon, Lance J.; Kosower, David A.; Smirnov, Vladimir A.
2006-11-15
We present an expression for the leading-color (planar) four-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon} = 0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/e{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing {zeta}{sub 3}{sup 2}, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimate the two constants in the strong-coupling expansion of the cusp anomalous dimension that are known from string theory. The estimate works to 2.6% and 5% accuracy, providing non-trivial evidence in support of the AdS/CFT correspondence. We also use the known constants in the strong-coupling expansion as additional input to provide approximations to the cusp anomalous dimension which should be accurate to under one percent for all values of the coupling. When the evaluations of the integrals are completed through the finite terms, it will be possible to test the iterative, exponentiated structure of the finite terms in the four-loop four-point amplitude, which was uncovered earlier at two and three loops.
Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory
Energy Technology Data Exchange (ETDEWEB)
Dixon, Lance J.; /SLAC; Drummond, James M.; /CERN /Annecy, LAPTH; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study
2012-02-15
We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory
Energy Technology Data Exchange (ETDEWEB)
Dixon, Lance J.; /SLAC; Drummond, James M.; /CERN /Annecy, LAPTH; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study
2012-02-15
We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
Composite inflation from super Yang-Mills theory, orientifold, and one-flavor QCD
DEFF Research Database (Denmark)
Channuie, P.; Jorgensen, J. J.; Sannino, F.
2012-01-01
Recent investigations have shown that inflation can be driven by four-dimensional strongly interacting theories nonminimally coupled to gravity. We explore this paradigm further by considering composite inflation driven by orientifold field theories. The advantage of using these theories resides ...... nonminimally coupled QCD theory of inflation. The scale of composite inflation, for all the models presented here, is of the order of 10(16) GeV. Unitarity studies of the inflaton scattering suggest that the cutoff of the model is at the Planck scale. DOI: 10.1103/PhysRevD.86.125035...
Conformal Higher Spin Theory and Twistor Space Actions
Haehnel, Philipp
2016-01-01
We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincare invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we introduce anti-self-dual interaction terms to define a twistor action for the full conformal higher spin theory.
Holographic Wilson loops in symmetric representations in N=2{sup ∗} super-Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Chen-Lin, Xinyi [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, Stockholm, SE-106 91 (Sweden); Department of Physics and Astronomy, Uppsala University,Uppsala, SE-751 08 (Sweden); Dekel, Amit [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, Stockholm, SE-106 91 (Sweden); Zarembo, Konstantin [Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, Stockholm, SE-106 91 (Sweden); Department of Physics and Astronomy, Uppsala University,Uppsala, SE-751 08 (Sweden)
2016-02-17
We construct the D3-brane solution in the holographic dual of the N=2{sup ∗} theory that describes Wilson lines in symmetric representations of the gauge group. The results perfectly agree with the direct field-theory predictions based on localization.
Einstein-Yang-Mills-Lorentz Black Holes
Cembranos, Jose A R
2015-01-01
Different black hole solutions of the coupled Einstein-Yang-Mills equations are well known from long time. They have attracted much attention from mathematicians and physicists from their discovery. In this work, we analyze black holes associated with the gauge Lorentz group. In particular, we study solutions which identify the gauge connection with the spin connection. This ansatz allows to find exact solutions to the complete system of equations. By using this procedure, we show the equivalence between the Yang-Mills-Lorentz model in curved space-time and a particular set of extended gravitational theories.
Conference on Yang-Mills Gauge Field Theories : C. N. Yang's Contributions to Physics
Phua, K K
2016-01-01
During the last six decades, Yang–Mills theory has increasingly become the cornerstone of theoretical physics. It is seemingly the only fully consistent relativistic quantum many-body theory in four space-time dimensions. As such it is the underlying theoretical framework for the Standard Model of Particle Physics, which has been shown to be the correct theory at the energies we now can measure. It has been investigated also from many other perspectives, and many new and unexpected features have been uncovered from this theory. In recent decades, apart from high energy physics, the theory has been actively applied in other branches of physics, such as statistical physics, condensed matter physics, nonlinear systems, etc. This makes the theory an indispensable topic for all who are involved in physics.The conference celebrated the exceptional achievements using Yang–Mills theory over the years but also many other truly remarkable contributions to different branches of physics from Prof C N Yang. This volum...
Unitary background gauges and hamiltonian approach to Yang-Mills theories
Dubin, A Yu
1995-01-01
A variety of unitary gauges for perturbation theory in a background field is considered in order to find those most suitable for a Hamiltonian treatment of the system. We select two convenient gauges and derive the propagators D_{\\mu\
The effective potential of the N = 0* Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Patir, Assaf E-mail: assaf.patir@weizmann.ac.il; Reichmann, Dori
2004-05-01
We study the N = 4 SYM theory with SU(N) gauge group in the large N limit, deformed by giving equal mass to the four adjoint fermions. With this modification, a potential is dynamically generated for the six scalars in the theory, {phi}{sup i}. We show that the resulting theory is stable (perturbatively in the 't Hooft coupling), and that there are some indications that <{phi} > = 0 is the vacuum of the theory. Using the AdS/CFT correspondence, we compare the results to the corresponding supergravity computation, i.e. brane probing a deformed AdS{sub 5} x S{sup 5} background, and we find qualitative agreement. (author)
Higgs branch, hyperkahler quotient and duality in SUSY N=2 Yang-Mills theories
Antoniadis, Ignatios
1996-01-01
Low--energy limits of N=2 supersymmetric field theories in the Higgs branch are described in terms of a non--linear 4--dimensional sigma--model on a \\hk target space, classically obtained as a \\hk quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given to the singularities emerging in the low--energy theory. In particular, we thoroughly study the Higgs branch singularity of Seiberg--Witten SU(2) theory with N_f flavors, interpreted by Witten as a small instanton singularity in the moduli space of one instanton on \\RR^4. By explicitly evaluating the metric, we show that this Higgs branch coincides with the Higgs branch of a U(1) N=2 SUSY theory with the number of flavors predicted by the singularity structure of Seiberg--Witten's theory in the Coulomb phase. We find another example of Higgs phase duality, namely between the Higgs phases of U(N_c)\\; N_f flavors and U(N_f-N_c)\\; N_...
Covariant Renormalizable Anisotropic Theories and Off-Diagonal Einstein-Yang-Mills-Higgs Solutions
Vacaru, Sergiu I
2011-01-01
We use an important decoupling property of gravitational field equations in the general relativity theory and modifications, written with respect to nonholonomic frames with 2+2 spacetime decomposition. This allows us to integrate the Einstein equations in very general forms with generic off--diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (broken and un-broken) symmetry parameters. We associate families of off-diagonal Einstein manifolds to certain classes of covariant gravity theories which have a nice ultraviolet behavior and seem to be (super) renormalizable in a sense of covariant modifications of Ho\\v{r}ava-Lifshits gravity. The apparent breaking of Lorentz invariance is present in some "partner" anisotropically induced theories due to nonlinear coupling with effective parametric interactions determined by nonholonomic constraints and generic off-diagonal gravitational and matter fields configurations. Finally, we show how the constructions can...
Einstein-Yang-Mills-Dirac systems from the discretized Kaluza-Klein theory
Nguyen, Ai Viet; Nguyen, Suan Han; Wali, Kameshwar C
2016-01-01
A unified theory of the non-Abelian gauge interactions with gravity in the framework of a discretized Kaluaza-Kleine theory is constructed with a modified Dirac operator and wedge product. All the couplings of chiral spinors to the non-Abelian gauge fields emerge naturally as components of the couplings of the chiral spinors to the generalized gravity together with some new interactions. In particular, the currently prevalent gravity-QCD-quark and gravity-electroweak-quark-lepton models are shown to follow as special cases of the general framework.
Dimensional transmutation in the longitudinal sector of equivariantly gauge-fixed Yang-Mills theory
Golterman, Maarten
2014-01-01
We study the pure-gauge sector of an $SU(N)$ gauge theory, equivariantly gauge fixed to $SU(N-1)\\times U(1)$, which is an asymptotically free non-linear sigma model in four dimensions. We show that dimensional transmutation takes place in the large-$N$ limit, and elaborate on the relevance of this result for a speculative scenario in which the strong longitudinal dynamics gives rise to a novel Higgs-Coulomb phase.
Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes
Bena, I; Kosower, D A
2004-01-01
Using twistor space intuition, Cachazo, Svrcek and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) vertices. We define non-MHV vertices, and show how to use them to give a recursive construction of these amplitudes. We also use them to illustrate the equivalence of various twistor-space prescriptions, and to determine the associated combinatoric factors.
Hamiltonian formulations of Yang-Mills quantum theory and the Gribov problem
Heinzl, T
1996-01-01
We review the status of quantising (non-abelian) gauge theories using different versions of a Hamiltonian formulation corresponding to Dirac's instant and front form of dynamics, respectively. In order to control infrared divergences we work in a finite spatial volume, chosing a torus geometry for convenience. We focus on the determination of the physical configuration space of gauge invariant variables via gauge fixing. This naturally leads us to the issue of the Gribov problem. We discuss it for different gauge choices, in particular finite volume modifications of the axial gauge. Conventional and light-front quantisation are compared and the differences pointed out.
The Gauge Hierarchy Problem and High Dimensional Yang-Mills Theories
Hatanaka, H; Lim, C S
1998-01-01
We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter fields, and a way to fix it dynamically is presented. We also point out that on the simply-connected space $S^2$ even the finite mass correction vanishes.
Abelian Yang-Mills Theory on Real Tori and Theta Divisors of Klein Surfaces
Okonek, Christian; Teleman, Andrei
2013-11-01
The purpose of this paper is to compute determinant index bundles of certain families of Real Dirac type operators on Klein surfaces as elements in the corresponding Grothendieck group of Real line bundles in the sense of Atiyah. On a Klein surface these determinant index bundles have a natural holomorphic description as theta line bundles. In particular we compute the first Stiefel-Whitney classes of the corresponding fixed point bundles on the real part of the Picard torus. The computation of these classes is important, because they control to a large extent the orientability of certain moduli spaces in Real gauge theory and Real algebraic geometry.
Two loop computation of a running coupling in lattice Yang-Mills theory
Narayanan, R A; Narayanan, Rajamani; Wolff, Ulli
1995-01-01
We compute the two loop coefficient in the relation between the lattice bare coupling and the running coupling defined through the Schroedinger functional for the case of pure SU(2) gauge theory. This result is needed as one computational component to relate the latter to the MSbar-coupling, and it allows us to implement O(a) improvement of the Schroedinger functional to two-loop order. In addition, the two-loop beta-function is verified in a perturbative computation on the lattice, and the behavior of an improved bare coupling is investigated beyond one loop.
Physical observables from boundary artifacts: scalar glueball in Yang-Mills theory
Chowdhury, Abhishek; Maiti, Jyotirmoy
2015-01-01
By relating the functional averages of the time slice energy density in simulations with Open (O) and Periodic (P) boundary conditions (BCs) respectively for $SU(3)$ lattice gauge theory, we show that the scalar glueball mass and the glueball to vacuum matrix element can be extracted very efficiently from the former. The results are compared with those extracted from the two point function of the time slice energy density (both PBC and OBC). The scaling properties of the mass and the matrix element are studied with the help of Wilson (gradient) flow.
Exploring new horizons of the Gribov problem in Yang-Mills theories
Pereira, A D
2016-01-01
The understanding of the non-perturbative regime of YM theories remains a challenging open problem in theoretical physics. Notably, a satisfactory description of the confinement of gluons is not at our disposal so far. In this thesis, the RGZ framework, designed to provide a proper quantization of YM theories by taking into account the existence of the so-called Gribov copies is explored. Successfully introduced in the Landau gauge, the RGZ set up does not extend easily to different gauges. The main reason is that a clear formulation of the analogue of the Gribov horizon in the Landau gauge is obstructed by technical difficulties when more sophisticated gauges are chosen. Moreover, the RGZ action breaks BRST symmetry explicitly, making the task of extracting gauge invariant results even more difficult. The main goal of the present thesis is precisely to provide a consistent framework to extend the RGZ action to gauges that are connected to Landau gauge via a gauge parameter. Our main result is the reformulati...
Effect of Self-Interaction on Vacuum Energy for Yang-Mills System in Kaluza-Klein Theory
Shiraishi, Kiyoshi
2015-01-01
We calculate the vacuum energy for Yang--Mills (YM) system in the background space-time $M^4 \\times S^3$, taking the effect of self-interaction of the YM fields into account. The compactification scale obtained by Candelas--Weinberg mechanism becomes large if the YM coupling is large. The case with an extra space $S^3/Z_2$ is also considered, and it is shown that the vacuum associated with broken gauge symmetry is unstable.
Pitts, J Brian
2016-01-01
Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang-Mills theories display similar approximate equivalence classically, quantization typically ...
Yang-Baxter σ -models, conformal twists, and noncommutative Yang-Mills theory
Araujo, T.; Bakhmatov, I.; Colgáin, E. Ó.; Sakamoto, J.; Sheikh-Jabbari, M. M.; Yoshida, K.
2017-05-01
The Yang-Baxter σ -model is a systematic way to generate integrable deformations of AdS5×S5 . We recast the deformations as seen by open strings, where the metric is undeformed AdS5×S5 with constant string coupling, and all information about the deformation is encoded in the noncommutative (NC) parameter Θ . We identify the deformations of AdS5 as twists of the conformal algebra, thus explaining the noncommutativity. We show that the unimodularity condition on r -matrices for supergravity solutions translates into Θ being divergence-free. Integrability of the σ -model for unimodular r -matrices implies the existence and planar integrability of the dual NC gauge theory.
The Framed Standard Model (I) - A Physics Case for Framing the Yang-Mills Theory?
Chan, HM
2015-01-01
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: * the standard Higgs scalar as the framon in the electroweak sector; * a global $\\widetilde{su}(3)$ symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale $\\mu$. From previous work, it is known already that a rotatiing mass matrix will lead automatically to: * CKM mixing and neutrino oscillations, * hierarachical masses for quarks and leptons, * a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the FSM, the renormalization group equation has some special properties which explain the main qualitative feaures seen in experiment both for mixing matrices ...
Confining k-string tensions with D-Branes in Super Yang-Mills theories
Ridgway, Jefferson M
2008-01-01
We discuss confining k strings in four dimensional gauge theories using D5 branes in AdS5xS5, and D3 branes in Klebanov-Strassler and Maldacena-Nunez backgrounds. We present two results: The first that confining k string tensions in N=4 can be calculated using D5 branes in AdS5xS5 with a cut-off in the bulk AdS. Using an embedding of R2 times S4 in S5, we show that the D5 brane replicates a string of rank k in the antisymmetric representation. The second result shows that the S-Dual calculation to hep-th/0111078 reproduces the action in the Klebanov-Strassler and Maldacena-Nunez backgrounds exactly, while providing a more natural manifestation of the string charge k.
Drechsler, Wolfgang; Havas, Peter; Rosenblum, Arnold
1984-02-01
In two recent papers, the general form of the laws of motion for point particles which are multipole sources of the classical coupled Yang-Mills-Higgs fields was determined by Havas, and for the special case of monopole singularities of a Yang-Mills field an iteration procedure was developed by Drechsler and Rosenblum to obtain the equations of motion of mass points, i.e., the laws of motion including the explicit form of the fields of all interacting particles. In this paper we give a detailed derivation of the laws of motion of monopole-dipole singularities of the coupled Yang-Mills-Higgs fields for point particles with mass and spin, following a procedure first applied by Mathisson and developed by Havas. To obtain the equations of motion, a systematic approximation method is developed in the following paper for the solution of the nonlinear field equations and determination of the fields entering the laws of motion found here to any given order in the coupling constant g.
The Framed Standard Model (I) -- A Physics Case for Framing the Yang-Mills Theory?
Chan, Hong-Mo; Tsou, Sheung Tsun
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: * the standard Higgs scalar as the framon in the electroweak sector; * a global widetilde{su}(3) symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale μ. From previous work, it is known already that a rotating mass matrix will lead automatically to: * CKM mixing and neutrino oscillations, * hierarchical masses for quarks and leptons, * a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter...
The framed Standard Model (I) — A physics case for framing the Yang-Mills theory?
Chan, Hong-Mo; Tsou, Sheung Tsun
2015-10-01
Introducing, in the underlying gauge theory of the Standard Model, the frame vectors in internal space as field variables (framons), in addition to the usual gauge boson and matter fermions fields, one obtains: the standard Higgs scalar as the framon in the electroweak sector; a global su˜(3) symmetry dual to colour to play the role of fermion generations. Renormalization via framon loops changes the orientation in generation space of the vacuum, hence also of the mass matrices of leptons and quarks, thus making them rotate with changing scale μ. From previous work, it is known already that a rotating mass matrix will lead automatically to: CKM mixing and neutrino oscillations, hierarchical masses for quarks and leptons, a solution to the strong-CP problem transforming the theta-angle into a Kobayashi-Maskawa phase. Here in the framed standard model (FSM), the renormalization group equation has some special properties which explain the main qualitative features seen in experiment both for mixing matrices of quarks and leptons, and for their mass spectrum. Quantitative results will be given in Paper II. The present paper ends with some tentative predictions on Higgs decay, and with some speculations on the origin of dark matter.
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...
Energy Technology Data Exchange (ETDEWEB)
Kneipp, Marco A.C. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Dept. de Fisica Teorica; Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas
2004-12-01
We review some recent developments on BPS string solutions and monopole confinement in the Higgs (or color) superconducting phase of N = 2 and N = 4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z{sub N}, the BPS string tension satisfies the Casimir scaling law. Furthermore, in the SU(3) case the string solutions are such that they allow the formation of a confining system with three monopoles. (author)
Energy Technology Data Exchange (ETDEWEB)
Montesinos, M. [CINVESTAV-IPN, 07360 Mexico D.F. (Mexico); Flores, E. [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)]. E-mail: merced@fis.cinvestav.mx
2006-07-01
The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)
Du, Yi-Jian; Wu, Yong-Shi
2016-01-01
In this paper we extend our techniques, developed in a previous paper (Du, etc, JHEP 05(2016)086) for direct evaluation of arbitrary $n$-point tree-level MHV amplitudes in 4d Yang-Mills and gravity theory using the Cachazo-He-Yuan (CHY) formalism, to the 4d Einstein-Yang-Mills (EYM) theory. Any single-trace color-ordered $n$-point tree-level MHV amplitude in EYM theory, obtained by a direct evaluation of the CHY formula, is of an elegant factorized form of a Parke-Taylor factor and a Hodges determinant, much simpler and more compact than the existing formulas in the literature. We prove that our new expression is equivalent to the conjectured Selivanov-Bern-De Freitas-Wong (SBDW) formula, with the help of a new theorem showing that the SBDW generating function has a graph theory interpretation. Together with Ref. (Du, etc, JHEP 05(2016)086), we provide strong analytic evidence for hidden simplicity in quantum field theory.
Noncommutative Yang-Mills in IIB Matrix Model
Aoki, H; Iso, S; Kawai, H; Kitazawa, Y; Tada, T
2000-01-01
We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.
Bourjaily, Jacob L.; Heslop, Paul; Tran, Vuong-Viet
2016-05-01
We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, conformal integrands grouped according to a hidden symmetry discovered for correlation functions. The answer we find exposes a fundamental tension between manifest locality and planarity with manifest conformality not seen at lower loops. For the first time, the integrand must include terms that are finite even on-shell and terms that are divergent even off-shell (so-called pseudoconformal integrals). We describe these novelties and their consequences in this Letter, and we make the full correlator and amplitude available as part of the Supplemental Material.
Bourjaily, Jacob L; Heslop, Paul; Tran, Vuong-Viet
2016-05-13
We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, conformal integrands grouped according to a hidden symmetry discovered for correlation functions. The answer we find exposes a fundamental tension between manifest locality and planarity with manifest conformality not seen at lower loops. For the first time, the integrand must include terms that are finite even on-shell and terms that are divergent even off-shell (so-called pseudoconformal integrals). We describe these novelties and their consequences in this Letter, and we make the full correlator and amplitude available as part of the Supplemental Material.
World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory
Sato, H T; Sato, Haru-Tada; Schmidt, Michael G.
1999-01-01
Based on the world-line formalism with a sewing method, we derive the Yang-Mills effective action in a form useful to generate the Bern-Kosower-type master formulae for gluon scattering amplitudes at the two-loop level. It is shown that four-gluon ($\\Phi^4$ type sewing) contributions can be encapsulated in the action with three-gluon ($\\Phi^3$ type) vertices only, the total action thus becoming a simple expression. We then derive a general formula for a two-loop Euler-Heisenberg type action in a pseudo-abelian $su(2)$ background. The ghost loop and fermion loop cases are also studied.
From the holomorphic Wilson loop to `d log' loop-integrands for super-Yang-Mills amplitudes
Lipstein, Arthur E
2012-01-01
The S-matrix for planar N = 4 super Yang-Mills theory can be computed as the correlation function for a holomorphic polygonal Wilson loop in twistor space. In an axial gauge, this leads to the construction of the all-loop integrand via MHV diagrams in twistor space. We show that at MHV, this formulation leads directly to expressions for loop integrands in d log form; i.e., the integrand is a product of exterior derivatives of logarithms of rational functions. For higher MHV degree, it is in d log form multiplied by delta functions. The parameters appearing in the d log form arise geometrically as the coordinates of insertion points of propagators on the holomorphic Wilson loop or on MHV vertices. We discuss a number of examples at one and two loops and give a preliminary discussion of the evaluation of the 1-loop MHV amplitude.
Schnitzer, Howard J
2016-01-01
R\\'enyi and entanglement entropies are constructed for 2d q-deformed topological Yang-Mills theories with gauge group $U(N)$, as well as the dual 3d Chern-Simons (CS) theory on Seifert manifolds. When $q=\\exp[2\\pi i/(N+K)]$, and $K$ is odd, the topological R\\'enyi entropy and Wilson line observables of the CS theory can be expressed in terms of the modular transformation matrices of the WZW theory, $\\rm{\\hat{U}(N)}_{K,N(K+N)}$. If both $K$ and $N$ are odd, there is a level-rank duality of the 2d qYM theory and of the associated CS theory, as well as that of the R\\'enyi and entanglement entropies, and Wilson line observables.
Gußmann, Alexander
2016-01-01
The existence of classical solutions of the Einstein-Yang-Mills-Higgs equations describing black holes inside 't Hooft-Polyakov magnetic monopoles implies that not all stationary magnetically charged black holes can be uniquely described by their asymptotic characteristics. In fact, in a certain domain of parameters, there exist different spherically-symmetric, non-rotating and asymptotically-flat classical black hole solutions of the Einstein-Yang-Mills-Higgs equations which have the same ADM mass and the same magnetic charge but significantly different geometries in the near-horizon regions. (These are black hole solutions which are described by a Reissner-Nordstr\\"om metric on the one hand and the "magnetic monopole black hole solutions" which can be interpreted as black holes inside 't Hooft-Polyakov magnetic monopoles described by a metric which is not of Reissner-Nordstr\\"om form on the other hand.) One can experimentally distinguish such black holes with same asymptotic characteristics but different ne...
Gravity as the square of Yang-Mills?
Borsten, L
2016-01-01
In these lectures we review how the symmetries of gravitational theories may be regarded as originating from those of "Yang-Mills squared". We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in the context of scattering amplitudes. We then introduce a concrete dictionary for the covariant fields of (super)gravity in terms of the product of two (super) Yang-Mills theories. The dictionary implies that the symmetries of each (super) Yang-Mills factor generate the symmetries of the corresponding (super)gravity theory: general covariance, $p$-form gauge invariance, local Lorentz invariance, local supersymmetry, R-symmetry and U-duality.
Galvez, Richard; Joseph, Anosh; Mehta, Dhagash
2012-01-01
Recently there has been some controversy in the literature concerning the existence of a fermion sign problem in the $\\mathcal{N}=(2,2)$ supersymmetric Yang--Mills (SYM) theories on the lattice. In this work, we address this issue by conducting Monte Carlo simulations not only for $\\mathcal{N}=(2,2)$ but also for $\\mathcal{N}=(8,8)$ SYM in two dimensions for the U(N) theories with N=2, using the new ideas derived from topological twisting followed by geometric discretization. Our results from simulations provide the evidence that these theories do {\\it not} suffer from a sign problem as the continuum limit is approached. These results thus boost confidence that these new lattice formulations can be used successfully to explore the nonperturbative aspects of the four-dimensional $\\mathcal{N}=4$ SYM theory.
Exact solutions for classical Yang-Mills fields
2014-01-01
We provide a set of exact solutions of the classical Yang-Mills equations. They have the property to satisfy a massive dispersion relation and hold in all gauges. These solutions can be used to describe the vacuum of the quantum Yang-Mills theory and so, they provide a general framework to build a quantum field theory. The components of the field become separated on a generic gauge but are all equal just in the Lorenz (Landau) gauge.
Energy Technology Data Exchange (ETDEWEB)
Baker, M.
1979-01-01
It was shown using the Schwinger-Dyson equations and the Slavnov-Taylor identities of Yang-Mills theory that no inconsistency arises if the gluon propagator behaves like (1/p/sup 2/)/sup 2/ for small p/sup 2/. To see whether the theory actually contains such singular long range behavior, a nonperturbative closed set of equations was formulated by neglecting the transverse parts of GAMMA and GAMMA/sub 4/ in the Schwinger-Dyson equations. This simplification preserves all the symmetries of the theory and allows the possibility for a singular low-momentum behavior of the gluon propagator. The justification for neglecting GAMMA/sup (T)/ and GAMMA/sub 4//sup (T)/ is not evident but it is expected that the present study of the resulting equations will elucidate this simplification, which leads to a closed set of equations.
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Saaidi, K.; Sajadi, H.M. [Dept. of Physics, Univ. of Tehran (Iran)
2001-01-01
Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) on nonlocal generalized 2D Yang-Mills theories (nlgYM{sub 2}'s), which are nonlocal in the auxiliary field. This has been considered before by Saaidi and Khorrami. Our calculations are done for general surfaces. We find a general expression for the free energy of W({phi}) ={phi}{sup 2k} in nlgYM{sub 2} theories at the strong coupling phase (SCP) regime (A > A{sub c}) for large groups. In the specific {phi}{sup 4} model, we show that the theory has a third order phase transition. (orig.)
Analytic representations of Yang-Mills amplitudes
Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.; Feng, Bo
2016-12-01
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space-fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Möbius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is the foundations of a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.
Analytic Representations of Yang-Mills Amplitudes
Bjerrum-Bohr, N E J; Damgaard, Poul H; Feng, Bo
2016-01-01
Scattering amplitudes in Yang-Mills theory can be represented in the formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary projective space---fully localized on the support of the scattering equations. Because solving the scattering equations is difficult and summing over the solutions algebraically complex, a method of directly integrating the terms that appear in this representation has long been sought. We solve this important open problem by first rewriting the terms in a manifestly Mobius-invariant form and then using monodromy relations (inspired by analogy to string theory) to decompose terms into those for which combinatorial rules of integration are known. The result is a systematic procedure to obtain analytic, covariant forms of Yang-Mills tree-amplitudes for any number of external legs and in any number of dimensions. As examples, we provide compact analytic expressions for amplitudes involving up to six gluons of arbitrary helicities.
Twin Supergravities from Yang-Mills Squared
Anastasiou, A; Duff, M J; Hughes, M J; Marrani, A; Nagy, S; Zoccali, M
2016-01-01
We consider `twin supergravities' - pairs of supergravities with $\\mathcal{N}_+$ and $\\mathcal{N}_-$ supersymmetries, $\\mathcal{N}_+>\\mathcal{N}_-$, with identical bosonic sectors - in the context of tensoring super Yang-Mills multiplets. It is demonstrated that the pairs of twin supergravity theories are related through their left and right super Yang-Mills factors. This procedure generates new theories from old. In particular, the matter coupled $\\mathcal{N}_-$ twins in $D=3,5,6$ and the $\\mathcal{N}_-=1$ twins in $D=4$ have not, as far as we are aware, been obtained previously using the double-copy construction, adding to the growing list of double-copy constructible theories. The use of fundamental matter multiplets in the double-copy construction leads us to introduce a bi-fundamental scalar that couples to the well-known bi-adjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorisation into left and right super Yang-Mills-matter theories.
Conformal higher-spin symmetries in twistor string theory
Directory of Open Access Journals (Sweden)
D.V. Uvarov
2014-12-01
Full Text Available It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains psl(4|4,R superalgebra. In quantum theory this infinite-dimensional symmetry breaks down to SL(4|4,R one.
Confluence of general Schlesinger systems and Twistor theory
Kimura, Hironobu; Tseveennamjil, Damiran
2016-01-01
We give a description of confluence for the general Schlesinger systems (GSS) from the view point of twistor theory. GSS is a system of nonlinear di¤erential equations on the Grassmannian manifold $G_{2,N}(\\mathbf{C}$ which is obtained, for any partition $\\lambda$ of $N$, as the integrability condition of a connection $\
AdS twistors for higher spin theory
Cederwall, M
2004-01-01
We construct spectra of supersymmetric higher spin theories in D=4, 5 and 7 from twistors describing massless (super-)particles on AdS spaces. A massless twistor transform is derived in a geometric way from classical kinematics. Relaxing the spin-shell constraints on twistor space gives an infinite tower of massless states of a ``higher spin particle'', generalising previous work of Bandos et al. This can generically be done in a number of ways, each defining the states of a distinct higher spin theory, and the method provides a systematic way of finding these. We reproduce known results in D=4, minimal supersymmetric 5- and 7-dimensional models, as well as supersymmetrisations of Vasiliev's Sp-models as special cases. In the latter models a dimensional enhancement takes place, meaning that the theory lives on a space of higher dimension than the original AdS space, and becomes a theory of doubletons. This talk was presented at the XIXth Max Born Symposium ``Fundamental Interactions and Twistor-Like Methods''...
Baxter, J Erik
2016-01-01
We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called "regular" case. We here generalise results for the asymptotically flat case, and compare our system with similar results from the well-researched adS $\\mathfrak{su}(N)$ system. We find the analysis differs from the asymptotically flat case in some important ways: the biggest difference is that for $\\Lambda<0$, solutions are much less constrained as $r\\rightarrow\\infty$, making it possible to prove the existence of global solutions to the field equations in some neighbourhood of existing trivial solutions, and in the limit of $|\\Lambda|\\rightarrow\\infty$. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the $\\mathfrak{su}(N)$ case proved important to stability.
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Baxter, J. Erik, E-mail: e.baxter@shu.ac.uk [Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield S11WB (United Kingdom)
2016-02-15
We investigate dyonic black hole and dyon solutions of four-dimensional su(N) Einstein-Yang-Mills theory with a negative cosmological constant. We derive a set of field equations in this case, and prove the existence of non-trivial solutions to these equations for any integer N, with 2N − 2 gauge degrees of freedom. We do this by showing that solutions exist locally at infinity, and at the event horizon for black holes and the origin for solitons. We then prove that we can patch these solutions together regularly into global solutions that can be integrated arbitrarily far into the asymptotic regime. Our main result is to show that dyonic solutions exist in open sets in the parameter space, and hence that we can find non-trivial dyonic solutions in a number of regimes whose magnetic gauge fields have no zeros, which is likely important to the stability of the solutions.
Georgiou, George; Grossardt, Andre; Plefka, Jan
2012-01-01
We report on a systematic perturbative study of three-point functions in planar SU(N) N=4 super Yang-Mills theory at the one-loop level involving scalar field operators up to length five. For this we have computed a sample of 40 structure constants involving primary operators of up to and including length five which are built entirely from scalar fields. A combinatorial dressing technique has been developed to promote tree-level correlators to one-loop level. In addition we have resolved the mixing up to the order (g_YM)^2 level of the operators involved, which amounts to mixings with bi-fermions, with bi-derivative insertions as well as self-mixing contributions in the scalar sector. This work supersedes a preprint by two of the authors from 2010 which had neglected the mixing contributions.
Baxter, J. Erik
2016-10-01
We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called regular case. We here generalise results for the asymptotically flat case, and compare our system with similar results from the well-researched adS {mathfrak {su}}(N) system. We find the analysis differs from the asymptotically flat case in some important ways: the biggest difference is that for Λ global solutions to the field equations in some neighbourhood of existing trivial solutions, and in the limit of |Λ |→ infty . In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the {mathfrak {su}}(N) case proved important to stability.
Baxter, J Erik
2015-01-01
We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional ${\\mathfrak {su}}(N)$ Einstein-Yang-Mills theory with a negative cosmological constant $\\Lambda $. These solutions are described by $N-1$ magnetic gauge field functions $\\omega _{j}$. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any $N$, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions $\\omega _{j}$ have no zeros, and satisfy a set of $N-1$ inequalities. In the gravitational sector, we are able to prove that there are solutions which have no instabilities in a neighbourhood of stable embedded ${\\mathfrak {su}}(2)$ solutions, provided the magnitude of the cosmological constant $\\left| \\Lambda \\right| $ is sufficiently large.
From d logs to dilogs; the super Yang-Mills MHV amplitude revisited
Energy Technology Data Exchange (ETDEWEB)
Lipstein, Arthur E.; Mason, Lionel [The Mathematical Institute, University of Oxford,24-29 St Giles’, Oxford, OX1 3LB (United Kingdom)
2014-01-30
Recently, loop integrands for certain Yang-Mills scattering amplitudes and correlation functions have been shown to be systematically expressible in d log form, raising the possibility that these loop integrals can be performed directly without Feynman parameters. We do so here to give a new description of the planar 1-loop MHV amplitude in N=4 super Yang-Mills theory. We explicitly incorporate the standard Feynman iϵ prescription into the integrands. We find that the generic MHV diagram contributing to the 1-loop MHV amplitude, known as Kermit, is dual conformal invariant up to the choice of reference twistor explicit in our axial gauge (the generic MHV diagram was already known to be finite). The new formulae for the amplitude are nontrivially related to previous ones in the literature. The divergent diagrams are evaluated using mass regularization. Our techniques extend directly to higher loop diagrams, and we illustrate this by sketching the evaluation of a non-trivial 2-loop example. We expect this to lead to a simple and efficient method for computing amplitudes and correlation functions with less supersymmetry and without the assumption of planarity.
Lattice gradient flow with tree-level $\\mathcal{O}(a^4)$ improvement in pure Yang-Mills theory
Kamata, Norihiko
2015-01-01
Following a recent paper by Fodor et al. (arXiv:1406.0827), we reexamine several types of tree-level improvements on the flow action with various gauge actions in order to reduce the lattice discretization errors in the Yang-Mills gradient flow method. We propose two types of tree-level, $\\mathcal{O}(a^4)$ improved lattice gradient flow including the rectangle term in both the flow and gauge action within the minimal way. We then perform numerical simulations with the simple plaquette gauge action for testing our proposal. Our numerical results of the expectation value of the action density, $\\langle E(t)\\rangle$, show that two $\\mathcal{O}(a^4)$ improved flows significantly eliminate the discretization corrections in the small flow time $t$ regime. On the other hand, the values of $t^2\\langle E(t)\\rangle$ in the large $t$ regime, where the lattice spacing dependence of the tree-level term dies out as inverse powers of $t/a^2$, are different between the results given by two optimal flows leading to the same $...
The one and a half monopoles solution of the SU(2) Yang-Mills-Higgs field theory
Teh, Rosy; Ng, Ban-Loong; Wong, Khai-Ming
2014-04-01
Recently we have reported on the existence of finite energy SU(2) Yang-Mills-Higgs particle of one-half topological charge. In this paper, we show that this one-half monopole can co-exist with a ’t Hooft-Polyakov monopole. The magnetic charge of the one-half monopole is of opposite sign to the magnetic charge of the ’t Hooft-Polyakov monopole. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive z-axis that carries the other half of the magnetic monopole charge. The solution possesses gauge potentials that are singular along the z-axis, elsewhere they are regular. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ. However the dipole separation and the magnetic dipole moment decrease with λ. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.
Twistor Transform in d Dimensions and a Unifying Role for Twistors
Bars, Itzhak; Bars, Itzhak; Picon, Moises
2006-01-01
Twistors in four dimensions d=4 have provided a convenient description of massless particles with any spin, and this led to remarkable computational techniques in Yang-Mills field theory. Recently it was shown that the same d=4 twistor provides also a unified description of an assortment of other particle dynamical systems, including special examples of massless or massive particles, relativistic or non-relativistic, interacting or non-interacting, in flat space or curved spaces. In this paper, using 2T-physics as the primary theory, we derive the general twistor transform in d-dimensions that applies to all cases, and show that these more general twistor transforms provide d dimensional holographic images of an underlying phase space in flat spacetime in d+2 dimensions. Certain parameters, such as mass, parameters of spacetime metric, and some coupling constants appear as moduli in the holographic image while projecting from d+2 dimensions to (d-1)+1 dimensions or to twistors. We also extend the concept of t...
String Scale in Noncommutative Yang-Mills
Ishibashi, N; Kawai, H; Kitazawa, Y
2000-01-01
We identify the effective string scale of noncommutative Yang-Mills theory (NCYM) with the noncommutativity scale through its dual supergravity description. We argue that Newton's force law may be obtained with 4 dimensional NCYM with maximal SUSY. It provides a nonperturbative compactification mechanism of IIB matrix model. We can associate NCYM with the von Neumann lattice by the bi-local representation. We argue that it is superstring theory on the von Neumann lattice. We show that our identification of its effective string scale is consistent with exact T-duality (Morita equivalence) of NCYM.
Torrielli, Alessandro
2003-01-01
The results of our research on noncommutative perturbative quantum field theory and its relation to string theory are exposed with details. 1) We give an introduction to noncommutative quantum field theory and its derivation from open string theory in an antisymmetric background. 2) We perform a perturbative Wilson loop calculation for 2D NCYM. We compare the LCG results for the WML and the PV prescription. With WML the loop is well-defined and regular in the commutative limit. With PV the result is singular. This is intriguing: in the commutative theory their difference is related to topological excitations, moreover PV provides a point-like potential. 3) Commutative 2D YM exhibits an interplay between geometrical and U(N) gauge properties: in the exact expression of a Wilson loop with n windings a scaling intertwines n and N. In the NC case the interplay becomes tighter due to the merging of space-time and ``internal'' symmetries. Surprisingly, in our up to O(g^6) (and beyond) crossed graphs calculations the scaling we mentioned occurs for large n, N and theta. 4) We discuss the breakdown of perturbative unitarity of noncommutative electric-type QFT in the light of strings. We consider the analytic structure of string loop two-point functions suitably continuing them off-shell, and then study the Seiberg-Witten limit. In this way we pick up how the unphysical tachyonic branch cut appears in the NC field theory.
Torrielli, A
2003-01-01
The results of our research on noncommutative perturbative quantum field theory and its relation to string theory are exposed with details. 1) We give an introduction to noncommutative quantum field theory and its derivation from open string theory in an antisymmetric background. 2) We perform a perturbative Wilson loop calculation for 2D NCYM. We compare the LCG results for the WML and the PV prescription. With WML the loop is well-defined and regular in the commutative limit. With PV the result is singular. This is intriguing: in the commutative theory their difference is related to topological excitations, moreover PV provides a point-like potential. 3) Commutative 2D YM exhibits an interplay between geometrical and U(N) gauge properties: in the exact expression of a Wilson loop with n windings a scaling intertwines n and N. In the NC case the interplay becomes tighter due to the merging of space-time and ``internal'' symmetries. Surprisingly, in our up to O(g^6) (and beyond) crossed graphs calculations th...
Capri, M A L; Pereira, A D; Fiorentini, D; Guimaraes, M S; Mintz, B W; Palhares, L F; Sorella, S P
2016-01-01
In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it turns out that the poles of are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST invariant formulation introduced before. Moreover, the correlator enables us to attach a BRST invariant meaning to the possible positivity violation of ...
Drechsler, Wolfgang; Havas, Peter; Rosenblum, Arnold
1984-02-01
In the preceding paper, the laws of motion were established for classical particles with spin which are monopole-dipole singularities of Yang-Mills-Higgs fields. In this paper, a systematic approximation scheme is developed for solving the coupled nonlinear field equations in any order and for determining the corresponding equations of motion. In zeroth order the potentials are taken as the usual Liénard-Wiechert and Bhabha-Harish-Chandra potentials (generalized to isospace); in this order the solutions are necessarily Abelian, since the isovector describing the charge is constant. The regularization necessary to obtain expressions finite on the world lines of the particles is achieved by the method of Riesz potentials. All fields are taken as retarded and are expressed in integral form. Omitting dipole interactions, the integrals for the various terms are carried out as far as possible for general motions, including radiation-reaction terms. In first order, the charge isovectors are no longer necessarily constant; thus the solutions are not necessarily Abelian, and it is possible for charge to be radiated away. The cases of time-symmetric field theory and of an action-at-a-distance formulation of the theory are discussed in an appendix.
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Chankowski, Piotr H. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Lewandowski, Adrian [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Meissner, Krzysztof A. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland)
2016-11-18
We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional (MS)-bar scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the (MS)-bar scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.
Chankowski, Piotr H.; Lewandowski, Adrian; Meissner, Krzysztof A.
2016-11-01
We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional overline{MS} scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the overline{MS} scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.
Energy Technology Data Exchange (ETDEWEB)
None, None
2014-06-19
We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar NN = 4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra. From the remainder function, we extract the BFKL eigenvalue at next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at N3LLA. We plot the remainder function along various lines and on one surface, studying ratios of successive loop orders. As seen previously through three loops, these ratios are surprisingly constant over large regions in the space of cross ratios, and they are not far from the value expected at asymptotically large orders of perturbation theory.
Landau gauge Yang-Mills correlation functions
Cyrol, Anton K.; Fister, Leonard; Mitter, Mario; Pawlowski, Jan M.; Strodthoff, Nils
2016-09-01
We investigate Landau gauge S U (3 ) Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalization group. Particular focus is put on the dynamical creation of the gluon mass gap at nonperturbative momenta and the consistent treatment of quadratic divergences. The nonperturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as the only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.
Dixon, Lance J.; Duhr, Claude; Pennington, Jeffrey
2014-01-01
We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar N=4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra. From the remainder function, we extract the BFKL eigenvalue at next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at NNNLLA. We plot the remainder function along various lines and on one surface, studying ratios of successive loop orders. As seen previously through three loops, these ratios are surprisingly constant over large r...
Chankowski, Piotr H; Meissner, Krzysztof A
2016-01-01
We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with an explicit UV momentum cutoff $\\Lambda$. We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional $\\overline{\\rm MS}$ scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the $\\overline{\\rm MS}$ scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action express...
Directory of Open Access Journals (Sweden)
Trunev A. P.
2015-04-01
Full Text Available Metric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Maxwell's equations and Yang-Mills theory are converted to the moving axes in metric describes the acceleration and rotating reference frame in the general relativity in the case of an arbitrary dependence of acceleration and angular velocity of the system from time. The article discusses the known effects associated with acceleration and (or the rotation of the reference frame - the Sagnac effect, the effect of the Stewart-Tolman and other similar effects. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It has been shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed
Deconfinement in N=1 super Yang-Mills theory on R^3 x S^1 via dual-Coulomb gas and "affine" XY-model
Anber, Mohamed M; Poppitz, Erich; Strimas-Mackey, Seth; Teeple, Brett
2013-01-01
We study finite-temperature N=1 SU(2) super Yang-Mills theory, compactified on a spatial circle of size L with supersymmetric boundary conditions. In the semiclassical small-L regime, a deconfinement transition occurs at T_c <<1/L. The transition is due to a competition between non-perturbative topological "molecules"---magnetic and neutral bion-instantons---and electrically charged W-bosons and superpartners. Compared to deconfinement in non-supersymmetric QCD(adj) arXiv:1112.6389, the novelty is the relevance of the light modulus scalar field. It mediates interactions between neutral bions (and W-bosons), serves as an order parameter for the Z_2^{L} center symmetry associated with the non-thermal circle, and explicitly breaks the electric-magnetic (Kramers-Wannier) duality enjoyed by non-supersymmetric QCD(adj) near T_c. We show that deconfinement can be studied using an effective two-dimensional gas of electric and magnetic charges with (dual) Coulomb and Aharonov-Bohm interactions, or, equivalently,...
Duarte, Anthony G.; Oliveira, Orlando; Silva, Paulo J.
2016-07-01
The dependence of the Landau gauge two-point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to 1284 and for two lattice spacings 0.10 fm and 0.06 fm corresponding to volumes of ˜(13 fm )4 and ˜(8 fm )4 , respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing a in the infrared region, with the gluon propagator having a stronger dependence on a compared to the ghost propagator. In what concerns the strong coupling constant αs(p2), as defined from gluon and ghost two-point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to ˜1 GeV .
Duarte, Anthony G; Silva, Paulo J
2016-01-01
The dependence of the Landau gauge two point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to $128^4$ and for two lattice spacings $0.10$ fm and $0.06$ fm corresponding to volumes of $\\sim$ (13 fm)$^4$ and $\\sim$ (8 fm)$^4$, respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing $a$ in the infrared region, with the gluon propagator having a stronger dependence on $a$ compared to the ghost propagator. In what concerns the strong coupling constant $\\alpha_s (p^2)$, as defined from gluon and ghost two point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to $\\sim 1$ GeV.
Equivariance on Discrete Space and Yang-Mills-Higgs Model
Ikemori, Hitoshi; Matsui, Yoshimitsu; Otsu, Hideharu; Sato, Toshiro
2015-01-01
We introduce the basic equivariant quantity $Q$ in the gauge theory on the noncommutative descrete $Z_{2}$ space, which plays an important role for the equivariant dimensional reduction. If the gauge configuration of the ground state on the extra dimensional space is described by the equivariant $Q$, then the extra dimensional space is invisible. Especially, using the equivariance principle, we show that the Yang-Mills theory on $R^{2}\\times Z_{2}$ space is equivalent to the Yang-Mills-Higgs model on $R^{2}$ space. It can be said that this model is the simplest model of this type.
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.
Scattering amplitudes and BCFW recursion in twistor space
Mason, Lionel; Skinner, David
2010-01-01
Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for n-particle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N2MHV super-amplitude. We also give simple closed form formulae for the mathcal{N} = 8 supergravity recursion and the MHV and overline {text{MHV}} amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N k MHV, the amplitudes are given by 2 n - 4 integrals in the form of Hilbert transforms of a product of n - k - 2 purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in mathcal{N} = 4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan.
Quantum Yang--Mills Dark Energy
Pasechnik, Roman
2016-01-01
In this short review, I discuss basic qualitative characteristics of quantum non-Abelian gauge dynamics in the non-stationary background of the expanding Universe in the framework of the standard Einstein--Yang--Mills formulation. A brief outlook of existing studies of cosmological Yang--Mills fields and their properties will be given. Quantum effects have a profound impact on the gauge field-driven cosmological evolution. In particular, a dynamical formation of the spatially-homogeneous and isotropic gauge field condensate may be responsible for both early and late-time acceleration, as well as for dynamical compensation of non-perturbative quantum vacua contributions to the ground state of the Universe. The main properties of such a condensate in the effective QCD theory at the flat Friedmann--Lema\\'itre--Robertson--Walker (FLRW) background will be discussed within and beyond perturbation theory. Finally, a phenomenologically consistent dark energy can be induced dynamically as a remnant of the QCD vacua co...
N=2 SYM Action as a BRST Exact Term, Topological Yang Mills and Instantons
Ulker, K
2003-01-01
By defining an extended BRST operator that includes the chiral part of N=2 global supersymmetry, it is shown that the full N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term. The action written in this form suggests that the fields of the Topological Yang Mills theory can be defined in terms of composite fields of supersymmetry ghosts and N=2 fields in a natural way. Topological Yang Mills theory is obtained from the ordinary Euclidean N=2 SYM directly as field redefinitions without using twisting procedure. With the help of these results, relation between the recent instanton calculations in N=2 Super Yang Mills and Topological Yang Mills theories is also discussed.
Global symmetries of Yang-Mills squared in various dimensions
Energy Technology Data Exchange (ETDEWEB)
Anastasiou, A. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); Borsten, L. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); School of Theoretical Physics, Dublin Institute for Advanced Studies,10 Burlington Road, Dublin 4 (Ireland); Hughes, M.J. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); Nagy, S. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); Department of Mathematics, Instituto Superior Técnico,Av. Rovisco Pais, 1049-001 Lisbon (Portugal)
2016-01-25
Tensoring two on-shell super Yang-Mills multiplets in dimensions D≤10 yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) D with each dimension 3≤D≤10 we obtain a formula for the supergravity U-duality G and its maximal compact subgroup H in terms of the internal global symmetry algebras of each super Yang-Mills theory. We extend our analysis to include supergravities coupled to an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor product.
Yang-Mills analogues of the Immirzi ambiguity
Gambini, R; Pullin, J
1999-01-01
We draw parallels between the recently introduced ``Immirzi ambiguity'' of the Ashtekar-like formulation of canonical quantum gravity and other ambiguities that appear in Yang-Mills theories, like the $\\theta$ ambiguity. We also discuss ambiguities in the Maxwell case, and implication for the loop quantization of these theories.
Yang-Mills for historians and philosophers
Crease, R. P.
2016-01-01
The phrase “Yang-Mills” can be used (1) to refer to the specific theory proposed by Yang and Mills in 1954; or (2) as shorthand for any non-Abelian gauge theory. The 1954 version, physically speaking, had a famous show-stopping defect in the form of what might be called the “Pauli snag,” or the requirement that, in the Lagrangian for non-Abelian gauge theory the mass term for the gauge field has to be zero. How, then, was it possible for (1) to turn into (2)? What unfolding sequence of events made this transition possible, and what does this evolution say about the nature of theories in physics? The transition between (1) and (2) illustrates what historians and philosophers a century from now might still find instructive and stimulating about the development of Yang-Mills theory.
On Form Factors and Correlation Functions in Twistor Space
Koster, Laura; Staudacher, Matthias; Wilhelm, Matthias
2016-01-01
In this paper, we continue our study of form factors and correlation functions of gauge-invariant local composite operators in the twistor-space formulation of N=4 super Yang-Mills theory. Using the vertices for these operators obtained in our recent papers arXiv:1603.04471 and arXiv:1604.00012, we show how to calculate the twistor-space diagrams for general N^kMHV form factors via the inverse soft limit, in analogy to the amplitude case. For general operators without $\\dot\\alpha$ indices, we then reexpress the NMHV form factors from the position-twistor calculation in terms of momentum twistors, deriving and expanding on a relation between the two twistor formalisms previously observed in the case of amplitudes. Furthermore, we discuss the calculation of generalized form factors and correlation functions as well as the extension to loop level, in particular providing an argument promised in arXiv:1410.6310.
Cui, Xiaoyi; Shifman, M.
2012-02-01
We consider two-dimensional N=(0,2) sigma models with the CP(1) target space. A minimal model of this type has one left-handed fermion. Nonminimal extensions contain, in addition, Nf right-handed fermions. Our task is to derive expressions for the β functions valid to all orders. To this end we use a variety of methods: (i) perturbative analysis; (ii) instanton calculus; (iii) analysis of the supercurrent supermultiplet (the so-called hypercurrent) and its anomalies, and some other arguments. All these arguments, combined, indicate a direct parallel between the heterotic N=(0,2) CP(1) models and four-dimensional super-Yang-Mills theories. In particular, the minimal N=(0,2) CP(1) model is similar to N=1 supersymmetric gluodynamics. Its exact β function can be found; it has the structure of the Novikov-Shifman-Vainshtein-Zakharov (NSVZ) β function of supersymmetric gluodynamics. The passage to nonminimal N=(0,2) sigma models is equivalent to adding matter. In this case an NSVZ-type exact relation between the β function and the anomalous dimensions γ of the “matter” fields is established. We derive an analog of the Konishi anomaly. At large Nf our β function develops an infrared fixed point at small values of the coupling constant (analogous to the Banks-Zaks fixed point). Thus, we reliably predict the existence of a conformal window. At Nf=1 the model under consideration reduces to the well-known N=(2,2) CP(1) model.
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...
A nonperturbative method for the Yang Mills Lagrangian
Jora, Renata
2014-01-01
Using the properties of the partition function for a Yang Mills theory we compute simple relations among the renormalization constants. In the particular case of the background gauge field method we obtain that the all orders beta function for the gauge coupling constant contains only the first two orders coefficients different than zero and thus corresponds to the 't Hooft scheme.
Eigenvalue spectrum of lattice N=4 super Yang-Mills
Weir, D.; Catterall, S.; Mehta, D. B.
We present preliminary results for the eigenvalue spectrum of four-dimensional ${\\cal N}=4$ super Yang-Mills theory on the lattice. In particular, by studying the the spectral density a measurement of the anomalous dimension is made and found to be consistent with zero.
SO(3) vs. SU(2) Yang-Mills theory on the lattice: an investigation at non-zero temperature
Barresi, A; Müller-Preussker, M
2003-01-01
The adjoint SU(2) lattice gauge theory in 3+1 dimensions with the Wilson plaquette action modified by a Z(2) monopole suppression term is reinvestigated with special emphasis on the existence of a finite-temperature phase transition decoupling from the well-known bulk transitions.
Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy
Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; Roiban, Radu
2017-07-01
Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + ϕ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism. Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.
N=2 Conformal Supergravity from Twistor-String Theory
Ahn, C
2004-01-01
A chiral superfield strength in N=2 conformal supergravity at linearized level is obtained by acting two superspace derivatives on N=4 chiral superfield strength which can be described in terms of N=4 twistor superfields. By decomposing SU(4)_R representation of N=4 twistor superfields into the SU(2)_R representation with an invariant U(1)_R charge, the surviving N=2 twistor superfields contain the physical states of N=2 conformal supergravity. These N=2 twistor superfields are functions of homogeneous coordinates of weighted complex projective space WCP^{3|4} where the two weighted fermionic coordinates have weight -1 and 3.
Galtsov, D V; Volkov, M S; Davydov, Evgeny A.; Gal'tsov, Dmitri V.; Volkov, Mikhail S.
2006-01-01
We present globally regular vortex-type solutions for a pure SU(2) Yang-Mills field coupled to gravity in 3+1 dimensions. These gravitating vortices are static, cylindrically symmetric and purely magnetic, and they support a non-zero chromo-magnetic flux through their cross section. In addition, they carry a constant non-Abelian current, and so in some sense they are analogs of the superconducting cosmic strings. They have a compact central core dominated by a longitudinal magnetic field and endowed with an approximately Melvin geometry. This magnetic field component gets color screened in the exterior part of the core, outside of which the fields approach exponentially fast those of the electrovacuum Bonnor solutions with a circular magnetic field. In the far field zone the solutions are not asymptotically flat but tend to vacuum Kasner metrics.
A Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry
Institute of Scientific and Technical Information of China (English)
WANG Dian-Fu; SONG He-Shan
2005-01-01
A generalized Yang-Mills model, which contains, besides the vector part Vμ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Exact solutions for classical Yang-Mills fields
Frasca, Marco
2014-01-01
Some years ago we displayed a set of classical solutions for the classical Yang-Mills field theory having the property to satisfy a dispersion relation typical of a massive theory. But such solutions seemed to be exact only in the Landau gauge making all the argument an asymptotic one for the most general case of a generic gauge. These solutions can be used to describe the vacuum of the quantum Yang-Mills theory and so, to prove that they are always exact can grant a general framework to build a quantum field theory. Here we show that these solutions are always exact changing just the normalization factor. The components of the field become separated on a generic gauge being all equal just in the Landau gauge.
An exploratory study of Yang-Mills three-point functions at non-zero temperature
Huber, Markus Q
2016-01-01
Results for three-point functions of Landau gauge Yang-Mills theory at non-vanishing temperature are presented and compared to lattice results. It is found that the three-gluon vertex is enhanced for temperatures below the phase transition. At very low momenta it becomes negative for all temperatures. Furthermore, truncation effects in functional equations are discussed at the example of three-dimensional Yang-Mills theory for which a self-contained solution is presented.
An exploratory study of Yang-Mills three-point functions at non-zero temperature
Huber, Markus Q.
2017-03-01
Results for three-point functions of Landau gauge Yang-Mills theory at non-vanishing temperature are presented and compared to lattice results. It is found that the three-gluon vertex is enhanced for temperatures below the phase transition. At very low momenta it becomes negative for all temperatures. Furthermore, truncation effects in functional equations are discussed at the example of three-dimensional Yang-Mills theory for which a self-contained solution is presented.
(Super)Yang-Mills at Finite Heavy-Quark Density
Faedo, Anton F; Mateos, David; Tarrio, Javier
2014-01-01
We study the gravitational duals of $d$-dimensional Yang-Mills theories with $d\\leq 6$ in the presence of an ${\\cal O} (N^2)$ density of heavy quarks, with $N$ the number of colors. For concreteness we focus on maximally supersymmetric Yang-Mills, but our results apply to a larger class of theories with or without supersymmetry. The gravitational solutions describe renormalization group flows towards infrared scaling geometries characterized by fixed dynamical and hyperscaling-violating exponents. The special case $d=5$ yields an $AdS_3 \\times \\mathbb{R}^4 \\times S^4$ geometry upon uplifting to M-theory. We discuss the multitude of physical scales that separate different dynamical regimes along the flows, as well as the validity of the supergravity description. We also present exact black brane solutions that encode the low-temperature thermodynamics.
Einstein-Yang-Mills solitons towards new degrees of freedom
Galtsov, D V
1998-01-01
A recent progress in obtaining non-spherical and non-static solitons in the four-dimensional Einstein--Yang--Mills (EYM) theory is discussed, and a non-perturbative formulation of the stationary axisymmetric problem is attempted. First a 2D dilaton gravity model is derived for the spherically symmetric time-dependent configurations. Then a similar Euclidean representation is constructed for the stationary axisymmetric non-circular SU(2) EYM system using the (2+1)+1 reduction scheme suggested by Maeda, Sasaki, Nakamura and Miyama. The crucial role in this reduction is played by the extra terms entering the reduced Yang--Mills and Kaluza--Klein two-forms similarly to Chern--Simons terms in the theories with higher rank antisymmetric tensor fields. We also derive a simple 2D action describing static axisymmetric magnetic EYM configurations and discuss a possibility of existence of cylindrical EYM sphalerons.
Towards a Loop Quantum Gravity and Yang-Mills unification
Energy Technology Data Exchange (ETDEWEB)
Alexander, Stephon, E-mail: stephonalexander@mac.com [Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755 (United States); Department of Physics and Astronomy, Haverford College, Haverford, PA 19041 (United States); Department of Physics, Princeton University, NJ 08544 (United States); Institute for Gravitation and the Cosmos, Department of Physics, Penn State, University Park, PA 16802 (United States); Marciano, Antonino [Department of Physics and Astronomy, Haverford College, Haverford, PA 19041 (United States); Department of Physics, Princeton University, NJ 08544 (United States); Tacchi, Ruggero Altair [Department of Physics, University of California, Davis, CA 95616 (United States)
2012-09-19
We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2) Yang-Mills interaction and 3D general relativity by considering a constrained Spin(4){approx}SO(4) Plebanski action. The theory is quantized a la spin-foam by implementing the analogue of the simplicial constraints for the Spin(4) symmetry, providing a way to couple Yang-Mills fields to spin-foams. A natural 4D extension of the theory is introduced. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.
HYM-flation: Yang-Mills cosmology with Horndeski coupling
Davydov, E.; Gal'tsov, D.
2016-02-01
We propose new mechanism for inflation using classical SU (2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.
HYM-flation: Yang-Mills cosmology with Horndeski coupling
Davydov, E
2016-01-01
We propose new mechanism for inflation using classical SU(2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.
A Classical Solution of Massive Yang-Mills Fields
Mogami, Tsuguo
2016-01-01
Recent researches on the solution of Schwinger-Dyson equations, as well as lattice simulations of pure QCD, suggest that the gluon propagator is massive. In this letter, we assume that the classical counterpart of this massive gluon field may be represented with the equation of motion for Yang-Mills theory with a mass term added. A new classical solution is given for this equation. It is discussed that this solution may have some role in confinement.
Slavnov determinants, Yang-Mills structure constants, and discrete KP
Foda, O
2012-01-01
Using Slavnov's scalar product of a Bethe eigenstate and a generic state in closed XXZ spin-1/2 chains, with possibly twisted boundary conditions, we obtain determinant expressions for tree-level structure constants in 1-loop conformally-invariant sectors in various planar (super) Yang-Mills theories. When certain rapidity variables are allowed to be free rather than satisfy Bethe equations, these determinants become discrete KP tau-functions.
Roiban, Radu; Volovich, Anastasia
2004-09-24
It has recently been proposed that the D-instanton expansion of the open topological B model on P(3|4) is equivalent to the perturbative expansion of the maximally supersymmetric Yang-Mills theory in four dimensions. In this letter we show how to construct the gauge theory results for all n-point conjugate-maximal-helicity-violating amplitudes by computing the integral over the moduli space of curves of degree n-3 in P(3|4), providing strong support to the string theory construction.
Honda, Masazumi; Nishimura, Jun; Tsuchiya, Asato
2011-01-01
We test the AdS/CFT correspondence by calculating Wilson loops in N = 4 super Yang-Mills theory on R*S^3 in the planar limit. Our method is based on a novel large-N reduction, which reduces the problem to Monte Carlo calculations in the plane-wave matrix model or the BMN matrix model, which is a 1d gauge theory with 16 supercharges. By using the gauge-fixed momentumspace simulation, we obtain results respecting 16 supersymmetries. We report on the Monte Carlo results for the BPS circular Wilson loop, which reproduce the exact result up to strong coupling. As a future prospect, we calculate a track-shapedWilson loop from the gravity side, which shows that a clear test of the AdS/CFT for the non-BPS case is also feasible.
New relations for Einstein-Yang-Mills amplitudes
Stieberger, Stephan; Taylor, Tomasz R.
2016-12-01
We obtain new relations between Einstein-Yang-Mills (EYM) amplitudes involving N gauge bosons plus a single graviton and pure Yang-Mills amplitudes involving N gauge bosons plus one additional vector boson inserted in a way typical for a gauge boson of a "spectator" group commuting with the group associated to original N gauge bosons. We show that such EYM amplitudes satisfy U(1) decoupling relations similar to Kleiss-Kuijf relations for Yang-Mills amplitudes. We consider a D-brane embedding of EYM amplitudes in the framework of disk amplitudes involving open and closed strings. A new set of monodromy relations is derived for mixed open-closed amplitudes with one closed string inserted on the disk world-sheet and a number of open strings at the boundary. These relations allow expressing the latter in terms of pure open string amplitudes and, in the field-theory limit, they yield the U(1) decoupling relations for EYM amplitudes.
Latest results from lattice N=4 supersymmetric Yang--Mills
Schaich, David; Damgaard, Poul H; Giedt, Joel
2016-01-01
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, we recently developed an improved lattice action that is now being employed in large-scale calculations. Here we update our studies of the static potential using this new action, also applying tree-level lattice perturbation theory to improve the analysis of the potential itself. Considering relatively weak couplings, we obtain results for the Coulomb coefficient that are consistent with continuum perturbation theory.
Loop formulation of supersymmetric Yang-Mills quantum mechanics
Steinhauer, Kyle
2014-01-01
We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.
Fate of Yang-Mills black hole in early Universe
Energy Technology Data Exchange (ETDEWEB)
Nakonieczny, Lukasz; Rogatko, Marek [Institute of Physics Maria Curie-Sklodowska University 20-031 Lublin, pl. Marii Curie-Sklodowskiej 1 (Poland)
2013-02-21
According to the Big Bang Theory as we go back in time the Universe becomes progressively hotter and denser. This leads us to believe that the early Universe was filled with hot plasma of elementary particles. Among many questions concerning this phase of history of the Universe there are questions of existence and fate of magnetic monopoles and primordial black holes. Static solution of Einstein-Yang-Mills system may be used as a toy model for such a black hole. Using methods of field theory we will show that its existence and regularity depend crucially on the presence of fermions around it.
Maximally supersymmetric Yang-Mills on the lattice
Schaich, David
2015-01-01
We summarize recent progress in lattice studies of four-dimensional N=4 supersymmetric Yang--Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, and we review a new procedure to regulate flat directions by modifying the moduli equations in a manner compatible with this supersymmetry. This procedure defines an improved lattice action that we have begun to use in numerical calculations. We discuss some highlights of these investigations, including the static potential and an update on the question of a possible sign problem in the lattice theory.
Studies In Non-anticommutative Gauge Theories, Geometric Dualities, And Twistor Strings
Robles Llana, D
2005-01-01
In this Dissertation we consider three different topics. The first one is the study of instantons in U(2) super Yang-Mills theories defined on non-anticommutative superspace. We extend the ordinary instanton calculus to this class of theories by solving the appropriate equations of motion iteratively in the deformation parameter C. In the case without matter, we solve the equations exactly. We find that the SU(2) part of the instanton is the same as in ordinary SU (2) N = 1 super Yang-Mills, but acquires in addition a non-trivial U(1) part which depends on the fermionic collective coordinates and the deformation parameter C. In the case with matter we solve the equations of motion to leading order in the coupling constant. We find that also the profile of the matter fields is deformed through linear and quadratic corrections in C. The instanton effective action for pure gluodynamics is unaffected by C, but gets a contribution of order C2 in addition to the usual 't Hooft term when the matter is included....
BOOK REVIEW: Solitons, Instantons, and Twistors Solitons, Instantons, and Twistors
Witt, Donald M.
2011-04-01
Solitons and instantons play important roles both in pure and applied mathematics as well as in theoretical physics where they are related to the topological structure of the vacuum. Twistors are a useful tool for solving nonlinear differential equations and are useful for the study of the antiself-dual Yang-Mills equations and the Einstein equations. Many books and more advanced monographs have been written on these topics. However, this new book by Maciej Dunajski is a complete first introduction to all of the topics in the title. Moreover, it covers them in a very unique way, through integrable systems. The approach taken in this book is that of mathematical physics à la field theory. The book starts by giving an introduction to integrable systems of ordinary and partial differential equations and proceeds from there. Gauge theories are not covered until chapter 6 which means the reader learning the material for the first time can build up confidence with simpler models of solitons and instantons before encountering them in gauge theories. The book also has an extremely clear introduction to twistor theory useful to both mathematicians and physicists. In particular, the twistor theory presentation may be of interest to string theorists wanting understand twistors. There are many useful connections to research into general relativity. Chapter 9 on gravitational instantons is great treatment useful to anyone doing research in classical or quantum gravity. There is also a nice discussion of Kaluza-Klein monopoles. The three appendices A-C cover the necessary background material of basic differential geometry, complex manifolds, and partial differential equations needed to fully understand the subject. The reader who has some level of expertise in any of the topics covered can jump right into that material without necessarily reading all of the earlier chapters because of the extremely clear writing style of the author. This makes the book an excellent reference on
Stabilizing Perturbative Yang-Mills Free Energy with Gribov Quantization
Fukushima, Kenji
2013-01-01
We evaluate the free energy of the Yang-Mills theory using the Gribov quantization that copes with non-perturbative resummation. The magnetic scale is automatically incorporated in the framework and we find it efficient to stabilize the perturbative expansion of the free energy. In the range of the temperature T=T_c~2T_c major uncertainty in our results comes from the non-perturbative running coupling that is adopted from the lattice simulation, while the convergence above 2T_c is impressively robust.
On Landau gauge Yang-Mills correlation functions
Cyrol, Anton K; Mitter, Mario; Pawlowski, Jan M; Strodthoff, Nils
2016-01-01
We investigate Landau gauge $SU(3)$ Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.
Aspects of lattice N=4 supersymmetric Yang--Mills
Schaich, David
2015-01-01
Non-perturbative investigations of $\\mathcal N = 4$ supersymmetric Yang--Mills theory formulated on a space-time lattice have advanced rapidly in recent years. Large-scale numerical calculations are currently being carried out based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing. A recent development is the creation of an improved lattice action through a new procedure to regulate flat directions in a manner compatible with this supersymmetry, by modifying the moduli equations. In this proceedings I briefly summarize this new procedure and discuss the parameter space of the resulting improved action that is now being employed in numerical calculations.
Implementing the Gribov-Zwanziger framework in N=1 Super Yang-Mills in the Landau gauge
Capri, M A L; Guimaraes, M S; Justo, I F; Palhares, L F; Sorella, S P; Vercauteren, D
2014-01-01
The Gribov-Zwanziger framework accounting for the existence of Gribov copies is extended to N=1 Super Yang--Mills theories quantized in the Landau gauge. We show that the restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon can be implemented in a way to recover non-perturbative features of N=1 Super Yang--Mills theories, namely: the existence of the gluino condensate as well as the vanishing of the vacuum energy.
Massive and mass-less Yang-Mills and gravitational fields
Veltman, M.J.G.; Dam, H. van
1970-01-01
Massive and mass-less Yang-Mills and gravitational fields are considered. It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the case of gravitation, comparison of massive and mass-less theories with experiment, in
Massive and mass-less Yang-Mills and gravitational fields
Veltman, M.J.G.; Dam, H. van
1970-01-01
Massive and mass-less Yang-Mills and gravitational fields are considered. It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the case of gravitation, comparison of massive and mass-less theories with experiment, in partic
Yang-Mills correlators across the deconfinement phase transition
Reinosa, U; Tissier, M; Tresmontant, A
2016-01-01
We compute the finite temperature ghost and gluon propagators of Yang-Mills theory in the Landau-DeWitt gauge. The background field that enters the definition of the latter is intimately related with the (gauge-invariant) Polyakov loop and serves as an equivalent order parameter for the deconfinement transition. We use an effective gauge-fixed description where the nonperturbative infrared dynamics of the theory is parametrized by a gluon mass which, as argued elsewhere, may originate from the Gribov ambiguity. In this scheme, one can perform consistent perturbative calculations down to infrared momenta, which have been shown to correctly describe the phase diagram of Yang-Mills theories in four dimensions as well as the zero-temperature correlators computed in lattice simulations. In this article, we provide the one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon propagators for a large class of gauge groups and present explicit results for the SU(2) case. These are substantially dif...
Yang-Mills correlators across the deconfinement phase transition
Reinosa, U.; Serreau, J.; Tissier, M.; Tresmontant, A.
2017-02-01
We compute the finite temperature ghost and gluon propagators of Yang-Mills theory in the Landau-DeWitt gauge. The background field that enters the definition of the latter is intimately related with the (gauge-invariant) Polyakov loop and serves as an equivalent order parameter for the deconfinement transition. We use an effective gauge-fixed description where the nonperturbative infrared dynamics of the theory is parametrized by a gluon mass which, as argued elsewhere, may originate from the Gribov ambiguity. In this scheme, one can perform consistent perturbative calculations down to infrared momenta, which have been shown to correctly describe the phase diagram of Yang-Mills theories in four dimensions as well as the zero-temperature correlators computed in lattice simulations. In this article, we provide the one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon propagators for a large class of gauge groups and present explicit results for the SU(2) case. These are substantially different from those previously obtained in the Landau gauge, which corresponds to a vanishing background field. The nonanalyticity of the order parameter across the transition is directly imprinted onto the propagators in the various color modes. In the SU(2) case, this leads, for instance, to a cusp in the electric and magnetic gluon susceptibilities as well as similar signatures in the ghost sector. We mention the possibility that such distinctive features of the transition could be measured in lattice simulations in the background field gauge studied here.
Stiffler, Kory M.
Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put toward this goal. A set of specific tools which are used in this effort are gauge/gravity dualities. This thesis consists of a specific implementation of gauge/gravity dualities to describe k-strings of strongly coupled gauge theories as objects dual to Dp-branes embedded in confining supergravity backgrounds from low energy superstring field theory. Along with superstring theory, k-strings are also commonly investigated with lattice gauge theory and Hamiltonian methods. A k-string is a colorless combination of quark-antiquark source pairs, between which a color flux tube develops. The two most notable terms of the k-string energy are, for large quark anti-quark separation L, the tension term, proportional to L, and the Coulombic 1/L correction, known as the Luscher term. This thesis provides an overview of superstring theories and how gauge/gravity dualities emerge from them. It shows in detail how these dualities can be used for the specific problem of calculating the k-string energy in 2 + 1 and 3 + 1 space-time dimensions as the energy of D p-branes in the dual gravitational theory. A detailed review of k-string tension calculations is given where good agreement is found with lattice gauge theory and Hamiltonian methods. In reviewing the k-string tension, we also touch on how different representations of k-strings can be described with Dp-branes through gauge/gravity dualities. The main result of this thesis is how the Luscher term is found to emerge as the one loop quantum corrections to the Dp-brane energy. In 2+1 space-time dimensions, we have Luscher term data to compare with from lattice gauge theory, where we find good agreement.
Gauge-covariant decomposition and magnetic monopole for G(2) Yang-Mills field
Matsudo, Ryutaro
2016-01-01
We give a gauge-covariant decomposition of the Yang-Mills field with an exceptional gauge group $G(2)$, which extends the field decomposition invented by Cho, Duan-Ge, and Faddeev-Niemi for the $SU(N)$ Yang-Mills field. As an application of the decomposition, we derive a new expression of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of $G(2)$. The resulting new form is used to define gauge-invariant magnetic monopoles in the $G(2)$ Yang-Mills theory. Moreover, we obtain the quantization condition to be satisfied by the resulting magnetic charge. The method given in this paper is general enough to be applicable to any semi-simple Lie group other than $SU(N)$ and $G(2)$.
Maximally Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A maximally generalized Yang-Mills model, which contains, besides the vector part Vμ, also an axial-vector part Aμ, a scalar part S, a pseudoscalar part P, and a tensor part Tμv, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the maximally generalized Yang-Mills model. The combination of the maximally generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Yang-Mills Solutions and Dyons on Cylinders over Coset Spaces with Sasakian Structure
Tormählen, Maike
2014-01-01
We present solutions of the Yang-Mills equation on cylinders $\\mathbb R\\times G/H$ over coset spaces with Sasakian structure and odd dimension $2m+1$. The gauge potential is assumed to be $SU(m)$-equivariant, parametrized by two real, scalar-valued functions. Yang-Mills theory with torsion in this setup reduces to the Newtonian mechanics of a point particle moving in $\\mathbb R^2$ under the influence of an inverted potential. We analyze the critical points of this potential and present an analytic as well as several numerical finite-action solutions. Apart from the Yang-Mills solutions that constitute $SU(m)$-equivariant instanton configurations, we construct periodic sphaleron solutions on $S^1\\times G/H$ and dyon solutions on $i\\mathbb R\\times G/H$.
Stiffler, Kory
2010-01-01
Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put toward this goal. A set of specific tools which are used in this effort are gauge/gravity dualities. This thesis consists of a specific implementation of gauge/gravity dualities to describe k-strings of strongly coupled gauge theories as objects dual to Dp-branes embedded in confining supergravity backgrounds from low energy superstring field theory. Along with superstring theory, k-strings are also commonly investigated with lattice gauge theory and Hamiltonian methods. A k-string is a colorless combination of quark-antiquark source pairs, between which a color flux tube develops. The two most notable terms of the k-string energy are, for large quark anti-quark separation L, the tension term, proportional to L, and the Coulombic 1/L correction, known as the Luscher term. ...
2PI Effective Action and Evolution Equations of N = 4 super Yang-Mills
Smolic, Jelena
2011-01-01
We employ nPI effective action techniques to study N = 4 super Yang-Mills, and write down the 2PI effective action of the theory. We also supply the evolution equations of two-point correlators within the theory.
2PI effective action and evolution equations of N=4 super Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Smolic, Jelena; Smolic, Milena [University of Amsterdam, Institute for Theoretical Physics, Amsterdam (Netherlands)
2012-08-15
We employ nPI effective action techniques to study N=4 super Yang-Mills, and write down the 2PI effective action of the theory to two-loop order in the symmetric phase. We also supply the evolution equations of two-point correlators within the theory. (orig.)
The complete one-loop spin chain for N=2 Super-Yang-Mills
Vecchia, P D
2004-01-01
We show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap.
Gauged twistor spinors and symmetry operators
Ertem, Ümit
2016-01-01
We consider gauged twistor spinors which are supersymmetry generators of supersymmetric and superconformal field theories in curved backgrounds. We show that the spinor bilinears of gauged twistor spinors satify the gauged conformal Killing-Yano equation. We prove that the symmetry operators of the gauged twistor spinor equation can be constructed from ordinary conformal Killing-Yano forms in constant curvature backgrounds. This provides a way to obtain gauged twistor spinors from ordinary twistor spinors.
HEAT FLOW FOR YANG-MILLS-HIGGS FIELDS, PART I
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.
Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
Chiodaroli, Marco; Johansson, Henrik; Roiban, Radu
2015-01-01
We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which th...
BPS Preons in Supergravity and Higher Spin Theories. An Overview From the Hill of Twistor Approach
Bandos, I. A.
2005-04-01
We review briefly the notion of BPS preons, first introduced in 11-dimensional context as hypothetical constituents of M-theory, in its generalization to arbitrary dimensions and emphasizing the relation with twistor approach. In particular, the use of a "twistor-like" definition of BPS preon (almost) allows us to remove supersymmetry arguments from the discussion of the relation of the preons with higher spin theories and also of the treatment of BPS preons as constituents. We turn to the supersymmetry in the second part of this contribution, where we complete the algebraic discussion with supersymmetric arguments based on the M-algebra (generalized Poincaré superalgebra), discuss the possible generalization of BPS preons related to the osp(1|n) (generalized AdS) superalgebra, review a twistor-like κ-symmetric superparticle in tensorial superspace, which provides a point-like dynamical model for BPS preon, and the rôle of BPS preons in the analysis of supergravity solutions. Finally we describe resent results on the concise superfield description of the higher spin field equations and on superfield supergravity in tensorial superspaces.
BPS preons in supergravity and higher spin theories. An overview from the hill of twistor appraoch
Bandos, I A
2005-01-01
We review briefly the notion of BPS preons, first introduced in 11-dimensional context as hypothetical constituents of M-theory, in its generalization to arbitrary dimensions and emphasizing the relation with twistor approach. In particular, the use of a 'twistor-like' definition of BPS preon (almost) allows us to remove supersymmetry arguments from the discussion of the relation of the preons with higher spin theories and also of the treatment of BPS preons as constituents. We turn to the supersymmetry in the second part of this contribution, where we complete the algebraic discussion with supersymmetric arguments based on the M-algebra (generalized Poincare superalgebra), discuss the possible generalization of BPS preons related to the osp(1|n) (generalized AdS) superalgebra, review a twistor-like kappa-symmetric superparticle in tensorial superspace, which provides a point-like dynamical model for BPS preon, and the role of BPS preons in the analysis of supergravity solutions. Finally we describe resent re...
Eigenvalue spectrum of lattice $\\mathcal{N}=4$ super Yang-Mills
Weir, David J; Mehta, Dhagash
2013-01-01
We present preliminary results for the eigenvalue spectrum of four-dimensional ${\\cal N}=4$ super Yang-Mills theory on the lattice. In particular, by studying the the spectral density a measurement of the anomalous dimension is made and found to be consistent with zero.
Microscopic- versus Effective Coupling in N=2 Yang-Mills With Four Flavours
Sachs, I; Sachs, Ivo; Weir, Billy
2000-01-01
We determine the instanton corrections to the effective coupling in SU(2), N=2 Yang-Mills theory with four flavours to all orders. Our analysis uses the S(2,Z)-invariant curve and the two instanton contribution obtained earlier to fix the higher order contributions uniquely.
The leading term of the Yang-Mills free energy
Chatterjee, Sourav
2016-01-01
The construction of quantum Yang-Mills theories is a central open question in mathematical physics, famously posed as one of the millennium prize problems by the Clay Institute. Although huge strides were made in the Eighties, the problem has remained unsolved in dimensions three and four. This article makes a new contribution to this quest, by explicitly calculating the leading term of the free energy of three dimensional $U(N)$ lattice gauge theory for any $N$, as the lattice spacing tends to zero. This is a small step towards the complete solution of the above problem, since the main question can be rephrased as the problem of determining of the full asymptotics of the free energy, rather than only the leading term. The proof is based on a novel technique that avoids phase cell renormalization. The technique also yields a similar formula for the four dimensional theory, but only in the weak coupling limit.
Chiral symmetry and the Yang--Mills gradient flow
Lüscher, Martin
2013-01-01
In the last few years, the Yang--Mills gradient flow was shown to be an attractive tool for non-perturbative studies of non-Abelian gauge theories. Here a simple extension of the flow to the quark fields in QCD is considered. As in the case of the pure-gauge gradient flow, the renormalizability of correlation functions involving local fields at positive flow times can be established using a representation through a local field theory in 4+1 dimensions. Applications of the extended flow in lattice QCD include non-perturbative renormalization and O(a) improvement as well as accurate calculations of the chiral condensate and of the pseudo-scalar decay constant in the chiral limit.
General split helicity gluon tree amplitudes in open twistor string theory
Dolan, Louise; Goddard, Peter
2010-05-01
We evaluate all split helicity gluon tree amplitudes in open twistor string theory. We show that these amplitudes satisfy the BCFW recurrence relations restricted to the split helicity case and, hence, that these amplitudes agree with those of gauge theory. To do this we make a particular choice of the sextic constraints in the link variables that determine the poles contributing to the contour integral expression for the amplitudes. Using the residue theorem to re-express this integral in terms of contributions from poles at rational values of the link variables, which we determine, we evaluate the amplitudes explicitly, regaining the gauge theory results of Britto et al. [25].
Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence
Kassandrov, Vladimir V.; Rizcallah, Joseph A.
We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.
Penante, Brenda
2016-01-01
Planar maximally supersymmetric Yang-Mills theory (N=4 SYM) is a special quantum field theory. A few of its remarkable features are conformal symmetry at the quantum level, evidence of integrability and, moreover, it is a prime example of the AdS/CFT duality. Triggered by Witten's twistor string theory, the past 15 years have witnessed enormous progress in reformulating this theory to make as many of these special features manifest, from the choice of convenient variables to recursion relations that allowed new mathematical structures to appear, like the Grassmannian. These methods are collectively referred to as on-shell methods. The ultimate hope is that, by understanding N=4 SYM in depth, one can learn about other, more realistic quantum field theories. The overarching theme of this thesis is the investigation of how on-shell methods can aid the computation of quantities other than scattering amplitudes. In this spirit we study form factors and correlation functions, said to be partially and completely off...
Chaotic behavior of the lattice Yang-Mills on CUDA
Directory of Open Access Journals (Sweden)
Forster Richárd
2015-12-01
Full Text Available The Yang-Mills fields plays important role in the strong interaction, which describes the quark gluon plasma. The non-Abelian gauge theory provides the theoretical background understanding of this topic. The real time evolution of the classical fields is derived by the Hamiltonian for SU(2 gauge field tensor. The microcanonical equations of motion is solved on 3 dimensional lattice and chaotic dynamics was searched by the monodromy matrix. The entropy-energy relation was presented by Kolmogorov-Sinai entropy. We used block Hessenberg reduction to compute the eigenvalues of the current matrix. While the purely CPU based algorithm can handle effectively only a small amount of values, the GPUs provide enough performance to give more computing power to solve the problem.
Renormalization of the Yang-Mills spectral action
van Suijlekom, Walter D
2011-01-01
We prove renormalizability of the full spectral action for the Yang-Mills system on a flat 4-dimensional background manifold. Interpreting the spectral action as a higher-derivative gauge theory, a power-counting argument shows that it is superrenormalizable. We determine the counterterms at one-loop using zeta function regularization in a background field gauge and establish their gauge invariance. Consequently, the spectral action can be renormalized by a simple shift of the coefficients appearing in the asymptotic expansion of the spectral action. This manuscript provides more details than the shorter companion paper, where we have used a (formal) quantum action principle to arrive at gauge invariance of the counterterms. Here, we give in addition an explicit expression for the gauge propagator.
On the sign problem in 2D lattice super Yang--Mills
Catterall, Simon; Joseph, Anosh; Mehta, Dhagash
2011-01-01
In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the N=(2, 2) and N=(8, 8) supersymmetric Yang--Mills theories in two dimensions for the U(N) theories with N=2,3,4, using the new twisted lattice formulations. Our results provide evidence that these theories do not suffer from a sign problem in the continuum limit. These results thus boost confidence that the new lattice formulations can be used successfully to explore non-perturbative aspects of four-dimensional N=4 supersymmetric Yang--Mills theory.
Energy Technology Data Exchange (ETDEWEB)
Lin, C.-J. David; Ogawa, Kenji [Institute of Physics, National Chiao-Tung University,Hsinchu 30010, Taiwan (China); Ramos, Alberto [PH-TH, CERN,CH-1121 Geneva 23 (Switzerland)
2015-12-16
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g{sub G{sub F}}, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g{sub G{sub F}}. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g{sub G{sub F}{sup 2}}∼6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansätz a’la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g{sub G{sub F}{sup 2}}∼6 is still not governed by possible infrared conformality.
Lin, C.-J. David; Ogawa, Kenji; Ramos, Alberto
2015-12-01
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g GF , is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g GF . For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g GF 2 ˜ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansätz a' la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g GF 2 ˜ 6 is still not governed by possible infrared conformality.
Yang-Mills Instanton Sheaves with Arbitrary Topological Charges
Lai, Sheng-Hong; Lai, I-Hsun
2016-01-01
We use a set of ADHM 3-instanton data to systematically construct a class of SU(2) Yang-Mills instanton solutions with arbitrary topological charges. Moreover, by using the biquaternion calculation with biconjugation operation developed recently, these new ADHM data are used to construct a class of SL(2,C) Yang-Mills instanton sheaves on CP^3 with arbitrary topological charges k greater than 3. This result extends the previous construction of Yang-Mills 2-instanton sheaves to arbitrary higher k-instanton sheaves.
N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature
Kitazawa, Yoshihisa
2008-01-01
We investigate the large N reduced model of gauge theory on a curved spacetime through the plane wave matrix model. We formally derive the action of the N=4 supersymmetric Yang-Mills theory on R \\times S^3 from the plane wave matrix model in the large N limit. Furthermore, we evaluate the effective action of the plane wave matrix model up to the two-loop level at finite temperature. We find that the effective action is consistent with the free energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature limit where the planar contributions dominate. We conclude that the plane wave matrix model can be used as a large N reduced model to investigate nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \\times S^3.
Fiorentini, M A L Capri D; Mintz, B W; Palhares, L F; Sorella, S P
2016-01-01
We address the issue of the renormalizability of the gauge-invariant non-local dimension-two operator $A^2_{\\rm min}$, whose minimization is defined along the gauge orbit. Despite its non-local character, we show that the operator $A^2_{\\rm min}$ can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action which turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator $A^2_{\\rm min}$ turns out to be independent from the gauge parameter $\\alpha$ entering the gauge-fixing condition, being thus given by the anomalous dimension of the operator $A^2$ in the Landau gauge.
Lin, C -J David; Ramos, Alberto
2015-01-01
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g_GF, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g_GF. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g^2_GF ~ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, altho...
Light Dilaton at Fixed Points and Ultra Light Scale Super Yang Mills
DEFF Research Database (Denmark)
Antipin, Oleg; Mojaza, Matin; Sannino, Francesco
2012-01-01
We investigate the infrared dynamics of a nonsupersymmetric SU(X) gauge theory featuring an adjoint fermion, Nf Dirac flavors and an Higgs-like complex Nf x Nf scalar which is a gauge singlet. We first establish the existence of an infrared stable perturbative fixed point and then investigate...... the spectrum near this point. We demonstrate that this theory naturally features a light scalar degree of freedom to be identified with the dilaton and elucidate its physical properties. We compute the spectrum and demonstrate that at low energy the nonperturbative part of the spectrum of the theory is the one...... of pure supersymmetric Yang-Mills. We can therefore determine the exact nonperturbative fermion condensate and deduce relevant properties of the nonperturbative spectrum of the theory. We also show that the intrinsic scale of super Yang-Mills is exponentially smaller than the scale associated...
Cylindrically symmetric Einstein-Yang-Mills-Higgs gauge configurations.
Mondaini, R. P.
1985-02-01
Two solutions are obtained for coupled Einstein-Yang-Mills-Higgs fields with cylindrical symmetry and rigid rotation. The Higgs fields are responsible for the creation of singularities and infinite energy densities at the cylinder's axis.
Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
Bern, Z; Kosower, D A; Roiban, R; Smirnov, V A
2006-01-01
We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the integrand and evaluate the resulting integrals numerically using a Mellin--Barnes representation and the automated package of ref.~[1]. This confirmation of the iteration relation provides further evidence suggesting that N=4 gauge theory is solvable.
Coupling of Yang-Mills to N = 4, d = 4 supergravity
Bergshoeff, E.; Koh, I.G.; Sezgin, E.
1985-01-01
We couple N = 4, d = 4 supersymmetric Yang-Mills theory to supergravity. The scalars of the theory parametrize the coset (SO(n,6)/[SO(n)Ã—SO(6)])Ã—(SU(1,1)/U(1)). Keeping the composite local SO(n)Ã—SO(6)Ã—U(1) invariance intact, we gauge an (n + 6) parameter subgroup of SO(n,6) which is either (i) S
Gravitational and Yang-Mills instantons in holographic RG flows
Gava, Edi; Narain, K S
2011-01-01
We study various holographic RG flow solutions involving warped asymptotically locally Euclidean (ALE) spaces of $A_{N-1}$ type. A two-dimensional RG flow from a UV (2,0) CFT to a (4,0) CFT in the IR is found in the context of (1,0) six dimensional supergravity, interpolating between $AdS_3\\times S^3/\\mathbb{Z}_N$ and $AdS_3\\times S^3$ geometries. We also find solutions involving non trivial gauge fields in the form of SU(2) Yang-Mills instantons on ALE spaces. Both flows are of vev type, driven by the vacuum expectation value of a (not exactly) marginal operator. RG flows in four dimensional field theories are studied in the type IIB and type I$'$ context. In type IIB theory, the flow interpolates between $AdS_5\\times S^5/\\mathbb{Z}_N$ and $AdS_5\\times S^5$ geometries. The field theory interpretation is that of an N=2 $SU(n)^N$ quiver gauge theory flowing to N=4 SU(n) gauge theory. In type I$'$ theory the solution describes an RG flow from N=2 quiver gauge theory with a product gauge group to N=2 gauge theor...
N=4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
Huang, Xing
2014-01-01
We construct four-dimensional N=4 super-Yang-Mills theories on a conic sphere with various background R-symmetry gauge fields. We study free energy and supersymmetric Renyi entropy using heat kernel method as well as localization technique. We find that the universal contribution to the partition function in the free field limit is the same as that in the strong coupling limit, which implies that it may be protected by supersymmetry. Based on the fact that, the conic sphere can be conformally mapped to $S^1\\times H^3$ and the R-symmetry background fields can be supported by the R-charges of black hole, we propose that the holographic dual of these theories are five-dimensional, supersymmetric STU topological black holes. We demonstrate perfect agreement between N=4 super-Yang-Mills theories in the planar limit and the STU topological black holes.
Correspondence between Einstein-Yang-Mills-Lorentz systems and dynamical torsion models
Cembranos, Jose A R
2016-01-01
In the framework of Einstein-Yang-Mills theories, we study the gauge Lorentz group and establish a particular equivalence between this case and a certain class of theories with torsion within Riemann-Cartan space-times. This relation is specially useful in order to simplify the problem of finding exact solutions to the Einstein-Yang-Mills equations. Solutions for non-vanishing torsion with rotation and reflection symmetries are presented by the explicit use of this correspondence. Although these solutions were found in previous literature by a different approach, our method provides an alternative way to obtain them and it may be used in future research to find other exact solutions within this theory.
U(1) decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations in N=4 super Yang-Mills
Jia, Yin; Huang, Rijun; Liu, Chang-Yong
2010-09-01
By using the Britto-Cachazo-Feng-Witten recursion relation of N=4 super Yang-Mills theory, we proved the color reflection, U(1) decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered amplitudes of N=4 super Yang-Mills theory. This proof verified the conjectured Bern-Carrasco-Johansson relations of matter fields. The proof depended only on general properties of superamplitudes. We showed also that the color reflection relation and U(1)-decoupling relation are special cases of Kleiss-Kuijf relations.
Yang-Mills-Vlasov system in the temporal gauge. Systeme de Yang-Mills-Vlasov en jauge temporelle
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Y.; Noutchegueme, N. (Paris-6 Univ., 75 (FR))
1991-01-01
We prove a local in time existence theorem of a solution of the Cauchy problem for the Yang-Mills-Vlasov integrodifferential system. Such equations govern the evolution of plasmas, for instance of quarks and gluons (quagmas), where non abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charge. We work with the temporal gauge and use functional spaces with appropriate weight on the momenta, but no fall off is required in the space direction.
Yang-Mills matrix models with ghosts and derivations of the graded shuffle algebra
Krishnaswami, Govind S
2007-01-01
We consider large-N multi-matrix models that are inspired by the action of Yang-Mills theory including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations of such matrix models have a special algebraic property not shared by generic matrix models. When expressed in terms of the generating series of gluon and ghost correlations G(xi), they are quadratic equations S^i G = G xi^i G in concatenation of correlations. We express S^i in terms of the left annihilation operator and show that it is a derivation of the graded-shuffle product of correlation tensors. A corresponding property of Yang-Mills theory was observed by Makeenko and Migdal in the Wilson loop formulation, where S^i was expressed in terms of the path and area derivatives.
Topics In N = 4 Yang-mills And The Self-dual String
Basu, A
2005-01-01
We analyze some systematics of the coupling constant dependence of correlators in N = 4 Yang- Mills, which is the world-volume theory on D3-branes. We use the fact that the operator Ot that generates infinitesimal changes of the coupling constant in this theory sits in the same supermultiplet as the superconformal currents. We show how superconformal current Ward identities determine a class of terms in the operator product expansion of Ot with any other operator. In certain cases, this leads to constraints on the coupling dependence of correlation functions in N = 4 Yang-Mills. As an application, we demonstrate the exact non-renormalization of two and certain three-point correlation functions of BPS operators. We next approximate these integrated correlators by using a truncated OPE expansion. This leads to differential equations for the coupling dependence. When applied to a particular sixteen point correlator, the coupling dependence we find agrees with the corresponding amplitude computed via the Ad...
Twisted Superspace for N=D=2 Super BF and Yang-Mills with Dirac-K\\"ahler Fermion Mechanism
Kato, J; Uchida, Y; Kato, Junji; Kawamoto, Noboru; Uchida, Yukiya
2003-01-01
We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-K\\"ahler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.