Anatomy of isolated monopole in Abelian projection od SU(2) lattice gauge theory
Belavin, V A; Veselov, A I
2001-01-01
The structure of the isolated static monopolies in the maximum Abelian projection of the SU(2) gluodynamics on the lattice studied. The standard parametrization of the coupling matrix was used by determining the maximum Abelian projection of the R functional maximization relative to all scale transformations. The monopole radius R approx = 0.06 fm is evaluated
Koma, Y; Ilgenfritz, E M; Suzuki, T; Polikarpov, M I
2003-01-01
The structure of the flux-tube profile in Abelian-projected (AP) SU(2) gauge theory in the maximally Abelian gauge is studied. The connection between the AP flux tube and the classical flux-tube solution of the U(1) dual Abelian Higgs (DAH) model is clarified in terms of the path-integral duality transformation. This connection suggests that the electric photon and the magnetic monopole parts of the Abelian Wilson loop can act as separate sources creating the Coulombic and the solenoidal electric field inside a flux tube. The conjecture is confirmed by a lattice simulation which shows that the AP flux tube is composed of these two contributions.
Koma, Y.; Koma, M.; Ilgenfritz, E.-M.; Suzuki, T.; Polikarpov, M. I.
2003-11-01
The structure of the flux-tube profile in Abelian-projected (AP) SU(2) gauge theory in the maximally Abelian gauge is studied. The connection between the AP flux tube and the classical flux-tube solution of the U(1) dual Abelian Higgs model is clarified in terms of the path-integral duality transformation. This connection suggests that the electric photon and the magnetic monopole parts of the Abelian Wilson loop can act as separate sources creating the Coulombic and the solenoidal electric field inside a flux tube. The conjecture is confirmed by a lattice simulation which shows that the AP flux tube is composed of these two contributions.
Demons and abelian projection QCD action and crossover
Yee, K
1995-01-01
I evaluate S_{APQCD}, the exact action of Abelian projection QCD, using the microcanonical demon method. Starting with a trial action consisting of L=1, L=2, & L=3 LxL plaquettes plus a Smit-van-der-Sijs magnetic monopole ``mass'' operator, I show that coefficients of the L=2 and L=3 plaquettes vanish at all beta_{SU2}. In fact, at strong coupling S_{APQCD} is essentially the 1x1 compact QED action with beta_{U1}=beta_{SU2}/2. Beyond beta_{SU2}>=2, S_{APQCD} gains an exogenous negative 1x1x1 magnetic monopole mass shift. Note that my approach differs fundamentally from the Smit-van-der-Sijs approach in that I do not make an a priori assumption about monopole or plaquette size in S_{APQCD}. Indeed, these results suggest that QCD monopoles are pointlike, in contrast to the ``effective'' condensation picture put forth by Smit and van der Sijs.
Global Aspects of Abelian and Center Projections in SU(2) Gauge Theory
Zucchini, R
2003-01-01
We show that the global aspects of Abelian and center projection of a SU(2) gauge theory on an arbitrary manifold are naturally described in terms of smooth Deligne cohomology. This is achieved through the introduction of a novel type of differential topological structure, called Cho structure.
Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
Zohar, Erez; Burrello, Michele; Cirac, J Ignacio
2016-01-01
Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.
Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study
Zohar, Erez; Wahl, Thorsten B.; Burrello, Michele; Cirac, J. Ignacio
2016-11-01
Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.
Maximum entropy PDF projection: A review
Baggenstoss, Paul M.
2017-06-01
We review maximum entropy (MaxEnt) PDF projection, a method with wide potential applications in statistical inference. The method constructs a sampling distribution for a high-dimensional vector x based on knowing the sampling distribution p(z) of a lower-dimensional feature z = T (x). Under mild conditions, the distribution p(x) having highest possible entropy among all distributions consistent with p(z) may be readily found. Furthermore, the MaxEnt p(x) may be sampled, making the approach useful in Monte Carlo methods. We review the theorem and present a case study in model order selection and classification for handwritten character recognition.
Dual Superconductivity in Abelian Higgs Model of QCD
Rajput, B. S.
2017-04-01
The study of generalized field associated with Abelian dyons has been undertaken and it has been demonstrated that topologically, a non-Abelian gauge theory is equivalent to a set of Abelian gauge theories supplemented by dyons which undergo condensation leading to confinement and consequently to superconducting model of QCD vacuum, where the Higgs field plays the role of a regulator only. Constructing the effective action for dyonic field in Abelian projection of QCD, it has been demonstrated that any charge (electrical or magnetic) of dyon screens its own direct potential to which it minimally couples and anti-screens the dual potential leading to dual superconductivity in accordance with generalized Meissner effect. In this Abelian projection of QCD an Abelian Higgs model (AHM) has been successfully constructed and it has been shown to incorporate dual superconductivity and confinement as the consequence of dyonic condensation. It has been demonstrated that in AHM t' Hooft loop creates the string (AHM-string) around which the monopole current under London limit leads to vanishing coherence length in the chromo-magnetic superconductor. It has also been shown that in London limit the squared density of monopole current around AHM-string has a maximum at the distance of the order of penetration length.
Zhang, Yi; Vishwanath, Ashvin
2013-04-01
We use entanglement entropy signatures to establish non-Abelian topological order in projected Chern-insulator wave functions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C=2, whose wave function may also be viewed as the square of the Slater determinant of a band insulator. We demonstrate that this wave function is captured by the SU(2)2 Chern-Simons theory coupled to fermions. This is established most persuasively by calculating the modular S-matrix from the candidate ground-state wave functions, following a recent entanglement-entropy-based approach. This directly demonstrates the peculiar non-Abelian braiding statistics of Majorana fermion quasiparticles in this state. We also provide microscopic evidence for the field theoretic generalization, that the Nth power of a Chern number C Slater determinant realizes the topological order of the SU(N)C Chern-Simons theory coupled to fermions, by studying the SU(2)3 (Read-Rezayi-type state) and the SU(3)2 wave functions. An advantage of our projected Chern-insulator wave functions is the relative ease with which physical properties, such as entanglement entropy and modular S-matrix, can be numerically calculated using Monte Carlo techniques.
24 CFR 941.306 - Maximum project cost.
2010-04-01
...) project costs that are subject to the TDC limit (i.e., Housing Construction Costs and Community Renewal Costs); and (2) project costs that are not subject to the TDC limit (i.e., Additional Project Costs... expended for the project, and this becomes the maximum project cost for purposes of the ACC. (b) TDC...
Introduction to Abelian varieties
Murty, V Kumar
1993-01-01
The book represents an introduction to the theory of abelian varieties with a view to arithmetic. The aim is to introduce some of the basics of the theory as well as some recent arithmetic applications to graduate students and researchers in other fields. The first part contains proofs of the Abel-Jacobi theorem, Riemann's relations and the Lefschetz theorem on projective embeddings over the complex numbers in the spirit of S. Lang's book Introduction to algebraic and abelian functions. Then the Jacobians of Fermat curves as well as some modular curves are discussed. Finally, as an application, Faltings' proof of the Mordell conjecture and its intermediate steps, the Tate conjecture and the Shafarevich conjecture, are sketched. - H. Lange for MathSciNet.
Fuchs, László
2015-01-01
Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah’s seminal work on the undecidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, th...
On m-ω1-pω+n-Projective Abelian p-Groups
Danchev Peter
2014-12-01
Full Text Available For any non-negative integers m and n, we define the classes of m-ω1-pω+n- projective groups and strongly m-ω1-pω+n-projective groups, which properly encompass the classes of ω1-pω+n-projectives introduced by Keef in J. Algebra Numb. Th. Acad. (2010 and strongly ω1-pω+n-projectives introduced by the present author in Hacettepe J. Math. Stat. (2014, respectively. The new group structures share many interesting properties, which are closely related to these of the aforementioned two own subclasses. Moreover, certain basic results in this direction are also established.
Virtually Abelian quantum walks
Mauro D'Ariano, Giacomo; Erba, Marco; Perinotti, Paolo; Tosini, Alessandro
2017-01-01
We study discrete-time quantum walks on Cayley graphs of non-Abelian groups, focusing on the easiest case of virtually Abelian groups. We present a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system having larger dimension. This method allows one to extend the notion of wave-vector to the virtually Abelian case and study analytically the walk dynamics. We apply the technique in the case of two quantum walks on virtually Abelian groups with planar Cayley graphs, finding the exact solution in terms of dispersion relation.
Condensation of an ideal gas obeying non-Abelian statistics.
Mirza, Behrouz; Mohammadzadeh, Hosein
2011-09-01
We consider the thermodynamic geometry of an ideal non-Abelian gas. We show that, for a certain value of the fractional parameter and at the relevant maximum value of fugacity, the thermodynamic curvature has a singular point. This indicates a condensation such as Bose-Einstein condensation for non-Abelian statistics and we work out the phase transition temperature in various dimensions.
Abelian Duality and Abelian Wilson Loops
Zucchini, R
2003-01-01
We consider a pure U(1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological selection rules. Finally, we show that, to have manifest duality, one must assume the existence of twisted topological sectors besides the standard untwisted one.
Abelian monopole or non-Abelian monopole responsible for quark confinement
Shibata, Akihiro; Kato, Seikou; Shinohara, Toru
2015-01-01
We have pointed out that the $SU(3)$ Yang-Mills theory has a new way of reformulation using new field variables (minimal option), in addition to the conventional option adopted by Cho, Faddeev and Niemi (maximal option). The reformulation enables us to change the original non-Abelian gauge field 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. In the minimal option, especially, the restricted field is non-Abelian $U(2)$ and involves the non-Abelian magnetic monopole. In the preceding lattice conferences, we have accumulated the numerical evidences for the non-Abelian magnetic-monopole dominance in addition to the restricted non-Abelian field dominance for quark confinement supporting the non-Abelian dual superconductivity using the minimal option for the SU(3) Yang-Mills theory. This should be compared with the maximal option which is a gauge invarient version of the Abelian projection in the maxim...
On the rank of abelian varieties over function fields
Pacheco, Amilcar
2004-01-01
Let $\\cac$ be a smooth projective curve defined over a number field $k$, $A/k(\\cac)$ an abelian variety and $(\\tau,B)$ the $k(\\cac)/k$-trace of $A$. We estimate how the rank of $A(k(\\cac))/\\tau B(k)$ varies when we take a finite cover $\\pi:\\cac'\\to\\cac$ defined over $k$ geometrically abelian.
Donets, E E; Volkov, M S
1993-01-01
An infinite family of cornucopions is found within the $SU(2)\\times U(1)$ sector of the 4--d heterotic string low-energy theory, the extremal $U(1)$ magnetic dilatonic black hole being the lowest energy state. Non-abelian cornucopions are interpreted as sphalerons associated with potential barriers separating topologically distinct Yang-Mills vacua on the $U(1)$ cornucopion background. A mass formula for non-abelian dilatonic black holes is derived, and the free energy is calculated through the Euclidean action.
Projective Power Entropy and Maximum Tsallis Entropy Distributions
Shinto Eguchi; Shogo Kato; Osamu Komori
2011-01-01
We discuss a one-parameter family of generalized cross entropy between two distributions with the power index, called the projective power entropy. The cross entropy is essentially reduced to the Tsallis entropy if two distributions are taken to be equal. Statistical and probabilistic properties associated with the projective power entropy are extensively investigated including a characterization problem of which conditions uniquely determine the projective power entropy up to the power index...
Abelian categories in dimension 2
Dupont, Mathieu
2008-01-01
The goal of this thesis is to define a 2-dimensional version of abelian categories, where symmetric 2-groups play the role that abelian groups played in 1-dimensional algebra. Abelian and 2-abelian groupoid enriched categories are defined and it is proved that homology can be developed in them, including the existence of a long exact sequence of homology corresponding to an extension of chain complexes. This generalises known results for symmetric 2-groups. The examples include, in addition to symmetric 2-groups, the 2-modules on a 2-ring, which form a 2-abelian groupoid enriched category. Moreover, internal groupoids, functors and natural transformations in an abelian category C (in particular, Baez-Crans 2-vector spaces) form a 2-abelian groupoid enriched category if and only if the axiom of choice holds in C.
Dyon Condensation and Dual Superconductivity in Abelian Higgs Model of QCD
B. S. Rajput
2010-01-01
Full Text Available Constructing the effective action for dyonic field in Abelian projection of QCD, it has been demonstrated that any charge (electrical or magnetic of dyon screens its own direct potential to which it minimally couples and antiscreens the dual potential leading to dual superconductivity in accordance with generalized Meissner effect. Taking the Abelian projection of QCD, an Abelian Higgs model, incorporating dual superconductivity and confinement, has been constructed and its representation has been obtained in terms of average of Wilson loop.
The Gribov ambiguity for maximal abelian and center gauges in SU(2) lattice gauge theory
Stack, John D.; Tucker, William W
2001-03-01
We present results for the fundamental string tension in SU(2) lattice gauge theory after projection to maximal abelian and direct maximal center gauges. We generate 20 Gribov copies/configuration. Abelian and center projected string tensions slowly decrease as higher values of the gauge functionals are reached.
Accelerating abelian gauge dynamics
Adler, Stephen Louis
1991-01-01
In this paper, we suggest a new acceleration method for Abelian gauge theories based on linear transformations to variables which weight all length scales equally. We measure the autocorrelation time for the Polyakov loop and the plaquette at β=1.0 in the U(1) gauge theory in four dimensions, for the new method and for standard Metropolis updates. We find a dramatic improvement for the new method over the Metropolis method. Computing the critical exponent z for the new method remains an important open issue.
Mohammad Mehdi Nasrabadi; Ali Gholamian
2014-11-01
Let be a group and $A = \\text{Aut}(G)$ be the group of automorphisms of . Then, the element $[g, ] = g^{-1}(g)$ is an autocommutator of $g \\in G$ and $ \\in A$. Hence, for any natural number the -th autocommutator subgroup of is defined as $K_{m}(G)=\\langle [g,_{1},\\ldots,_{m}]|g\\in G,_{1},\\ldots,_{m}\\in A\\rangle$, where $[g, _{1}, _{2},\\ldots, _{m}] = [[g,_{1},\\ldots,_{m−1}], _{m}]$. In this paper, we introduce the new notion of -nilpotent groups and classify all abelian groups which are -nilpotent groups.
Symmetries of Abelian Orbifolds
Hanany, Amihay
2010-01-01
Using the Polya Enumeration Theorem, we count with particular attention to C^3/Gamma up to C^6/Gamma, abelian orbifolds in various dimensions which are invariant under cycles of the permutation group S_D. This produces a collection of multiplicative sequences, one for each cycle in the Cycle Index of the permutation group. A multiplicative sequence is controlled by its values on prime numbers and their pure powers. Therefore, we pay particular attention to orbifolds of the form C^D/Gamma where the order of Gamma is p^alpha. We propose a generalization of these sequences for any D and any p.
Complex multiplication of abelian surfaces
Streng, Theodorus Cornelis
2010-01-01
The theory of complex multiplication makes it possible to construct certain class fields and abelian varieties. The main theme of this thesis is making these constructions explicit for the case where the abelian varieties have dimension 2. Chapter I is an introduction to complex multiplication
Clean Elements in Abelian Rings
Angelina Y M Chin
2009-04-01
Let be a ring with identity. An element in is said to be clean if it is the sum of a unit and an idempotent. is said to be clean if all of its elements are clean. If every idempotent in is central, then is said to be abelian. In this paper we obtain some conditions equivalent to being clean in an abelian ring.
Abelian theorems for Whittaker transforms
Richard D. Carmichael
1987-01-01
Full Text Available Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.
Non-Abelian Pseudocompact Groups
W. W. Comfort
2016-01-01
Full Text Available Here are three recently-established theorems from the literature. (A (2006 Every non-metrizable compact abelian group K has 2|K| -many proper dense pseudocompact subgroups. (B (2003 Every non-metrizable compact abelian group K admits 22|K| -many strictly finer pseudocompact topological group refinements. (C (2007 Every non-metrizable pseudocompact abelian group has a proper dense pseudocompact subgroup and a strictly finer pseudocompact topological group refinement. (Theorems (A, (B and (C become false if the non-metrizable hypothesis is omitted. With a detailed view toward the relevant literature, the present authors ask: What happens to (A, (B, (C and to similar known facts about pseudocompact abelian groups if the abelian hypothesis is omitted? Are the resulting statements true, false, true under certain natural additional hypotheses, etc.? Several new results responding in part to these questions are given, and several specific additional questions are posed.
Abelian Vortices with Singularities
Baptista, J M
2012-01-01
Let L --> X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle has parabolic structure. These conditions appear naturally in the study of vortex configurations with constraints, or configurations invariant under the action of a finite group. We first show that the moduli space of singular vortex solutions is the same as in the regular case. Then we compute the total volume and total scalar curvature of the moduli space singular vortex solutions. These numbers differ from the case of regular vortices by a very natural term. Finally we exhibit explicit non-trivial vortex solutions over the thrice punctured hyperbolic sphere.
The Abelian Heterotic Conifold
Halmagyi, Nick; Svanes, Eirik Eik
2016-01-01
We study heterotic supergravity on the conifold and its Z2 orbifold with Abelian gauge fields and three-form flux. At large distances, these solutions are locally Ricci-flat, have a magnetic flux through the two-sphere at infinity as well as non-zero five-brane charge. For a given flux, our family of solutions has three real parameters, the size of the pair of two spheres in the IR and the dilaton zero mode. We present an explicit analytic solution for the decoupled near horizon region where for a given flux, the size of the cycles is frozen and the only parameter is the dilaton zero mode. We also present an exactly solvable worldsheet CFT for this near horizon region. When one of the two cycles has vanishing size, the near horizon region no longer exists but we obtain a solution on the (unorbifolded) resolved conifold.
Optimum Projection Angle for Attaining Maximum Distance in a Rugby Place Kick
Nicholas P. Linthorne
2014-03-01
Full Text Available This study investigated the effect of projection angle on the distance attained in a rugby place kick. A male rugby player performed 49 maximum-effort kicks using projection angles of between 20 and 50°. The kicks were recorded by a video camera at 50 Hz and a 2 D biomechanical analysis was conducted to obtain measures of the projection velocity and projection angle of the ball. The player’s optimum projection angle was calculated by substituting a mathematical expression for the relationship between projection velocity and projection angle into the equations for the aerodynamic flight of a rugby ball. We found that the player’s calculated optimum projection angle (30.6°, 95% confidence limits ± 1.9° was in close agreement with his preferred projection angle (mean value 30.8°, 95% confidence limits ± 2.1°. The player’s calculated optimum projection angle was also similar to projection angles previously reported for skilled rugby players. The optimum projection angle in a rugby place kick is considerably less than 45° because the projection velocity that a player can produce decreases substantially as projection angle is increased. Aerodynamic forces and the requirement to clear the crossbar have little effect on the optimum projection angle.
Hewson, S F
1996-01-01
We investigate non-abelian gaugings of WZNW models. When the gauged group is semisimple we are able to present exact formulae for the dual conformal field theory, for all values of the level k. The results are then applied to non-abelian target space duality in string theory, showing that the standard formulae are quantum mechanically well defined in the low energy limit if the gauged group is semisimple.
On Non-Abelian Symplectic Cutting
Martens, Johan; Thaddeus, Michael
2012-01-01
We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact groups. By using a degeneration based on the Vinberg monoid we give, in good cases, a global quotient description of a surgery construction introduced by Woodward and Meinrenken, and show it can be interpreted in algebro......-geometric terms. A key ingredient is the `universal cut' of the cotangent bundle of the group itself, which is identified with a moduli space of framed bundles on chains of projective lines recently introduced by the authors....
Einstein Manifolds, Abelian Instantons, Bundle Reduction, and the Cosmological Constant
Soo, C P
2001-01-01
The anti-self-dual projection of the spin connections of certain four-dimensional Einstein manifolds can be Abelian in nature. These configurations signify bundle reductions. By a theorem of Kobayashi and Nomizu such a process is predicated on the existence of a covariantly constant field. It turns out that even without fundamental Higgs fields and other physical matter, gravitational self-interactions can generate this mechanism if the cosmological constant is non-vanishing. This article identifies the order parameter, and clarifies how these Abelian instanton solutions are associated with a Higgs triplet which causes the bundle reduction from SO(3) gauge group to U(1).
Non abelian tensor square of non abelian prime power groups
2010-01-01
For every $p$-group of order $p^n$ with the derived subgroup of order $p^m$, Rocco in \\cite{roc} has shown that the order of tensor square of $G$ is at most $p^{n(n-m)}$. In the present paper not only we improve his bound for non-abelian $p$-groups but also we describe the structure of all non-abelian $p$-groups when the bound is attained for a special case. Moreover, our results give as well an upper bound for the order of $\\pi_3(SK(G, 1))$.
Limber, Mark A.; Manteuffel, Thomas A.; Mccormick, Stephen F.; Sholl, David S.
1993-01-01
We consider the problem of image reconstruction from a finite number of projections over the space L(sup 1)(Omega), where Omega is a compact subset of the set of Real numbers (exp 2). We prove that, given a discretization of the projection space, the function that generates the correct projection data and maximizes the Boltzmann-Shannon entropy is piecewise constant on a certain discretization of Omega, which we call the 'optimal grid'. It is on this grid that one obtains the maximum resolution given the problem setup. The size of this grid grows very quickly as the number of projections and number of cells per projection grow, indicating fast computational methods are essential to make its use feasible. We use a Fenchel duality formulation of the problem to keep the number of variables small while still using the optimal discretization, and propose a multilevel scheme to improve convergence of a simple cyclic maximization scheme applied to the dual problem.
Two-component Abelian sandpile models.
Alcaraz, F C; Pyatov, P; Rittenberg, V
2009-04-01
In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic Abelian algebras. We show that Abelian sandpile models with two conservation laws have only trivial avalanches.
Countably determined compact abelian groups
Dikranjan, Dikran
2008-01-01
For an abelian topological group G let G^* be the dual group of all continuous characters endowed with the compact open topology. A subgroup D of G determines G if the restriction homomorphism G^* --> D^* of the dual groups is a topological isomorphism. Given a scattered compact subset X of an infinite compact abelian group G such that |X|
Self compensation of classical non abelian charge
Bartnik, E. A.
2009-01-01
A new classical, non singular solution with arbitrarily low energy is found for SU(2) non abelian fields in the presence of a static charge. Physically it means that a classical charge coupled to any SU(N) non abelian gauge field will develop a pure gauge field, carrying no energy, that will completely screen it - there are no visible classical non abelian charges.
Abelian avalanches and Tutte polynomials
Gabrielov, Andrei
1993-04-01
We introduce a class of deterministic lattice models of failure, Abelian avalanche (AA) models, with continuous phase variables, similar to discrete Abelian sandpile (ASP) models. We investigate analytically the structure of the phase space and statistical properties of avalanches in these models. We show that the distributions of avalanches in AA and ASP models with the same redistribution matrix and loading rate are identical. For an AA model on a graph, statistics of avalanches is linked to Tutte polynomials associated with this graph and its subgraphs. In the general case, statistics of avalanches is linked to an analog of a Tutte polynomial defined for any symmetric matrix.
Determination of Maximum Follow-up Speed of Electrode System of Resistance Projection Welders
Wu, Pei; Zhang, Wenqi; Bay, Niels
2004-01-01
the weld process settings for the stable production and high quality of products. In this paper, the maximum follow-up speed of electrode system was tested by using a special designed device which can be mounted to all types of machine and easily to be applied in industry, the corresponding mathematical......The maximum follow-up speed of electrode system represents the dynamic mechanical response capacity of resistance projection welding machines, which is important to make the diffrernce from one machine to the other and to consider the individual behavior of machines in designing or optimizing...
The ACT{sup 2} project: Demonstration of maximum energy efficiency in real buildings
Crawley, D.B. [Pacific Northwest Lab., Richland, WA (United States); Krieg, B.L. [Pacific Gas and Electric Co., San Ramon, CA (United States)
1991-11-01
A large US utility recently began a project to determine whether the use of new energy-efficient end-use technologies and systems would economically achieve substantial energy savings (perhaps as high as 75% over current practice). Using a field-based demonstration approach, the Advanced Customer Technology Test (ACT{sup 2}) for Maximum Energy Efficiency is providing information on the maximum energy savings possible when integrated packages of new high-efficiency end-use technologies are incorporated into commercial and residential buildings and industrial and agricultural processes. This paper details the underlying rationale, approach, results to date, and future plans for ACT{sup 2}. The ultimate goal is energy efficiency (doing more with less energy) rather than energy conservation (freezing in the dark). In this paper, we first explain why a major United States utility is committed to pursuing demand-side management so aggressively. Next, we discuss the approach the utility chose for conducting the ACT{sup 2} project. We then review results obtained to date from the project`s pilot demonstration site. Last, we describe other related demonstration projects being proposed by the utility.
Localization in abelian Chern-Simons theory
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed...... using the technique of non-abelian localization. This study leads to a natural identification of the abelian Reidemeister-Ray-Singer torsion as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections for the class of Sasakian three...
Hyland, D. C.
1985-01-01
The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modelling and reduced order control design method for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed and the application of the methodology to several large space structure (LSS) problems of representative complexity is illustrated.
Hyland, D. C.; Bernstein, D. S.
1987-01-01
The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated.
Abelianization of QCD plasma instabilities
Arnold, Peter; Lenaghan, Jonathan
2004-12-01
QCD plasma instabilities appear to play an important role in the equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical limit of weak coupling (i.e. asymptotically high energy). It is important to understand what nonlinear physics eventually stops the exponential growth of unstable modes. It is already known that the initial growth of plasma instabilities in QCD closely parallels that in QED. However, once the unstable modes of the gauge fields grow large enough for non-Abelian interactions between them to become important, one might guess that the dynamics of QCD plasma instabilities and QED plasma instabilities become very different. In this paper, we give suggestive arguments that non-Abelian self-interactions between the unstable modes are ineffective at stopping instability growth, and that the growing non-Abelian gauge fields become approximately Abelian after a certain stage in their growth. This in turn suggests that understanding the development of QCD plasma instabilities in the nonlinear regime may have close parallels to similar processes in traditional plasma physics. We conjecture that the physics of collisionless plasma instabilities in SU(2) and SU(3) gauge theory becomes equivalent, respectively, to (i) traditional plasma physics, which is U(1) gauge theory, and (ii) plasma physics of U(1)×U(1) gauge theory.
The ACT sup 2 project: Demonstration of maximum energy efficiency in real buildings
Crawley, D.B. (Pacific Northwest Lab., Richland, WA (United States)); Krieg, B.L. (Pacific Gas and Electric Co., San Ramon, CA (United States))
1991-11-01
A large US utility recently began a project to determine whether the use of new energy-efficient end-use technologies and systems would economically achieve substantial energy savings (perhaps as high as 75% over current practice). Using a field-based demonstration approach, the Advanced Customer Technology Test (ACT{sup 2}) for Maximum Energy Efficiency is providing information on the maximum energy savings possible when integrated packages of new high-efficiency end-use technologies are incorporated into commercial and residential buildings and industrial and agricultural processes. This paper details the underlying rationale, approach, results to date, and future plans for ACT{sup 2}. The ultimate goal is energy efficiency (doing more with less energy) rather than energy conservation (freezing in the dark). In this paper, we first explain why a major United States utility is committed to pursuing demand-side management so aggressively. Next, we discuss the approach the utility chose for conducting the ACT{sup 2} project. We then review results obtained to date from the project's pilot demonstration site. Last, we describe other related demonstration projects being proposed by the utility.
Session Types in Abelian Logic
Yoichi Hirai
2013-12-01
Full Text Available There was a PhD student who says "I found a pair of wooden shoes. I put a coin in the left and a key in the right. Next morning, I found those objects in the opposite shoes." We do not claim existence of such shoes, but propose a similar programming abstraction in the context of typed lambda calculi. The result, which we call the Amida calculus, extends Abramsky's linear lambda calculus LF and characterizes Abelian logic.
Degeneracy and non-Abelian statistics
Rowell, Eric C.; Wang, Zhenghan
2016-03-01
A non-Abelian anyon can only occur in the presence of ground-state degeneracy in the plane. It is conceivable that for some strange anyon with quantum dimension >1 that the resulting representations of all n -strand braid groups Bn are overall phases, even though the ground-state manifolds for n such anyons in the plane are in general Hilbert spaces of dimensions >1 . We observe that degeneracy is all that is needed: For an anyon with quantum dimension >1 the non-Abelian statistics cannot all be overall phases on the degeneracy ground-state manifold. Therefore, degeneracy implies non-Abelian statistics, which justifies defining a non-Abelian anyon as one with quantum dimension >1 . Since non-Abelian statistics presumes degeneracy, degeneracy is more fundamental than non-Abelian statistics.
Heterotic non-Abelian orbifolds
Fischer, Maximilian [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Ramos-Sanchez, Saul [UNAM, Mexico (Mexico). Dept. of Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We perform the first systematic analysis of particle spectra obtained from heterotic string compactifications on non-Abelian toroidal orbifolds. After developing a new technique to compute the particle spectrum in the case of standard embedding based on higher dimensional supersymmetry, we compute the Hodge numbers for all recently classified 331 non-Abelian orbifold geometries which yield N=1 supersymmetry for heterotic compactifications. Surprisingly, most Hodge numbers follow the empiric pattern h{sup (1,1)}-h{sup (2,1)}=0 mod 6, which might be related to the number of three standard model generations. Furthermore, we study the fundamental groups in order to identify the possibilities for non-local gauge symmetry breaking. Three examples are discussed in detail: the simplest non-Abelian orbifold S{sub 3} and two more elaborated examples, T{sub 7} and {Delta}(27), which have only one untwisted Kaehler and no untwisted complex structure modulus. Such models might be especially interesting in the context of no-scale supergravity. Finally, we briefly discuss the case of orbifolds with vanishing Euler numbers in the context of enhanced (spontaneously broken) supersymmetry.
Dyonic Non-Abelian Black Holes
Brihaye, Y; Kunz, J; Tell, N
1999-01-01
We study static spherically symmetric dyonic black holes in Einstein-Yang-Mills-Higgs theory. As for the magnetic non-abelian black holes, the domain of existence of the dyonic non-abelian black holes is limited with respect to the horizon radius and the dimensionless coupling constant $\\alpha$, which is proportional to the ratio of vector meson mass and Planck mass. At a certain critical value of this coupling constant, $\\hat \\alpha$, the maximal horizon radius is attained. We derive analytically a relation between $\\hat numerically. Besides the fundamental dyonic non-abelian black holes, we study radially excited dyonic non-abelian black holes and globally regular gravitating dyons.
Non Abelian Dual Maps in Path Space
Martin, I
1999-01-01
We study an extension of the procedure to construct duality transformations among abelian gauge theories to the non abelian case using a path space formulation. We define a pre-dual functional in path space and introduce a particular non local map among Lie algebra valued 1-form functionals that reduces to the ordinary Hodge-* duality map of the abelian theories. Further, we establish a full set of equations on path space representing the ordinary Yang Mills equations and Bianchi identities of non abelian gauge theories of 4-dimensional euclidean space.
Characteristic Properties of Large Subgroups in Primary Abelian Groups
Peter V Danchev
2004-08-01
Suppose is an arbitrary additively written primary abelian group with a fixed large subgroup . It is shown that is (a) summable; (b)$\\sum$-summable; (c) a $\\sum$-group; (d) $p^{+1}$-projective only when so is . These claims extend results of such a kind obtained by Benabdallah, Eisenstadt, Irwin and Poluianov, Acta Math. Acad. Sci. Hungaricae (1970) and Khan, Proc. Indian Acad. Sci. Sect. A (1978).
Weil classes on abelian varieties
Moonen, B J J; Zarhin, Yu. G.
1996-01-01
Consider a complex abelian variety X on which a field F acts. Generalizing a construction of A. Weil, one associates to this a subspace W_F of the cohomology of X, which we call the space of Weil classes w.r.t. F. The purpose of this paper is to answer the following two questions: Q1: under what conditions on F does the space W_F contain, or even consist of, Hodge classes?, Q2: if W_F contains Hodge classes, under what conditions on F are these exceptional? In case X is defined over a number field, we also answer the analogous questions for Tate classes.
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another
Ortin, Tomas
2016-01-01
We construct a supersymmetric black ring solution of SU(2) N=1, d=5 Super-Einstein-Yang-Mills (SEYM) theory by adding a distorted BPST instanton to an Abelian black ring solution of the same theory. The change cannot be observed from spatial infinity: neither the mass, nor the angular momenta or the values of the scalars at infinity differ from those of the Abelian ring. The entropy is, however, sensitive to the presence of the non-Abelian instanton, and it is smaller than that of the Abelian ring, in analogy to what happens in the supersymmetric coloured black holes recently constructed in the same theory and in N=2, d=4 SEYM. By taking the limit in which the two angular momenta become equal we derive a non-Abelian generalization of the BMPV rotating black-hole solution.
Uncertainties in transient projections of maximum and minimum flows over the United States
Giuntoli, Ignazio; Villarini, Gabriele; Prudhomme, Christel; Hannah, David M.
2016-04-01
Global multi-model ensemble experiments provide a valuable basis for the examination of potential future changes in runoff. However, these projections suffer from uncertainties that originate from different sources at different levels in the modelling chain. We present the partitioning of uncertainty into four distinct sources of projections of decadally-averaged annual maximum (AMax) and minimum (AMin) flows over the USA. More specifically, we quantify the relative contribution of the uncertainties arising from internal variability, global impact models (GIMs), global climate models (GCMs), and representative concentration pathways (RCPs). We use a set of nine state-of-the-art GIMs driven by five CMIP5 GCMs under four RCPs from the ISI-MIP multi-model ensemble. We examine the temporal changes in the relative contribution of each source of uncertainty over the course of the 21st century. Results show that GCMs and GIMs are responsible for the majority of uncertainty over most of the study area, followed by internal variability and RCPs. Proportions vary regionally and depend on the end of the runoff spectrum (AMax, AMin) considered. In particular, for AMax, large fractions of uncertainty are attributable to GCMs throughout the century with the GIMs increasing their share especially in mountainous and cold areas. For Amin, the contribution of GIMs to uncertainty increases with time, becoming the dominant source over most of the country by the end of the 21st century. Importantly, compared to the other sources, the RCPs contribution to uncertainty is negligible generally (for AMin especially). This finding indicates that the effects of different emission scenarios are barely noticeable in hydrological impact studies, while GIMs and GCMs make up most of the amplitude of the ensemble spread (uncertainty).
Fishman, Elliot K; Ney, Derek R; Heath, David G; Corl, Frank M; Horton, Karen M; Johnson, Pamela T
2006-01-01
The introduction and widespread availability of 16-section multi-detector row computed tomographic (CT) technology and, more recently, 64-section scanners, has greatly advanced the role of CT angiography in clinical practice. CT angiography has become a key component of state-of-the-art imaging, with applications ranging from oncology (eg, staging of pancreatic or renal cancer) to classic vascular imaging (eg, evaluation of aortic aneurysms and renal artery stenoses) as well as newer techniques such as coronary artery imaging and peripheral runoff studies. With an average of 400-1000 images in each volume data set, three-dimensional postprocessing is crucial to volume visualization. Radiologists now have workstations that provide capabilities for evaluation of these data sets by using a range of software programs and processing tools. Although different systems have unique capabilities and functionality, all provide the options of volume rendering and maximum intensity projection for image display and analysis. These two postprocessing techniques have different advantages and disadvantages when used in clinical practice, and it is important that radiologists understand when and how each technique should be used. Copyright RSNA, 2006.
CT-maximum intensity projection is a clinically useful modality for the detection of gastric varices
Toru Ishikawa; Tomoteru Kamimura; Takashi Ushiki; Ken-ichi Mizuno; Tadayuki Togashi; Kouji Watanabe; Kei-ichi Seki; Hironobu Ohta; Toshiaki Yoshida; Keiko Takeda
2005-01-01
AIM: To evaluate the efficacy of CT-maximum intensity projection (CT-MIP) in the detection of gastric varicesand their inflowing and outflowing vessels in patientswith gastric varices scheduled to undergo balloonoccluded retrograde transvenous obliteration (B-RTO). METHODS: Sixteen patients with endoscopicallyconfirmed gastric varices were included in this study. All patients were evaluated with CT-MIP using threedimensional reconstructions, before and after B-RTO. RESULTS: CT-MIP clearly depicted gastric varices in 16 patients (100%), the left gastric vein in 6 (32.5%),the posterior gastric vein in 12 (75.0%), the short gastric veins in 13 (81.3%), gastrorenal shunts in 16 (100%), the hemiazygos vein (HAZV) in 4 (25.0%), the pericardiophrenic vein (PCPV) in 9 (56.3%), and the left inferior phrenic vein in 9 patients (56.3%). Although flow direction itself cannot be determined from CT-MIP,this modality provided clear images of the inflowing and the outflowing vessels. Moreover, in one patient, short gastric veins were not seen on conventional angiographic portography images of the spleen, but were clearly revealed on CT-MIP,CONCLUSION: We suggest that CT-MIP should be considered as a routine method for detecting and diagnosing collateral veins in patients with gastric varices scheduled for B-RTO. Furthermore, CT-MIP is more useful than endoscopy in verifying the early therapeutic effects of B-RTO.
Kilburn-Toppin, Fleur; Arthurs, Owen J.; Tasker, Angela D.; Set, Patricia A.K. [Addenbrooke' s Hospital, Cambridge University Teaching Hospitals NHS Foundation Trust, Department of Radiology, Box 219, Cambridge (United Kingdom)
2013-07-15
Maximum intensity projection (MIP) images might be useful in helping to differentiate small pulmonary nodules from adjacent vessels on thoracic multidetector CT (MDCT). The aim was to evaluate the benefits of axial MIP images over axial source images for the paediatric chest in an interobserver variability study. We included 46 children with extra-pulmonary solid organ malignancy who had undergone thoracic MDCT. Three radiologists independently read 2-mm axial and 10-mm MIP image datasets, recording the number of nodules, size and location, overall time taken and confidence. There were 83 nodules (249 total reads among three readers) in 46 children (mean age 10.4 {+-} 4.98 years, range 0.3-15.9 years; 24 boys). Consensus read was used as the reference standard. Overall, three readers recorded significantly more nodules on MIP images (228 vs. 174; P < 0.05), improving sensitivity from 67% to 77.5% (P < 0.05) but with lower positive predictive value (96% vs. 85%, P < 0.005). MIP images took significantly less time to read (71.6 {+-} 43.7 s vs. 92.9 {+-} 48.7 s; P < 0.005) but did not improve confidence levels. Using 10-mm axial MIP images for nodule detection in the paediatric chest enhances diagnostic performance, improving sensitivity and reducing reading time when compared with conventional axial thin-slice images. Axial MIP and axial source images are complementary in thoracic nodule detection. (orig.)
Modular Abelian Varieties of Odd Modular Degree
Yazdani, Soroosh
2009-01-01
In this paper, we will study modular Abelian varieties with odd congruence numbers by examining the cuspidal subgroup of $J_0(N)$. We will show that the conductor of such Abelian varieties must be of a special type. For example, if $N$ is the conductor of an absolutely simple modular Abelian variety with an odd congruence number, then $N$ has at most two prime divisors, and if $N$ is odd, then $N=p^\\alpha$ or $N=pq$ for some prime $p$ and $q$. In the second half of this paper, we will focus o...
Galtsov, D V
2003-01-01
We discuss isotropic and homogeneous D-brane-world cosmology with non-Abelian Born-Infeld (NBI) matter on the brane. In the usual Friedmann-Robertson-Walker (FRW) model the scale non-invariant NBI matter gives rise to an equation of state which asymptotes to the string gas equation $p=-\\epsilon/3$ and ensures a start-up of the cosmological expansion with zero acceleration. We show that the same state equation in the brane-world setup leads to the Tolman type evolution as if the conformal symmetry was effectively restored. This is not precisely so in the NBI model with symmetrized trace, but the leading term in the expansion law is still the same. A cosmological sphaleron solution on the D-brane is presented.
M supergravity and abelian semigroups
Izaurieta, Fernando; RodrIguez, Eduardo; Salgado, Patricio [Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)], E-mail: fizaurie@gmail.com, E-mail: edurodriguez@udec.cl, E-mail: pasalgad@udec.cl
2008-11-01
A gauge theory for the M algebra in eleven-dimensional spacetime is put forward. The gauge-invariant Lagrangian corresponds to a transgression form. This class of Lagrangians modifies Chern-Simons theory with the addition of a regularizing boundary term.The M algebra-invariant tensor required to define the theory comes from regarding the algebra as an abelian semigroup expansion of the orthsymplectic algebra osp (32|1). The explicit form of the Lagrangian is found by means of a transgression-specific subspace separation method. Dynamical properties are briefly analyzed through an example. The equations of motion are found to place severe constraints on the geometry, which might be partially alleviated by allowing for nonzero torsion.
Moduli Spaces of Abelian Vortices on Kahler Manifolds
Baptista, J M
2012-01-01
We consider the self-dual vortex equations on a positive line bundle L --> M over a compact Kaehler manifold of arbitrary dimension. When M is simply connected, the moduli space of vortex solutions is a projective space. When M is an abelian variety, the moduli space is the projectivization of the Fourier-Mukai transform of L. We extend this description of the moduli space to general abelian GLSM, i.e. to vortex equations with a torus gauge group acting linearly on a complex vector space. In this case the vortex moduli space becomes a toric orbifold and a toric fibration over a cartesian product of Pic^0(M)'s, respectively. In all these examples we compute the Kaehler class of the natural L^2-metric on the moduli space. In the simplest examples we compute the volume and total scalar curvature of the muduli space. Finally, in the case of abelian GLSM, we note that the vortex moduli space is a compactification of the space of holomorphic maps from M to toric targets, just as in the usual case of M being a Riema...
Conformal field theory approach to Abelian and non-Abelian quantum Hall quasielectrons.
Hansson, T H; Hermanns, M; Regnault, N; Viefers, S
2009-04-24
The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.
Dualization of non-abelian lattice gauge theory with Abelian Color Cycles (ACC)
Marchis, Carlotta
2016-01-01
We discuss a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theories. The Wilson gauge action is decomposed into a sum over "abelian color cycles" (ACC), which are loops around plaquettes visiting different colors at the corners. ACCs are complex numbers and thus commute such that a dual representation of a non-abelian theory can be obtained as in the abelian case. We apply the ACC approach to SU(2) and SU(3) lattice gauge theory and exactly rewrite the two partition sums in a strong coupling series where all gauge integrals are known in closed form.
Dendritic tree extraction from noisy maximum intensity projection images in C. elegans.
Greenblum, Ayala; Sznitman, Raphael; Fua, Pascal; Arratia, Paulo E; Oren, Meital; Podbilewicz, Benjamin; Sznitman, Josué
2014-06-12
Maximum Intensity Projections (MIP) of neuronal dendritic trees obtained from confocal microscopy are frequently used to study the relationship between tree morphology and mechanosensory function in the model organism C. elegans. Extracting dendritic trees from noisy images remains however a strenuous process that has traditionally relied on manual approaches. Here, we focus on automated and reliable 2D segmentations of dendritic trees following a statistical learning framework. Our dendritic tree extraction (DTE) method uses small amounts of labelled training data on MIPs to learn noise models of texture-based features from the responses of tree structures and image background. Our strategy lies in evaluating statistical models of noise that account for both the variability generated from the imaging process and from the aggregation of information in the MIP images. These noisy models are then used within a probabilistic, or Bayesian framework to provide a coarse 2D dendritic tree segmentation. Finally, some post-processing is applied to refine the segmentations and provide skeletonized trees using a morphological thinning process. Following a Leave-One-Out Cross Validation (LOOCV) method for an MIP databse with available "ground truth" images, we demonstrate that our approach provides significant improvements in tree-structure segmentations over traditional intensity-based methods. Improvements for MIPs under various imaging conditions are both qualitative and quantitative, as measured from Receiver Operator Characteristic (ROC) curves and the yield and error rates in the final segmentations. In a final step, we demonstrate our DTE approach on previously unseen MIP samples including the extraction of skeletonized structures, and compare our method to a state-of-the art dendritic tree tracing software. Overall, our DTE method allows for robust dendritic tree segmentations in noisy MIPs, outperforming traditional intensity-based methods. Such approach provides a
Soldering Chiralities; 2, Non-Abelian Case
Wotzasek, C
1996-01-01
We study the non-abelian extension of the soldering process of two chiral WZW models of opposite chiralities, resulting in a (non-chiral) WZW model living in a 2D space-time with non trivial Riemanian curvature.
Dyonic Non-Abelian Black Holes
Brihaye, Y.; Hartmann, B.; Kunz, J; Tell, N.
1999-01-01
We study static spherically symmetric dyonic black holes in Einstein-Yang-Mills-Higgs theory. As for the magnetic non-abelian black holes, the domain of existence of the dyonic non-abelian black holes is limited with respect to the horizon radius and the dimensionless coupling constant $\\alpha$, which is proportional to the ratio of vector meson mass and Planck mass. At a certain critical value of this coupling constant, $\\hat \\alpha$, the maximal horizon radius is attained. We derive analyti...
Chiral Decomposition For Non-Abelian Bosons
Braga, N R F; Braga, Nelson R. F.; Wotzasek, Clovis
1996-01-01
We study the non-abelian extension for the splitting of a scalar field into chiral components. Using this procedure we find a non ambiguous way of coupling a non abelian chiral scalar field to gravity. We start with a (non-chiral) WZW model covariantly coupled to a background metric and, after the splitting, arrive at two chiral Wess-Zumino-Witten (WZW) models coupled to gravity.
Constraining differential renormalization in abelian gauge theories
del Águila, F; Tapia, R M; Pérez-Victoria, M
1998-01-01
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a basis of singular functions. The local terms appearing in the renormalization of these functions are determined by requiring consistency with the propagator equation. Previous results in abelian theories, with and without supersymmetry, are discussed in this context.
$q\\bar{q}$ Pair production in non-Abelian gauge fields
S M Puzhakkal; V M Bannur
2007-08-01
We calculate the $q\\bar{q}$ pair production probability in the colour-flux tube model by considering the effect of non-Abelian interactions in the theory. Non-Abelian interactions in the colour field are time-dependent and hence should oscillate with a characteristic frequency 0 , which depends on the amplitude of the field strength. Using the WKB approximation in complex time, we calculated the pair production probability. When the strength of the field is comparable to the quark masses, the corresponding pair creation probability is maximum, and for the static field 0 → 0, we recovered the well-known Schwinger result.
Particles in non-Abelian gauge potentials: Landau problem and insertion of non-Abelian flux
Estienne, B.; Haaker, S.M.; Schoutens, K.
2011-01-01
In this paper, we study charged spin-1/2 particles in two dimensions, subjected to a perpendicular non-Abelian magnetic field. Specializing to a choice of vector potential that is spatially constant but non-Abelian, we investigate the Landau level spectrum in planar and spherical geometry, paying pa
Josephson junction of non-Abelian superconductors and non-Abelian Josephson vortices
Nitta, Muneto
2015-01-01
A Josephson junction is made of two superconductors sandwiching an insulator, and a Josephson vortex is a magnetic vortex absorbed into the Josephson junction, whose dynamics can be described by the sine-Gordon equation. In a field theory framework, a flexible Josephson junction was proposed, in which the Josephson junction is represented by a domain wall separating two condensations and a Josephson vortex is a sine-Gordon soliton in the domain wall effective theory. In this paper, we propose a Josephson junction of non-Abelian color superconductors, that is described by a non-Abelian domain wall, and show that a non-Abelian vortex (color magnetic flux tube) absorbed into it is a non-Abelian Josephson vortex represented as a non-Abelian sine-Gordon soliton in the domain wall effective theory.
Non-Abelian bubbles in microstate geometries
Ramirez, Pedro F
2016-01-01
We find the first smooth microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of $\\mathcal{N}=1$, $d=5$ Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon. The non-Abelian fields make their presence at the very heart of the microstate structure: the physical size of the bubbles is affected by the non-Abelian topological charge they carry, which combines with the Abelian flux threading the bubbles to hold them up. Interestingly the non-Abelian fields carry a set of adjustable continuous parameters that do not alter the asymptotics of the solutions but modify the local geometry. This feature can be used to obtain a classically infinite number of microstate solutions with the asymptotics of a single black hole or black ring.
Sullivan, Terry [Brookhaven National Lab. (BNL), Upton, NY (United States)
2016-02-22
The objectives of this report are; To present a simplified conceptual model for release from the buildings with residual subsurface structures that can be used to provide an upper bound on contaminant concentrations in the fill material; Provide maximum water concentrations and the corresponding amount of mass sorbed to the solid fill material that could occur in each building for use in dose assessment calculations; Estimate the maximum concentration in a well located outside of the fill material; and Perform a sensitivity analysis of key parameters.
Perfect Abelian dominance of confinement in quark-antiquark potential in SU(3) lattice QCD
Suganuma, Hideo [Department of Physics, Kyoto University, Kitashirakawaoiwake, Sakyo, Kyoto 606-8502 (Japan); Sakumichi, Naoyuki [Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198 (Japan)
2016-01-22
In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with 32{sup 4} at β=6.4 (i.e., a ≃ 0.058 fm). We investigate the static quark-antiquark potential V(r), its Abelian part V{sub Abel}(r) and its off-diagonal part V{sub off}(r), respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., σ{sub Abel} ≃ σ for the string tension, on the fine and large-volume lattice. We find also a nontrivial summation relation of V (r) ≃ V{sub Abel}(r)+V{sub off}(r)
Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio
2016-08-01
Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.
Sullivan, Terry [Brookhaven National Lab. (BNL), Upton, NY (United States). Biological, Environmental, and Climate Sciences Dept.
2014-12-02
ZionSolutions is in the process of decommissioning the Zion Nuclear Power Plant in order to establish a new water treatment plant. There is some residual radioactive particles from the plant which need to be brought down to levels so an individual who receives water from the new treatment plant does not receive a radioactive dose in excess of 25 mrem/y⁻¹. The objectives of this report are: (a) To present a simplified conceptual model for release from the buildings with residual subsurface structures that can be used to provide an upper bound on contaminant concentrations in the fill material; (b) Provide maximum water concentrations and the corresponding amount of mass sorbed to the solid fill material that could occur in each building for use in dose assessment calculations; (c) Estimate the maximum concentration in a well located outside of the fill material; and (d) Perform a sensitivity analysis of key parameters.
Correlation induced non-Abelian quantum holonomies
Johansson, Markus; Singh, Kuldip; Sjoqvist, Erik; Williamson, Mark S
2010-01-01
In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the L\\'{e}vay geometric phase [2004 {\\it J. Phys. A: Math. Gen.} {\\bf 37} 1821] in the case of two-qubit systems undergoing local $SU(2)$ evolutions.
C++ PROGRAM IMPLEMENTING THE ABELIAN GROUP ABSTRACT
Ruiz L., Edgar; Universidad Nacional Mayor de San Marcos
2014-01-01
This article presents a C++ Program implementing the Commutative or Abelian Group Algebraic Concept. The whole Program code that manages abelian class objects as a new data abstract type, TAD, using concepts such as operators overcharge is shown. Implementation has been carried out in a Dev C++ 4.1 compiler, a GNU compiler with GLP licence. El artículo presenta un programa en C++ que implementa el concepto algebraico de grupo conmutativo o abeliano. Se muestra todo el código del programa q...
Josephson junction of non-Abelian superconductors and non-Abelian Josephson vortices
Muneto Nitta
2015-10-01
Full Text Available A Josephson junction is made of two superconductors sandwiching an insulator, and a Josephson vortex is a magnetic vortex (flux tube absorbed into the Josephson junction, whose dynamics can be described by the sine-Gordon equation. In a field theory framework, a flexible Josephson junction was proposed, in which the Josephson junction is represented by a domain wall separating two condensations and a Josephson vortex is a sine-Gordon soliton in the domain wall effective theory. In this paper, we propose a Josephson junction of non-Abelian color superconductors and show that a non-Abelian vortex (color magnetic flux tube absorbed into it is a non-Abelian Josephson vortex represented as a non-Abelian sine-Gordon soliton in the domain wall effective theory, that is the U(N principal chiral model.
He, Huan; von Keyserlingk, Curt
2016-01-01
Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting -- the goal of this work is to fill the gap in the literature, at least for a selection of DW models with abelian gauge groups but non-abelian topological order. As applications, various correlation functions and fusion rules of line operators are calculated. We discuss for example the appearance of non-abelian statistics in DW theories with abelian gauge groups.
Projection of Korean Probable Maximum Precipitation under Future Climate Change Scenarios
Okjeong Lee
2016-01-01
Full Text Available According to the IPCC Fifth Assessment Report, air temperature and humidity of the future are expected to gradually increase over the current. In this study, future PMPs are estimated by using future dew point temperature projection data which are obtained from RCM data provided by the Korea Meteorological Administration. First, bias included in future dew point temperature projection data which is provided on a daily basis is corrected through a quantile-mapping method. Next, using a scale-invariance technique, 12-hour duration 100-year return period dew point temperatures which are essential input data for PMPs estimation are estimated from bias-corrected future dew point temperature data. After estimating future PMPs, it can be shown that PMPs in all future climate change scenarios (AR5 RCP2.6, RCP 4.5, RCP 6.0, and RCP 8.5 are very likely to increase.
Non-abelian Born-Infeld revisited
Roo, M. de
2002-01-01
We discuss the non-abelian Born-Infeld action, including fermions, as a series in Î±'. We review recent work establishing the complete result to Î±'2, and its impact on our earlier attempts to derive the Born-Infeld action using Îº-symmetry.
About the autotopisms of abelian groups
Clavier, Lucien
2012-01-01
We describe the autotopism group Atp(G) of any abelian group G as being a semidirect product of its automorphism group Aut(G) and G^2. We then provide the subgroup structure of Atp(G) when G is a finite cyclic group.
Dual topologies on non-abelian groups
Ferrer, María V
2010-01-01
According to Comfort, Raczkowski and Trigos-Arrieta, a topological abelian group G is said to be determined if for each dense subgroup D of G the restriction mapping $r|_D: \\hat G\\longrightarrow \\hat D$ is a homeomorphism (equivalently, a topological isomorphism). The principal theorem in this area, given by Ausenhofer and Chasco independently, is this: every metrizable abelian group is determined (a generalization of that result to the non-abelian context was given by Lukacs: for every dense subgroup D of a metrizable group and for every compact Lie group K, the restriction mapping $r|_D: CHom(G, K)\\longrightarrow CHom(D, K)$ is a homeomorphism). Comfort, Raczkowski and Trigos-Arrieta established the following amazing inverse of this theorem for compact groups: under the Continuum Hypothesis CH, every determined compact abelian group is metrizable. Other authors have contributed subsequently to this area (Dikranjan, De Leo, Hernandez, Macario, Shakmatov, etc.) and it is known that CH is not needed in the pre...
The Abelianization of QCD Plasma Instabilities
Arnold, P; Arnold, Peter; Lenaghan, Jonathan
2004-01-01
QCD plasma instabilities appear to play an important role in the equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical limit of weak coupling (i.e. asymptotically high energy). It is important to understand what non-linear physics eventually stops the exponential growth of unstable modes. It is already known that the initial growth of plasma instabilities in QCD closely parallels that in QED. However, once the unstable modes of the gauge-fields grow large enough for non-Abelian interactions between them to become important, one might guess that the dynamics of QCD plasma instabilities and QED plasma instabilities become very different. In this paper, we give suggestive arguments that non-Abelian self-interactions between the unstable modes are ineffective at stopping instability growth, and that the growing non-Abelian gauge fields become approximately Abelian after a certain stage in their growth. This in turn suggests that understanding the development of QCD plasma instabilities i...
Abelian varieties isogenous to a Jacobian
Chai, C.-L.; Oort, F.
2012-01-01
We define a notion of Weyl CM points in the moduli space A g,1 of g -dimensional principally polarized abelian varieties and show that the André-Oort conjecture (or the GRH) implies the following statement: for any closed subvariety X⫋A g,1 over Q a , there exists a Weyl special point [(B,μ)]∈A g,1
A Massive Non-Abelian Vector Model
Chishtie, F A
2012-01-01
The introduction of a Lagrange multiplier field to ensure that the classical equations of motion are satisfied serves to restrict radiative corrections in a model to being only one loop. The consequences of this for a massive non-Abelian vector model are considered.
Classification of Irregular Varieties : Minimal Models and Abelian Varieties
Catanese, Fabrizio; Ciliberto, Ciro
1992-01-01
M. Andreatta,E.Ballico,J.Wisniewski: Projective manifolds containing large linear subspaces; - F.Bardelli: Algebraic cohomology classes on some specialthreefolds; - Ch.Birkenhake,H.Lange: Norm-endomorphisms of abelian subvarieties; - C.Ciliberto,G.van der Geer: On the jacobian of ahyperplane section of a surface; - C.Ciliberto,H.Harris,M.Teixidor i Bigas: On the endomorphisms of Jac (W1d(C)) when p=1 and C has general moduli; - B. van Geemen: Projective models of Picard modular varieties; - J.Kollar,Y.Miyaoka,S.Mori: Rational curves on Fano varieties; - R. Salvati Manni: Modular forms of the fourth degree; A. Vistoli: Equivariant Grothendieck groups and equivariant Chow groups; - Trento examples; Open problems
Five secrets to leveraging maximum buying power with your media project.
Hirsch, Lonnie
2010-11-01
Planning and executing a successful media campaign or project requires knowledge and expert execution of specific techniques and skills, including understanding of the requirements for proper media research and competitive intelligence, effective planning of media schedules, negotiation of best rates with media companies, monitoring the campaign, accurately tracking and evaluating results, and making smart adjustments based on tracking data to maximize the profitability and success of the enterprise. Some of the most important knowledge and techniques are not generally known by most advertisers, particularly small businesses like health care practices. This article reveals these tips that are the most effective and includes information on the use of experts and other professional resources that help increase the likelihood of a successful outcome for a well-planned and executed media campaign.
Sullivan, T. [Brookhaven National Lab. (BNL), Upton, NY (United States)
2016-05-20
ZionSolutions is in the process of decommissioning the Zion Nuclear Power Station (ZNPS). After decommissioning is completed, the site will contain two reactor Containment Buildings, the Fuel Handling Building and Transfer Canals, Auxiliary Building, Turbine Building, Crib House/Forebay, and a Waste Water Treatment Facility that have been demolished to a depth of 3 feet below grade. Additional below ground structures remaining will include the Main Steam Tunnels and large diameter intake and discharge pipes. These additional structures are not included in the modeling described in this report but the inventory remaining (expected to be very low) will be included with one of the structures that are modeled as designated in the Zion Station Restoration Project (ZSRP) License Termination Plan (LTP). The remaining underground structures will be backfilled with clean material. The final selection of fill material has not been made.
Quantum field theory I foundations and Abelian and non-Abelian gauge theories
Manoukian, Edouard B
2016-01-01
This textbook covers a broad spectrum of developments in QFT, emphasizing those aspects that are now well consolidated and for which satisfactory theoretical descriptions have been provided. The book is unique in that it offers a new approach to the subject and explores many topics merely touched upon, if covered at all, in standard reference works. A detailed and largely non-technical introductory chapter traces the development of QFT from its inception in 1926. The elegant functional differential approach put forward by Schwinger, referred to as the quantum dynamical (action) principle, and its underlying theory are used systematically in order to generate the so-called vacuum-to-vacuum transition amplitude of both abelian and non-abelian gauge theories, in addition to Feynman’s well-known functional integral approach, referred to as the path-integral approach. Given the wealth of information also to be found in the abelian case, equal importance is put on both abelian and non-abelian gauge theories. Pa...
The three-quark potential and perfect Abelian dominance in SU(3) lattice QCD
Suganuma, Hideo
2015-01-01
We study the static three-quark (3Q) potential for more than 300 different patterns of 3Q systems with high statistics, i.e., 1000-2000 gauge configurations, in SU(3) lattice QCD at the quenched level. For all the distances, the 3Q potential is found to be well described by the Y-ansatz, i.e., one-gluon-exchange (OGE) Coulomb plus Y-type linear potential. Also, we investigate Abelian projection of quark confinement in the context of the dual superconductor picture proposed by Yoichiro~Nambu~{\\it et al.} in SU(3) lattice QCD. Remarkably, quark confinement forces in both Q$\\bar{\\rm Q}$ and 3Q systems can be described only with Abelian variables in the maximally Abelian gauge, i.e., $\\sigma_{\\rm Q \\bar Q} \\simeq \\sigma_{\\rm Q \\bar Q}^{\\rm Abel} \\simeq \\sigma_{\\rm 3Q} \\simeq \\sigma_{\\rm 3Q}^{\\rm Abel}$, which we call ``perfect Abelian dominance'' of quark confinement.
Gravitating non-Abelian cosmic strings
Santo, Antônio de Padua
2015-01-01
In this paper we study regular cosmic string solutions of the non-Abelian Higgs model coupled with the Einstein gravity. In order to do that, we constructed a set of coupled differential ordinary equation. Because there is no closed solution for this set of equations, we solve it numerically. The solutions that we are interested in asymptote to a flat space-time with a planar angle deficit. This model under consideration present two bosonic sectors, besides the non-Abelian gauge one, coupled minimally with the gravitational fields. The two bosonic sectors may present a direct coupling, which plays an important role on the behavior of the matter and gauge fields and also on the behavior on the geometry of the spacetime. We explicitly analyze the behaviors of the energy density and planar angle deficit as function of the energy scale where the gauge symmetry is spontaneously broken and the coupling interaction between the bosonic sectors.
Non-abelian black string construction
Mazharimousavi, S Habib
2010-01-01
We present d+1-dimensional pure magnetic Yang-Mills (YM) black strings (or 1-branes) induced by the d-dimensional Einstein-Yang-Mills-Dilaton (EYMD) black holes. Incorporation of non-abelian fields in black strings, to our knowledge, has not been considered so far, for this reason we aim to fill this gap. Born-Infeld (BI) version of the YM field makes our starting point which goes to the standard YM field through a limiting procedure. The lifting from black holes to black strings, (with less number of fields) is by adding an extra, compact coordinate. This amounts to the change of horizon topology from S^{d-2} to a product structure. Our black string in 5-dimensions is a rather special one, with uniform Hawking temperature and non-asymptotically flat Local isometry in the abelian limit with the space of colliding plane waves is discussed.
Abelian Duality on Globally Hyperbolic Spacetimes
Becker, Christian; Benini, Marco; Schenkel, Alexander; Szabo, Richard J.
2017-01-01
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism in a manifestly covariant way and without the assumption of compact Cauchy surfaces. We construct semi-classical configuration spaces and corresponding presymplectic Abelian groups of observables, which are quantized by the CCR-functor to the category of C*-algebras. We demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories. We apply this formalism to develop a fully covariant quantum theory of self-dual fields.
Maxwell superalgebras and Abelian semigroup expansion
Concha, P.K.; Rodríguez, E.K. [Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Dipartimento di Scienza Applicata e Tecnologia (DISAT), Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via Pietro Giuria, 1, 10125 Torino (Italy)
2014-09-15
The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2) leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM{sup (N)} recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N). Moreover, we show that new minimal Maxwell superalgebras type sM{sub m+2} and their N-extended generalization can be obtained using the S-expansion procedure.
Anomalous Abelian symmetry in the standard model
Ramond, P.
1995-12-31
The observed hierarchy of quark and lepton masses can be parametrized by nonrenormalizable operators with dimensions determined by an anomalous Abelian family symmetry, a gauge extension to the minimal supersymmetric standard model. Such an Abelian symmetry is generic to compactified superstring theories, with its anomalies compensated by the Green-Schwarz mechanism. If we assume these two symmetries to be the same, we find the electroweak mixing angle to be sin {sup 2}{theta}{sub {omega}} = 3/8 at the string scale, just by setting the ratio of the product of down quark to charged lepton masses equal to one at the string scale. This assumes no GUT structure. The generality of the result suggests a superstring origin for the standard model. We generalize our analysis to massive neutrinos, and mixings in the lepton sector.
Hadamard states for quantum Abelian duality
Benini, Marco; Dappiaggi, Claudio
2016-01-01
Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C$^*$-algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states to such algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three C$^*$-algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors we obtain a state for the full theory, providing ultimately a unitary implementation of Abelian duality.
Gravitating non-Abelian cosmic strings
de Pádua Santos, Antônio; Bezerra de Mello, Eugênio R.
2015-08-01
In this paper, we study regular cosmic string solutions of the non-Abelian Higgs model coupled with gravity. In order to develop this analysis, we constructed a set of coupled non-linear differential equations. Because there is no closed solution for this set of equations, we solve it numerically. The solutions we are interested in asymptote to a flat spacetime with a planar angle deficit. The model under consideration presents two bosonic sectors, besides the non-Abelian gauge field. The two bosonic sectors may present a direct coupling, so we investigate the relevance of this coupling on the system, specifically in the linear energy density of the string and on the planar angle deficit. We also analyze the behaviors of these quantities as a function of the energy scale where the gauge symmetry is spontaneously broken.
Maxwell superalgebras and Abelian semigroup expansion
P.K. Concha
2014-09-01
Full Text Available The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2 leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM(N recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N. Moreover, we show that new minimal Maxwell superalgebras type sMm+2 and their N-extended generalization can be obtained using the S-expansion procedure.
Topological Charge of Lattice Abelian Gauge Theory
Fujiwara, T; Wu, K
2001-01-01
Configuration space of abelian gauge theory on a periodic lattice becomes topologically disconnected by excising exceptional gauge field configurations. It is possible to define a U(1) bundle from the nonexceptional link variables by a smooth interpolation of the transition functions. The lattice analogue of Chern character obtained by a cohomological technique based on the noncommutative differential calculus is shown to give a topological charge related to the topological winding number of the U(1) bundle.
Abelian Ashtekar formulation from the ADM action
Contreras, Ernesto
2013-01-01
We study the Ashtekar formulation of linear gravity starting from the ADM first order action for the non linear theory, linearizing it, and performing a canonical transformation that coordinatizes the phase space in terms of the already linearized Ashtekar variables. The results obtained in this way are in accordance with those obtained through the standard method, in which, after introducing the Ashtekar variables for the full theory, a linearization around the flat Abelian connection and its conjugate momentum is performed.
Loop Equations in Abelian Gauge Theories
Di Bartolo, C; Pe~na, F; Bartolo, Cayetano Di; Leal, Lorenzo; Peña, Francisco
2005-01-01
The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme for studying these loop-equations for lattice Maxwell theory is presented. The approximation leads to a partial difference equation in the area and length variables of the loop, and certain physically motivated ansatz is seen to reproduce the mean field results from a geometrical perspective.
Non-Abelian BIonic Brane Intersections
Cook, P; Murugan, J; Cook, Paul; Koch, Robert de Mello; Murugan, Jeff
2003-01-01
We study "fuzzy funnel" solutions to the non-Abelian equations of motion of the D-string. Our funnel describes n^6/360 coincident D-strings ending on n^3/6 D7-branes, in terms of a fuzzy six-sphere which expands along the string. We also provide a dual description of this configuration in terms of the world volume theory of the D7-branes.
Huber, Markus Q; Schwenzer, Kai
2011-01-01
Functional equations like exact renormalization group and Dyson-Schwinger equations have contributed to a better understanding of non-perturbative phenomena in quantum field theories in terms of the underlying Green functions. In Yang-Mills theory especially the Landau gauge has been used, as it is the most accessible gauge for these methods. The growing understanding obtained in this gauge allows to proceed to other gauges in order to obtain more information about the relation of different realizations of the confinement mechanism. In the maximally Abelian gauge first results are very encouraging as a variant of Abelian infrared dominance is found: The Abelian part of the gauge field propagator is enhanced at low momenta and thereby dominates the dynamics in the infrared. Its role is therefore similar to that of the ghost propagator in the Landau gauge, where one denotes the corresponding phenomenon as ghost dominance. Also the ambiguity of two different types of solutions (decoupling and scaling) exists in ...
Vacuum-Induced Abelian and Non-Abelian Gauge Potentials in Cavity Quantum Electrodynamics
张海龙; 梁奇锋; 俞立先; 陈刚
2011-01-01
Gauge potential plays an important role in exploring exotic phenomena in the single- and many-body quantum systems. In this paper, we propose a scheme to create both new Abelian and non-Abelian gauge potentials by adiabatically controlling the degenerate Dicke model in cavity quantum electrodynamics. It is shown that a non-Abelian gauge potential is achieved only for a single atom, whereas an Abelianizen diagonal gauge potential is realized for the atomic ensemble. More importantly, two interesting quantum phenomena such as the geometric phase and the magnetic monopole induced by our created gauge potentials are also predicted. The possible physical realization is presented in the macroscopic circuit quantum electrodynamics with the Cooper pair boxes, which act as the artificial two-level atoms controlled by the gate voltage and the external magnetic flux.
Anisotropic Inflation with Non-Abelian Gauge Kinetic Function
Murata, Keiju
2011-01-01
We study an anisotropic inflation model with a gauge kinetic function for a non-abelian gauge field. We find that, in contrast to abelian models, the anisotropy can be either a prolate or an oblate type, which could lead to a different prediction from abelian models for the statistical anisotropy in the power spectrum of cosmological fluctuations. During a reheating phase, we find chaotic behaviour of the non-abelian gauge field which is caused by the nonlinear self-coupling of the gauge field. We compute a Lyapunov exponent of the chaos which turns out to be uncorrelated with the anisotropy.
Netanel H. Lindner
2012-10-01
Full Text Available We study the non-Abelian statistics characterizing systems where counterpropagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of ν=1/m, while electrons of the opposite spin occupy a similar state with ν=-1/m. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-Abelian anyon of quantum dimension sqrt[2m]. We calculate the unitary transformations that are associated with the braiding of these anyons, and we show that they are able to realize a richer set of non-Abelian representations of the braid group than the set realized by non-Abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.
Non abelian hydrodynamics and heavy ion collisions
Calzetta, E. [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Ciudad Universitaria, Buenos Aires 1428 (Argentina)
2014-01-14
The goal of the relativistic heavy ion collisions (RHIC) program is to create a state of matter where color degrees of freedom are deconfined. The dynamics of matter in this state, in spite of the complexities of quantum chromodynamics, is largely determined by the conservation laws of energy momentum and color currents. Therefore it is possible to describe its main features in hydrodynamic terms, the very short color neutralization time notwithstanding. In this lecture we shall give a simple derivation of the hydrodynamics of a color charged fluid, by generalizing the usual derivation of hydrodynamics from kinetic theory to the non abelian case.
Emergent Abelian Gauge Fields from Noncommutative Gravity
Allen Stern
2010-02-01
Full Text Available We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.
Domain wall solutions with Abelian gauge fields
Rozowsky, J S; Wali, K C
2004-01-01
We study kink (domain wall) solutions in a model consisting of two complex scalar fields coupled to two independent Abelian gauge fields in a Lagrangian that has $U(1)\\times U(1)$ gauge plus $\\mathbb{Z}_2$ discrete symmetry. We find consistent solutions such that while the U(1) symmetries of the fields are preserved while in their respective vacua, they are broken on the domain wall. The gauge field solutions show that the domain wall is sandwiched between domains with constant magnetic fields.
Non abelian hydrodynamics and heavy ion collisions
Calzetta, Esteban
2013-01-01
The goal of the relativistic heavy ion collisions (RHIC) program is to create a state of matter where color degrees of freedom are deconfined. The dynamics of matter in this state, in spite of the complexities of quantum chromodynamics, is largely determined by the conservation laws of energy momentum and color currents. Therefore it is possible to describe its main features in hydrodynamic terms, the very short color neutralization time notwithstanding. In this lecture we shall give a simple derivation of the hydrodynamics of a color charged fluid, by generalizing the usual derivation of hydrodynamics from kinetic theory to the non abelian case.
The Dirac Operator over Abelian Finite Groups
Vaz, Jr., Jayme
1997-01-01
In this paper we show how to construct a Dirac operator on a lattice in complete analogy with the continuum. In fact we consider a more general problem, that is, the Dirac operator over an abelian finite group (for which a lattice is a particular example). Our results appear to be in direct connexion with the so called fermion doubling problem. In order to find this Dirac operator we need to introduce an algebraic structure (that generalizes the Clifford algebras) where we have quantities tha...
Screening in Hot Non-Abelian Plasma
Petreczky, P
1999-01-01
This thesis is devoted to the study of the screening masses in hot non-Abelian theories. Section 1 contain a brief introduction to the topic. In section 2 a detailed overview of the screening phenomena and their applications is given. In section 3 the screening masses are defined through the coupled gap equations. Section 4 deals with the determination of the screening masses of hot SU(2) gauge theory in the framework of the 3d lattice adjoint Higgs model considered as an effective theory. Finally in section 5 the screening masses of hot SU(2) Higgs model are examined.
Correlations between Abelian monopoles and center vortices
Hosseini Nejad, Seyed Mohsen; Deldar, Sedigheh
2017-04-01
We study the correlations between center vortices and Abelian monopoles for SU(3) gauge group. Combining fractional fluxes of monopoles, center vortex fluxes are constructed in the thick center vortex model. Calculating the potentials induced by fractional fluxes constructing the center vortex flux in a thick center vortex-like model and comparing with the potential induced by center vortices, we observe an attraction between fractional fluxes of monopoles constructing the center vortex flux. We conclude that the center vortex flux is stable, as expected. In addition, we show that adding a contribution of the monopole-antimonopole pairs in the potentials induced by center vortices ruins the Casimir scaling at intermediate regime.
Localization of abelian gauge fields on thick branes
Vaquera-Araujo, Carlos A. [Universidad de Colima, Facultad de Ciencias, CUICBAS, Colima (Mexico); Corradini, Olindo [Universidad Autonoma de Chiapas, Ciudad Universitaria, Facultad de Ciencias en Fisica y Matematicas, Tuxtla Gutierrez (Mexico); Universita di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Modena (Italy)
2015-02-01
In this work, we explore a mechanism for abelian gauge field localization on thick branes based on a five-dimensional Stueckelberg-like action. A normalizable zero mode is found through the identification of a suitable coupling function between the brane and the gauge field. The same mechanism is studied for the localization of the abelian Kalb-Ramond field. (orig.)
Non-Abelian anyons: when Ising meets Fibonacci
Grosfeld, E.; Schoutens, K.
2009-01-01
We consider an interface between two non-Abelian quantum Hall states: the Moore-Read state, supporting Ising anyons, and the k=2 non-Abelian spin-singlet state, supporting Fibonacci anyons. It is shown that the interface supports neutral excitations described by a (1+1)-dimensional conformal field
Abelian Chern-Simons theory and contact torsion
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas in ...... in quantum field theory. We compare the shift reduced partition function with other formulations of the abelian Chern-Simons partition function. This study naturally motivates an Atiyah-Patodi-Singer type index problem in contact geometry.......Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas...
Abelian Chern-Simons theory and contact torsion
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas in ...... in quantum field theory. We compare the shift reduced partition function with other formulations of the abelian Chern-Simons partition function. This study naturally motivates an Atiyah-Patodi-Singer type index problem in contact geometry.......Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas...
Test Rank of an Abelian Product of a Free Lie Algebra and a Free Abelian Lie Algebra
Naime Ekici; Nazar Şahin Öğüşlü
2011-08-01
Let be a free Lie algebra of rank ≥ 2 and be a free abelian Lie algebra of rank ≥ 2. We prove that the test rank of the abelian product $F× A$ is . Morever we compute the test rank of the algebra $F/ k(F)'$.
Bosmans, H.; Verbeeck, R.; Vandermeulen, D.; Suetens, P.; Wilms, G.; Maaly, M.; Marchal, G.; Baert, A.L. [Louvain Univ. (Belgium)
1995-12-01
The objective of this study was to validate a new post processing algorithm for improved maximum intensity projections (mip) of intracranial MR angiography acquisitions. The core of the post processing procedure is a new brain segmentation algorithm. Two seed areas, background and brain, are automatically detected. A 3D region grower then grows both regions towards each other and this preferentially towards white regions. In this way, the skin gets included into the final `background region` whereas cortical blood vessels and all brain tissues are included in the `brain region`. The latter region is then used for mip. The algorithm runs less than 30 minutes on a full dataset on a Unix workstation. Images from different acquisition strategies including multiple overlapping thin slab acquisition, magnetization transfer (MT) MRA, Gd-DTPA enhanced MRA, normal and high resolution acquisitions and acquisitions from mid field and high field systems were filtered. A series of contrast enhanced MRA acquisitions obtained with identical parameters was filtered to study the robustness of the filter parameters. In all cases, only a minimal manual interaction was necessary to segment the brain. The quality of the mip was significantly improved, especially in post Gd-DTPA acquisitions or using MT, due to the absence of high intensity signals of skin, sinuses and eyes that otherwise superimpose on the angiograms. It is concluded that the filter is a robust technique to improve the quality of MR angiograms.
Kinosada, Yasutomi; Okuda, Yasuyuki (Mie Univ., Tsu (Japan). School of Medicine); Ono, Mototsugu (and others)
1993-02-01
We developed a new noninvasive technique to visualize the anatomical structure of the nerve fiber system in vivo, and named this technique magnetic resonance (MR) tractography and the acquired image an MR tractogram. MR tractography has two steps. One is to obtain diffusion-weighted images sensitized along axes appropriate for depicting the intended nerve fibers with anisotropic water diffusion MR imaging. The other is to extract the anatomical structure of the nerve fiber system from a series of diffusion-weighted images by the maximum intensity projection method. To examine the clinical usefulness of the proposed technique, many contiguous, thin (3 mm) coronal two-dimensional sections of the brain were acquired sequentially in normal volunteers and selected patients with paralyses, on a 1.5 Tesla MR system (Signa, GE) with an ECG-gated Stejskal-Tanner pulse sequence. The structure of the nerve fiber system of normal volunteers was almost the same as the anatomy. The tractograms of patients with paralyses clearly showed the degeneration of nerve fibers and were correlated with clinical symptoms. MR tractography showed great promise for the study of neuroanatomy and neuroradiology. (author).
Akai, Takanori; Taniguchi, Daigo; Oda, Ryo; Asada, Maki; Toyama, Shogo; Tokunaga, Daisaku; Seno, Takahiro; Kawahito, Yutaka; Fujii, Yosuke; Ito, Hirotoshi; Fujiwara, Hiroyoshi; Kubo, Toshikazu
2016-04-01
Contrast-enhanced magnetic resonance imaging with maximum intensity projection (MRI-MIP) is an easy, useful imaging method to evaluate synovitis in rheumatoid hands. However, the prognosis of synovitis-positive joints on MRI-MIP has not been clarified. The aim of this study was to evaluate the relationship between synovitis visualized by MRI-MIP and joint destruction on X-rays in rheumatoid hands. The wrists, metacarpophalangeal (MP) joints, and proximal interphalangeal (PIP) joints of both hands (500 joints in total) were evaluated in 25 rheumatoid arthritis (RA) patients. Synovitis was scored from grade 0 to 2 on the MRI-MIP images. The Sharp/van der Heijde score and Larsen grade were used for radiographic evaluation. The relationships between the MIP score and the progression of radiographic scores and between the MIP score and bone marrow edema on MRI were analyzed using the trend test. As the MIP score increased, the Sharp/van der Heijde score and Larsen grade progressed severely. The rate of bone marrow edema-positive joints also increased with higher MIP scores. MRI-MIP imaging of RA hands is a clinically useful method that allows semi-quantitative evaluation of synovitis with ease and can be used to predict joint destruction.
Quantized Abelian principle connections on Lorentzian manifolds
Benini, Marco [Pavia Univ. (Italy); Istituto Nazionale di Fisica Nucleare, Pavia (Italy); Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Dappiaggi, Claudio [Pavia Univ. (Italy); Istituto Nazionale di Fisica Nucleare, Pavia (Italy); Schenkel, Alexander [Bergische Univ., Wuppertal (Germany). Fachgruppe Mathematik
2013-03-15
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group, namely the group of vertical principal bundle automorphisms. Properties of our functor are investigated in detail and, similar to earlier works, it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated. Furthermore, we prove that, for Abelian structure groups containing a nontrivial compact factor, the gauge invariant Borchers- Uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections. We introduce a topological generalization of the concept of locally covariant quantum fields. As examples, we construct for the full subcategory of principal U(1)-bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the Euler class and the electric charge. In this case we also prove that the electric charges can be consistently set to zero, which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory.
Scheff, J.; Seager, R.; Coats, S.; Liu, H.
2015-12-01
Precipitation (P) and Penman-Monteith potential evapotranspiration (PET) from global climate models (GCMs) have been used to infer that Earth's land areas will dry out under future greenhouse warming outside of the high latitudes. This has been argued using simulated declines in both the aridity index P/PET (by the present author among others) and the Palmer drought index, driven by warming-powered PET increases. However, this picture is at odds with the broad paleoclimate tenet that greenhouse eras in fact appear "wet" on land while cold intervals appear "dry." Here, we show that the same GCMs which project widespread P/PET declines for the greenhouse future also project fairly widespread P/PET increases (i.e. "wetting") for the last glacial maximum (LGM), when CO2 was half present levels and snow and ice were extensive. Yet, global pollen and dust records of the LGM suggest mostly "drier"-looking vegetation patterns than today, as we also review here. Thus, either the GCMs' P and/or PET responses to past global change are flawed, or, P/PET change is not relevant for the vegetation response to CO2-driven climate change. Either way, this calls into question the ecological relevance of the above "drying-out" conclusions. We also show parallel results for the Palmer index, and investigate whether the P/PET results seem any more relevant for lakes and other abiotic wetness indicators than for vegetation.
Jeng, K-S; Huang, C-C; Lin, C-K; Lin, C-C; Chen, K-H
2013-06-01
Early detection of Budd-Chiari syndrome (BCS) to give the appropriate therapy in time is crucial. Angiography remains the golden standard to diagnose BCS. However, to establish the diagnosis of BCS in complicated cirrhotic patients remains a challenge. We used maximum intensity projection (Max IP) and minimum intensity projection (Min IP) from computed tomographic (CT) images to detect this syndrome in such a patient. A 55-year-old man with a history of chronic hepatitis B infection and alcoholism had undergone previously a left lateral segmentectomy for hepatic epitheloid angiomyolipoma (4.6 × 3.5 × 3.3 cm) with a concomitant splenectomy. Liver decompensation with intractable ascites and jaundice occurred 4 months later. The reformed images of the venous phase of enhanced CT images with Max IP and Min IP showed middle hepatic vein thrombosis. He then underwent a living-related donor liver transplantation with a right liver graft from his daughter. Intraoperatively, we noted thrombosis of his middle hepatic vein protruding into inferior vena cava. The postoperative course was unevenful. Microscopic findings revealed micronodular cirrhosis with mixed inflammation in the portal areas. Some liver lobules exhibited congestion and sinusoidal dilation compatible with venous occlusion clinically. We recommend Max IP and Min IP of CT images as simple and effective techniques to establish the diagnosis of BCS, especially in complicated cirrhotic patients, thereby avoiding invasive interventional procedures. Copyright © 2013 Elsevier Inc. All rights reserved.
Some special classes of n-abelian groups
Costantino Delizia
2012-06-01
Full Text Available Let n be an integer. A group G is said to be n-abelian if the map phi_n that sends g to g^n is an endomorphism of G. Then (xy^n=x^ny^n for all x,y in G, from which it follows [x^n,y]=[x,y]^n=[x,y^n]. It is also easy to see that a group G is n-abelian if and only if it is (1-n-abelian. If nneq 0,1 and G is an n-abelian group, then the quotient group G/Z(G has finite exponent dividing n(n-1. This implies that every torsion-free n-abelian group is abelian. We denote by B_n and C_n the classes of all groups G for which phi_n is a monomorphism and an epimorphism of G, respectively. Then B_0=C_0 contains only the trivial group, B_1=C_1 is the class of all groups, and B_-1=C_-1 is the class of all abelian groups. Furthermore, with |n|>1, G is in B_n if and only if G is an n-abelian group having no elements of order dividing |n|. Similarly, G is in C_n if and only if G is n-abelian and for every g in G there exists an element x in G such that g=x^n. We also set A_n=B_ncap C_n. In this paper we give a characterization for groups in B_n and for groups in C_n. We also obtain an arithmetic description of the set of all integers n such that a group G is in A_n.
A Vector Non-abelian Chern-Simons Duality
García-Compéan, H; Ramírez, C
2002-01-01
Abelian Chern-Simons gauge theory it is known to possess a `S-self-dual' action where its coupling constant k is inverted i.e. k goes to 1/k. Here a vector non-abelian duality it is found in the pure non-abelian Chern-Simons action at the classical level. The procedure is given explicitly for the gauge group SU(2), but it is valid for any compact Lie group. The dimensional reduction of the dual Chern-Simons action to two-dimensions constitutes a dual Wess-Zumino-Witten action already given in the literature.
Charged Stringy Black Holes With Non-Abelian Hair
Donets, E E
1993-01-01
Static spherically symmetric asymptotically flat charged black hole solutions are constructed within the magnetic SU(3) sector of the 4-dimensional heterotic string effective action. They possess non-abelian hair in addition to the Coulomb magnetic field and are qualitatively similar to the Einstein-Yang-Mills colored SU(3) black holes except for the extremal case. In the extremality limit the horizon shrinks and the resulting geometry around the origin coincides with that of an extremal abelian dilatonic black hole with magnetic charge. Non-abelian hair exibits then typical sphaleron structure.
Vortices in generalized Abelian Chern-Simons-Higgs model
Casana, Rodolfo
2015-01-01
We study a generalization of abelian Chern-Simons-Higgs model by introducing nonstandard kinetic terms. We will obtain a generic form of Bogomolnyi equations by minimizing the energy functional of the model. This generic form of Bogomolnyi equations produce an infinity number of soliton solutions. As a particular limit of these generic Bogomolnyi equations, we obtain the Bogomolnyi equations of the abelian Maxwell-Higgs model and the abelian Chern-Simons Higgs model. Finally, novel soliton solutions emerge from these generic Bogomolnyi equations. We analyze these solutions from theoretical and numerical point of view.
Abelian Chern-Simons theory, Stokes' Theorem, and generalized connections
Sahlmannn, Hanno
2010-01-01
Generalized connections and their calculus have been developed in the context of quantum gravity. Here we apply them to abelian Chern-Simons theory. We derive the expectation values of holonomies in U(1) Chern-Simons theory using Stokes' Theorem, flux operators and generalized connections. A framing of the holonomy loops arises in our construction, and we show how, by choosing natural framings, the resulting expectation values nevertheless define a functional over gauge invariant cylindrical functions. The abelian theory considered in the present article is test case for our method. It can also be applied to the non-abelian theory. Results for that case will be reported elsewhere.
Structure of augmentation quotients of finite homocyclic abelian groups
Guo-ping TANG
2007-01-01
Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order pr, i.e., a finite homocyclic abelian group. Let △n (G) denote the n-th power of the augmentation ideal △(G) of the integral group ring ZG. The paper gives an explicit structure of the consecutive quotient group Qn (G) = △n (G)/△n+1 (G) for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.
Structure of augmentation quotients of finite homocyclic abelian groups
2007-01-01
Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order pr,i.e.,a finite homocyclic abelian group.LetΔn （G） denote the n-th power of the augmentation idealΔ（G） of the integral group ring ZG.The paper gives an explicit structure of the consecutive quotient group Qn（G）=Δn（G）/Δn+1（G） for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.
Non-Abelian Lattice Gauge Theories in Superconducting Circuits
Mezzacapo, A; Sabín, C; Egusquiza, I L; Lamata, L; Solano, E
2015-01-01
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure $SU(2)$ gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms.
Mesons from (non) Abelian T-dual backgrounds
Itsios, Georgios; Zoakos, Dimitrios
2016-01-01
In this work we study mesonic excitations in a Quantum Field Theory dual to the non Abelian T-dual of $AdS_5\\times S^5$, using a D6 brane probe on the Sfetsos-Thompson background. Before and after the duality, we observe interesting differences between the spectra and interpret them. The spectrum of masses and the interactions among mesonic excitations teach valuable lessons about the character of non-Abelian T-duality and its implications for Holography. The case of Abelian T-duality is also studied.
Universality Class in Abelian Sandpile Models with Stochastic Toppling Rules
无
2005-01-01
We present a stochastic critical slope sandpile model, where the amount of grains that fall in an overturning event is stochastic variable. The model is local, conservative, and Abelian. We apply the moment analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. Numerical results show that this model, Oslo model, and one-dimensional Abelian Manna model have the same critical behavior although the three models have different stochastic toppling rules, which provides evidences suggesting that Abelian sandpile models with different stochastic toppling rules are in the same universality class.
Extreme amenability of abelian $L_0$ groups
Sabok, Marcin
2012-01-01
We show that for any abelian topological group $G$ and arbitrary diffused submeasure $\\mu$, every continuous action of $L_0(\\mu,G)$ on a compact space has a fixed point. This generalizes earlier results of Herer and Christensen, Glasner, Furstenberg and Weiss, and Farah and Solecki. This also answers a question posed by Farah and Solecki. In particular, it implies that if $H$ is of the form $L_0(\\mu,\\mathbb{R})$, then $H$ is extremely amenable if and only if $H$ has no nontrivial characters, which gives an evidence for an affirmative answer to a question of Pestov. The proof is based on estimates of chromatic numbers of certain graphs on $\\mathbb{Z}^n$. It uses tools from algebraic topology and builds on the work of Farah and Solecki.
Vortex dynamics in nonrelativistic Abelian Higgs model
A.A. Kozhevnikov
2015-11-01
Full Text Available The dynamics of the gauge vortex with arbitrary form of a contour is considered in the framework of the nonrelativistic Abelian Higgs model, including the possibility of the gauge field interaction with the fermion asymmetric background. The equations for the time derivatives of the curvature and the torsion of the vortex contour generalizing the Betchov–Da Rios equations in hydrodynamics, are obtained. They are applied to study the conservation of helicity of the gauge field forming the vortex, twist, and writhe numbers of the vortex contour. It is shown that the conservation of helicity is broken when both terms in the equation of the vortex motion are present, the first due to the exchange of excitations of the phase and modulus of the scalar field and the second one due to the coupling of the gauge field forming the vortex, with the fermion asymmetric background.
Abelian reductions of deformed N=4 SYM
Carlos Cardona
2015-08-01
Full Text Available Following the work in [1], where the massive ABJM model in 2+1 dimensions was shown to have an abelian reduction to the relativistic Landau–Ginzburg, and motivated by the implications for condensed matter through AdS/CFT, we show that a FI deformation of N=4 SYM in 3+1 dimensions with a mass term can also be reduced to a relativistic Landau–Ginzburg model, with the possibility of coupling it to a real scalar, whereas the simply mass deformed N=4 SYM reduces only to a massive ϕ4 model (scalar QED coupled to a real scalar. We study the classical solutions of the model, in particular vortex solutions.
Butterflies in a Semi-Abelian Context
Abbad, Omar; Metere, Giuseppe; Vitale, Enrico M
2011-01-01
It is known that monoidal functors between internal groupoids in the category Grp of groups constitute the bicategory of fractions of the 2-category Grpd(Grp) of internal groupoids, internal functors and internal natural transformations in Grp with respect to weak equivalences. Monoidal functors can be described equivalently by a kind of weak morphisms introduced by B. Noohi under the name of "butter ies". In order to internalize monoidal functors in a wide context, we introduce the notion of internal butterflies between internal crossed modules in a semi-abelian category C, and we show that they are morphisms of a bicategory B(C): Our main result states that, when in C the notions of Huq commutator and Smith commutator coincide, then the bicategory B(C) of internal butterflies is the bicategory of fractions of Grpd(C) with respect to weak equivalences (that is, internal functors which are internally fully faithful and essentially surjective on objects).
The Structure of Non-Abelian Kinks
Hollowood, Timothy J; Schmidtt, David M
2013-01-01
We consider a class of integrable quantum field theories in 1+1 dimensions whose classical equations have kink solutions with internal collective coordinates that transform under a non-abelian symmetry group. These generalised sine-Gordon theories have been shown to be related to the world sheet theory of the string in the AdS/CFT correspondence. We provide a careful analysis of the boundary conditions at spatial infinity complicated by the fact that they are defined by actions with a WZ term. We go on to describe the local and non-local charges carried by the kinks and end by showing that their structure is perfectly consistent with the exact factorizable S-matrices that have been proposed to describe these theories.
Beauville surfaces with abelian Beauville group
González-Diez, Gabino; Torres-Teigell, David
2011-01-01
A Beauville surface is a rigid surface of general type arising as a quotient of a product of curves $C_{1}$, $C_{2}$ of genera $g_{1},g_{2}\\ge 2$ by the free action of a finite group $G$. In this paper we study those Beauville surfaces for which $G$ is abelian (so that $G\\cong \\mathbb{Z}_{n}^{2}$ with $\\gcd(n,6)=1$ by a result of Catanese). For each such $n$ we are able to describe all such surfaces, give a formula for the number of their isomorphism classes and identify their possible automorphism groups. This explicit description also allows us to observe that such surfaces are all defined over $\\mathbb{Q}$.
Instanton Counting Through Non-abelian Localization
Martens, J
2005-01-01
In this dissertation we study the problem of calculating equivariant volumes of moduli-spaces of framed instantons. The motivation for this is given by instanton counting, a recent development in theoretical physics that gives a direct approach to the non-perturbative study of certain super-symmetric quantum field theories. We develop a strategy for calculating the integrals using a combination of several techniques in symplectic geometry and equivariant cohomology. Most importantly we use an equivariant version of non-abelian localization, applied to the ADHM-construction of the moduli-spaces. Furthermore, we reduce the problem to a compact setting by means of varying compactifications using symplectic cuts, recovering the original integral over a non-compact space as the limit of integrals over compact spaces. In contrast with previous applications, in our case the contribution at infinity introduced by these compactifications turns out to be of primordial importance. We illustrate this method by explicitly...
Degrees of Curves in Abelian Varieties
Debarre, O
1992-01-01
The degree of a curve $C$ in a polarized abelian variety $(X,\\lambda)$ is the integer $d=C\\cdot\\lambda$. When $C$ generates $X$, we find a lower bound on $d$ which depends on $n$ and the degree of the polarization $\\lambda$. The smallest possible degree is $d=n$ and is obtained only for a smooth curve in its Jacobian with its principal polarization (Ran, Collino). The cases $d=n+1$ and $d=n+2$ are studied. Moreover, when $X$ is simple, it is shown, using results of Smyth on the trace of totally positive algebraic integers, that if $d\\le 1.7719\\, n$, then $C$ is smooth and $X$ is isomorphic to its Jacobian. We also get an upper bound on the geometric genus of $C$ in terms of its degree.
Non-Abelian Chern-Simons Vortices
Lozano, G S; Moreno, E F; Schaposnik, F A
2007-01-01
We consider the bosonic sector of a ${\\cal N} = 2$ supersymmetric Chern-Simons-Higgs theory in 2 + 1 dimensions. The gauge group is $U(1)\\times SU(N)$ and has $N_f$ flavors of fundamental matter fields. The model supports non-Abelian (axially symmetric) vortices when $N_f \\geq N$, which have internal (orientational) moduli. When $N_f > N$, the solutions acquire additional collective coordinates parameterizing their transverse size. We solve the BPS equations numerically and obtain local ($N_f = N$) and semi-local ($N_f > N$) string solutions. A $CP^{N-1}$ low-energy effective action for the orientational moduli is obtained in both cases. In the semilocal case there is an additional term in the effective action induced by the transverse size moduli. We find such term in the limit of large transverse size, where exact solutions can be obtained analytically.
Abelian varieties with many endomorphisms and their absolutely simple factors
Guitart, Xavier
2011-01-01
We characterize the abelian varieties arising as absolutely simple factors of GL2-type varieties over a number field k. In order to obtain this result, we study a wider class of abelian varieties: the k-varieties A/k satisfying that $\\End_k^0(A)$ is a maximal subfield of $\\End_k^0(A)$. We call them Ribet-Pyle varieties over k. We see that every Ribet-Pyle variety over k is isogenous over $\\bar k$ to a power of an abelian k-variety and, conversely, that every abelian k-variety occurs as the absolutely simple factor of some Ribet-Pyle variety over k. We deduce from this correspondence a precise description of the absolutely simple factors of the varieties over k of GL2-type.
Representation functions of additive bases for abelian semigroups
Melvyn B. Nathanson
2004-01-01
function has only finitely many zeros. It is proved that for a large class of countably infinite abelian semigroups, there exists a basis whose representation function is exactly equal to the given function for every element in the semigroup.
Product Integral Formalism and Non-Abelian Stokes Theorem
Karp, R L; Rno, J S; Karp, Robert L.; Mansouri, Freydoon; Rno, Jung S.
1999-01-01
We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes' theorem.
Engineering complex topological memories from simple Abelian models
Wootton, James R.; Lahtinen, Ville; Doucot, Benoit; Pachos, Jiannis K.
2011-09-01
In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviors. An exciting proposal for quantum computation is to employ anyonic statistics to manipulate information. Since such statistical evolutions depend only on topological characteristics, the resulting computation is intrinsically resilient to errors. The so-called non-Abelian anyons are most promising for quantum computation, but their physical realization may prove to be complex. Abelian anyons, however, are easier to understand theoretically and realize experimentally. Here we show that complex topological memories inspired by non-Abelian anyons can be engineered in Abelian models. We explicitly demonstrate the control procedures for the encoding and manipulation of quantum information in specific lattice models that can be implemented in the laboratory. This bridges the gap between requirements for anyonic quantum computation and the potential of state-of-the-art technology.
Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions
Fujiwara, T; Wu, K; Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
1999-01-01
Axial anomaly of lattice abelian gauge theory in hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a multiplicative constant for finite lattice spacing and can be interpreted as the Chern character of the abelian lattice gauge theory.
Fourier-like frames on locally compact abelian groups
Christensen, Ole; Goh, Say Song
2015-01-01
We consider a class of functions, defined on a locally compact abelian group by letting a class of modulation operators act on a countable collection of functions. We derive sufficient conditions for such a class of functions to form a Bessel sequence or a frame and for two such systems to be dual...... frames. Explicit constructions are obtained via various generalizations of the classical B-splines to the setting of locally compact abelian groups. (C) 2014 Elsevier Inc. All rights reserved....
From recollement of triangulated categories to recollement of abelian categories
无
2010-01-01
In this paper,we prove that if a triangulated category D admits a recollement relative to triangulated categories D’ and D″,then the abelian category D/T admits a recollement relative to abelian categories D’/i(T) and D″/j(T) where T is a cluster tilting subcategory of D and satisfies i i (T) T,j j (T) T.
Construction of Lie algebras and invariant tensors through abelian semigroups
Izaurieta, Fernando; RodrIguez, Eduardo; Salgado, Patricio [Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)], E-mail: fizaurie@gmail.com, E-mail: edurodriguez@udec.cl, E-mail: pasalgad@udec.cl
2008-11-01
The Abelian Semigroup Expansion Method for Lie Algebras is briefly explained. Given a Lie Algebra and a discrete abelian semigroup, the method allows us to directly build new Lie Algebras with their corresponding non-trivial invariant tensors. The Method is especially interesting in the context of M-Theory, because it allows us to construct M-Algebra Invariant Chern-Simons/Transgression Lagrangians in d = 11.
Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves
Matthew England
2010-03-01
Full Text Available We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain areas of the theory. We present solutions to the Jacobi inversion problem, sets of relations between the Abelian function, links to the Boussinesq equation and a new addition formula.
Non-Abelian Monopoles in the Higgs Phase
Nitta, Muneto
2010-01-01
We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N = 2 supersymmetric U(N) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus on the case of degenerate masses. In these special cases vortices acquire new orientational degrees of freedom, and become "non-Abelian". Kinks acquire new degrees of freedom too, and we will refer to them as "non-Abelian". As already noticed for the Abelian case, non-Abelian kinks must correspond to non-Abelian monopoles of the unbroken phase of SU(N) Yang-Mills. We show, in some special cases, that the moduli spaces of the two objects are in one-to-one correspondence. We argue that the corre- spondence holds in the most general case. The consequence of our result is two-fold. First, it gives an alternative way to construct non-Abelian monopoles, in addition to other well- known techniques (Nahm transform, spectral curves, rational maps). Second, it opens the way to the stu...
Auslander-Reiten sequences and $t$-structures on the homotopy category of an abelian category
Backelin, Erik
2009-01-01
Let $\\Cab$ be an abelian category and let $\\KC$ be the bounded homotopy category of cochain complexes in $\\Cab$. We consider a $t$-structure on $\\KC$ that maps to the standard $t$-structure on the derived category $\\DC$ under the localization functor. Let $\\A$ be the heart of the $t$-structure. In the case when $\\Cab$ has finite length we show that objects of $\\Cab$ correspond to projective objects of $\\A$ and that simple objects of $\\A$ (if they exist) are given by Auslander's and Reiten's almost split sequences in $\\Cab$.
Hsia, Wei-Shen
1986-01-01
In the Control Systems Division of the Systems Dynamics Laboratory of the NASA/MSFC, a Ground Facility (GF), in which the dynamics and control system concepts being considered for Large Space Structures (LSS) applications can be verified, was designed and built. One of the important aspects of the GF is to design an analytical model which will be as close to experimental data as possible so that a feasible control law can be generated. Using Hyland's Maximum Entropy/Optimal Projection Approach, a procedure was developed in which the maximum entropy principle is used for stochastic modeling and the optimal projection technique is used for a reduced-order dynamic compensator design for a high-order plant.
Understanding the physics of a possible non-Abelian fractional quantum hall effect state.
Pan, Wei; Crawford, Matthew; Tallakulam, Madhu; Ross, Anthony Joseph, III
2010-10-01
We wish to present in this report experimental results from a one-year Senior Council Tier-1 LDRD project that focused on understanding the physics of a possible non-Abelian fractional quantum Hall effect state. We first give a general introduction to the quantum Hall effect, and then present the experimental results on the edge-state transport in a special fractional quantum Hall effect state at Landau level filling {nu} = 5/2 - a possible non-Abelian quantum Hall state. This state has been at the center of current basic research due to its potential applications in fault-resistant topological quantum computation. We will also describe the semiconductor 'Hall-bar' devices we used in this project. Electron physics in low dimensional systems has been one of the most exciting fields in condensed matter physics for many years. This is especially true of quantum Hall effect (QHE) physics, which has seen its intellectual wealth applied in and has influenced many seemingly unrelated fields, such as the black hole physics, where a fractional QHE-like phase has been identified. Two Nobel prizes have been awarded for discoveries of quantum Hall effects: in 1985 to von Klitzing for the discovery of integer QHE, and in 1998 to Tsui, Stormer, and Laughlin for the discovery of fractional QHE. Today, QH physics remains one of the most vibrant research fields, and many unexpected novel quantum states continue to be discovered and to surprise us, such as utilizing an exotic, non-Abelian FQHE state at {nu} = 5/2 for fault resistant topological computation. Below we give a briefly introduction of the quantum Hall physics.
Gattringer, Christof; Marchis, Carlotta
2017-03-01
We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over "abelian color cycles" (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).
Residual non-Abelian dark matter and dark radiation
P. Ko
2017-05-01
Full Text Available We propose a novel particle physics model in which vector dark matter (VDM and dark radiation (DR originate from the same non-Abelian dark sector. We show an illustrating example where dark SU(3 is spontaneously broken into SU(2 subgroup by the nonzero vacuum expectation value (VEV of a complex scalar in fundamental representation of SU(3. The massless gauge bosons associated with the residual unbroken SU(2 constitute DR and help to relieve the tension in Hubble constant measurements between Planck and Hubble Space Telescope. In the meantime, massive dark gauge bosons associated with the broken generators are VDM candidates. Intrinsically, this non-Abelian VDM can interact with non-Abelian DR in the cosmic background, which results in a suppressed matter power spectrum and leads to a smaller σ8 for structure formation.
Topological boundary conditions in abelian Chern-Simons theory
Kapustin, Anton [California Institute of Technology, Pasadena, CA 91125 (United States); Saulina, Natalia, E-mail: saulina@theory.caltech.ed [Perimeter Institute, Waterloo (Canada)
2011-04-21
We study topological boundary conditions in abelian Chern-Simons theory and line operators confined to such boundaries. From the mathematical point of view, their relationships are described by a certain 2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern-Simons couplings). We argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group classifying bulk line operators (the discriminant group). We describe properties of boundary line operators; in particular we compute the boundary associator. We also study codimension one defects (surface operators) in abelian Chern-Simons theories. As an application, we obtain a classification of such theories up to isomorphism, in general agreement with the work of Belov and Moore.
Detecting unambiguously non-Abelian geometric phases with trapped ions
Zhang Xinding; Hu Liangbin; Zhu Shiliang [Institute for Condensed Matter Physics, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou (China); Wang, Z D [Department of Physics and Center of Theoretical and Computational Physics, University of Hong Kong, Pokfulam Road, Hong Kong (China); Zhang Zhiming [Laboratory of Photonic Information Technology, South China Normal University, Guangzhou (China)], E-mail: slzhu@scnu.edu.cn
2008-04-15
We propose an experimentally feasible scheme to disclose the noncommutative effects induced by a light-induced non-Abelian gauge structure with trapped ions. Under an appropriate configuration, a true non-Abelian gauge potential naturally arises in connection with the geometric phase associated with two degenerated dark states in a four-state atomic system interacting with three pulsed laser fields. We show that the population in the atomic state at the end of a composed path formed by two closed loops C{sub 1} and C{sub 2} in the parameter space can be significantly different from the composed counter-ordered path. This population difference is directly induced by the noncommutative feature of non-Abelian geometric phases and can be detected unambiguously with current technology.
Non-Abelian family symmetries as portals to dark matter
Varzielas, I. de Medeiros [School of Physics and Astronomy, University of Southampton,Highfield SO17 1BJ, Southampton (United Kingdom); Fischer, O. [Department of Physics, University of Basel,Klingelbergstr. 82, CH-4056 Basel (Switzerland)
2016-01-27
Non-Abelian family symmetries offer a very promising explanation for the flavour structure in the Standard Model and its extensions. We explore the possibility that dark matter consists in fermions that transform under a family symmetry, such that the visible and dark sector are linked by the familons - Standard Model gauge singlet scalars, responsible for spontaneously breaking the family symmetry. We study three representative models with non-Abelian family symmetries that have been shown capable to explain the masses and mixing of the Standard Model fermions. One of our central results is the possibility to have dark matter fermions and at least one familon with masses on and even below the experimentally accessible TeV scale. In particular we discuss the characteristic signatures in collider experiments from light familon fields with a non-Abelian family symmetry, and we show that run I of the LHC is already testing this class of models.
Non-Abelian Vortices on Riemann Surfaces: an Integrable Case
Popov, Alexander D
2008-01-01
We consider U(n+1) Yang-Mills instantons on the space \\Sigma\\times S^2, where \\Sigma is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n+1) instanton equations on \\Sigma\\times S^2 are equivalent to non-Abelian vortex equations on \\Sigma. Solutions to these equations are given by pairs (A,\\phi), where A is a gauge potential of the group U(n) and \\phi is a Higgs field in the fundamental representation of the group U(n). We briefly compare this model with other non-Abelian Higgs models considered recently. Afterwards we show that for g>1, when \\Sigma\\times S^2 becomes a gravitational instanton, the non-Abelian vortex equations are the compatibility conditions of two linear equations (Lax pair) and therefore the standard methods of integrable systems can be applied for constructing their solutions.
Abelian symmetries in multi-Higgs-doublet models
Ivanov, Igor P; Vdovin, Evgeny
2012-01-01
Classifying symmetry groups which can be implemented in the scalar sector of a model with $N$ Higgs doublets is a difficult and an unsolved task for $N>2$. Here, we make the first step towards this goal by classifying the Abelian symmetry groups. We describe a strategy that identifies all Abelian groups which can be realized as symmetry groups of the NHDM scalar potential. We give examples of the use of this strategy in 3HDM and 4HDM and prove several statements for arbitrary $N$.
Abelian Yang-Baxter deformations and TsT transformations
Osten, David; van Tongeren, Stijn J.
2017-02-01
We prove that abelian Yang-Baxter deformations of superstring coset σ models are equivalent to sequences of commuting TsT transformations, meaning T dualities and coordinate shifts. Our results extend also to fermionic deformations and fermionic T duality, and naturally lead to a TsT subgroup of the superduality group OSp (db ,db | 2df). In cases like AdS5 ×S5, fermionic deformations necessarily lead to complex models. As an illustration of inequivalent deformations, we give all six abelian deformations of AdS3. We comment on the possible dual field theory interpretation of these (super-)TsT models.
The Conformal Spectrum of Non-Abelian Anyons
Doroud, Nima; Turner, Carl
2016-01-01
We study the spectrum of multiple non-Abelian anyons in a harmonic trap. The system is described by Chern-Simons theory, coupled to either bosonic or fermionic non-relativistic matter, and has an SO(2,1) conformal invariance. We describe a number of special properties of the spectrum, focussing on a class of protected states whose energies are dictated by their angular momentum. We show that the angular momentum of a bound state of non-Abelian anyons is determined by the quadratic Casimirs of their constituents.
Abelian Yang-Baxter Deformations and TsT transformations
Osten, David
2016-01-01
We prove that abelian Yang-Baxter deformations of superstring coset sigma models are equivalent to sequences of commuting TsT transformations, meaning T dualities and coordinate shifts. Our results extend also to fermionic deformations and fermionic T duality, and naturally lead to a TsT subgroup of the superduality group OSp(d_b,d_b|2d_f). In cases like AdS_5 x S^5, fermionic deformations necessarily lead to complex models. As an illustration of inequivalent deformations, we give all six abelian deformations of AdS_3. We comment on the possible dual field theory interpretation of these (super-)TsT models.
Non-Abelian anyons: when Ising meets Fibonacci.
Grosfeld, E; Schoutens, K
2009-08-14
We consider an interface between two non-Abelian quantum Hall states: the Moore-Read state, supporting Ising anyons, and the k=2 non-Abelian spin-singlet state, supporting Fibonacci anyons. It is shown that the interface supports neutral excitations described by a (1+1)-dimensional conformal field theory with a central charge c=7/10. We discuss effects of the mismatch of the quantum statistical properties of the quasiholes between the two sides, as reflected by the interface theory.
Gribov ambiguities at the Landau -- maximal Abelian interpolating gauge
Pereira, A D
2014-01-01
In a previous work, we presented a new method to account for the Gribov ambiguities in non-Abelian gauge theories. The method consists on the introduction of an extra constraint which directly eliminates the infinitesimal Gribov copies without the usual geometric approach. Such strategy allows to treat gauges with non-hermitian Faddeev-Popov operator. In this work, we apply this method to a gauge which interpolates among the Landau and maximal Abelian gauges. The result is a local and power counting renormalizable action, free of infinitesimal Gribov copies. Moreover, the interpolating tree-level gluon propagator is derived.
Holographic flows in non-Abelian T-dual geometries
Macpherson, Niall T. [Dipartimento di Fisica, Università di Milano-Bicocca and INFN, sezione di Milano-Bicocca,I-20126 Milano (Italy); Núñez, Carlos [Department of Physics, Swansea University,Singleton Park, Swansea SA2 8PP (United Kingdom); Thompson, Daniel C. [Theoretische Natuurkunde, Vrije Universiteit Brussel & The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Zacarías, S. [Department of Nuclear and Particle Physics, Faculty of Physics, University of Athens,Athens 15784 (Greece); Departamento de Física, División de Ciencias e Ingenierías,Campus León, Universidad de Guanajuato,Loma del Bosque No. 103 Col. Lomas del Campestre, C.P. 37150, León, Guanajuato (Mexico)
2015-11-30
We use non-Abelian T-duality to construct new N=1 solutions of type IIA supergravity (and their M-theory lifts) that interpolate between AdS{sub 5} geometries. We initiate a study of the holographic interpretation of these backgrounds as RG flows between conformal fixed points. Along the way we give an elegant formulation of non-Abelian T-duality when acting on a wide class of backgrounds, including those corresponding to such flows, in terms of their SU(2) structure.
A Finite Abelian Group of Two-Letter Inversions
Sherwin E. Balbuena
2015-11-01
Full Text Available In abstract algebra, the study of concrete groups is fundamentally important to beginners. Most commonly used groups as examples are integer addition modulo n, real number addition and multiplication, permutation groups, and groups of symmetry. The last two examples are finite non-abelian groups and can be investigated with the aid of concrete representations. This study presents a finite abelian group of inversions of two letter symbols with vertical and horizontal axes of symmetry and whose binary operation is established through motions like alternation, rotation, reflection, and a combination of two or all motions.
Correlation-induced non-Abelian quantum holonomies
Johansson, Markus; Ericsson, Marie; Sjoeqvist, Erik [Department of Quantum Chemistry, Uppsala University, Box 518, Se-751 20 Uppsala (Sweden); Singh, Kuldip; Williamson, Mark S, E-mail: markus.johansson@kvac.uu.se, E-mail: marie.ericsson@kvac.uu.se, E-mail: sciks@nus.edu.sg, E-mail: erik.sjoqvist@kvac.uu.se, E-mail: m.s.williamson04@gmail.com [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore (Singapore)
2011-04-08
In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Levay geometric phase (2004 J. Phys. A: Math. Gen. 37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions.
Abelian Yang–Baxter deformations and TsT transformations
David Osten
2017-02-01
Full Text Available We prove that abelian Yang–Baxter deformations of superstring coset σ models are equivalent to sequences of commuting TsT transformations, meaning T dualities and coordinate shifts. Our results extend also to fermionic deformations and fermionic T duality, and naturally lead to a TsT subgroup of the superduality group OSp(db,db|2df. In cases like AdS5×S5, fermionic deformations necessarily lead to complex models. As an illustration of inequivalent deformations, we give all six abelian deformations of AdS3. We comment on the possible dual field theory interpretation of these (super-TsT models.
Sullivan, Terry [Brookhaven National Lab. (BNL), Upton, NY (United States). Biological, Environmental and Climate Sciences Dept.
2014-12-10
ZionSolutions is in the process of decommissioning the Zion Nuclear Power Plant in order to establish a new water treatment plant. There is some residual radioactive particles from the plant which need to be brought down to levels so an individual who receives water from the new treatment plant does not receive a radioactive dose in excess of 25 mrem/y⁻¹ as specified in 10 CFR 20 Subpart E. The objectives of this report are: (a) To present a simplified conceptual model for release from the buildings with residual subsurface structures that can be used to provide an upper bound on radionuclide concentrations in the fill material and the water in the interstitial spaces of the fill. (b) Provide maximum water concentrations and the corresponding amount of mass sorbed to the solid fill material that could occur in each building for use by ZSRP in selecting ROCs for detailed dose assessment calculations.
Stringy Sphalerons and Non-Abelian Black Holes
Donets, E E
1993-01-01
Static spherically symmetric asymptotically flat particle-like and black hole solutions are constructed within the SU(2) sector of 4-dimensional heterotic string effective action. They separate topologically distinct Yang-Mills vacua and are qualitatively similar to the Einstein-Yang-Mills spha- lerons and non-abelian black holes discussed recently. New solutions possess quantized values of the dilaton charge.
On the supersymmetric non-abelian Born-Infeld action
Bergshoeff, E.A.; Roo, M. de; Sevrin, A.
2001-01-01
We review an iterative construction of the supersymmetric non-abelian Born-Infeld action. We obtain the action through second order in the field strength. Kappa-invariance fixes the ordenings which turn out to deviate from the symmetrized trace proposal.
On the supersymmetric non-abelian Born-Infeld action
Bergshoeff, E. A.; de Roo, M.; Sevrin, A.
2000-01-01
We review an iterative construction of the supersymmetric non-abelian Born-Infeld action. We obtain the action through second order in the fieldstrength. Kappa-invariance fixes the ordenings which turn out to deviate from the symmetrized trace proposal.
Coleman Automorphisms of Holomorphs of Finite Abelian Groups
Zheng Xing LI; Jin Ke HAI
2014-01-01
Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for H .
ABELIAN-HIGGS HAIR FOR BLACK-HOLES
ACHUCARRO, A; GREGORY, R; KUIJKEN, K
1995-01-01
We find evidence for the existence of solutions of the Einstein and Abelian Higgs field equations describing a black hole pierced by a Nielsen-Olesen vortex. This situation falls outside the scope of the usual no-hair arguments due to the nontrivial topology of the vortex configuration and the
Quasiparticle operators with non-abelian braiding statistics
Cabra, D C; Rossini, G L; Cabra, Daniel C.; Moreno, Enrique F.; Rossini, Gerardo L.
1998-01-01
We study the gauge invariant fermions in the fermion coset representation of $SU(N)_k$ Wess-Zumino-Witten models which create, by construction, the physical excitations (quasiparticles) of the theory. We show that they provide an explicit holomorphic factorization of $SU(N)_k$ WZW primaries and satisfy non-abelian braiding relations.
Fibonacci anyons from Abelian bilayer quantum Hall states.
Vaezi, Abolhassan; Barkeshli, Maissam
2014-12-05
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out.
Non-Abelian vortices, Hecke modifications and singular monopoles
Baptista, J.M.
2010-01-01
In this note, we show that for the group G = U(N) the space of Hecke modifications of a rank N vector bundle over a Riemann surface C coincides with the moduli space of solutions of certain non-Abelian vortex equations over C. Through the recent work of Kapustin and Witten this then leads to an isom
Product integral formalism and non-Abelian Stokes theorem
Karp, R.L.; Mansouri, F. [Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221 (United States); Rno, J.S. [Department of Physics, University of Cincinnati-RWC, Cincinnati, Ohio 45236 (United States)
1999-11-01
We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-Abelian version of Stokes{close_quote} theorem. {copyright} {ital 1999 American Institute of Physics.}
Supersymmetric Wilson Loops and Super Non-Abelian Stokes Theorem
Karp, R L; Karp, Robert L.; Mansouri, Freydoon
2000-01-01
We generalize the standard product integral formalism to incorporateGrassmann valued matrices and show that the resulting supersymmetric productintegrals provide a natural framework for describing supersymmetric Wilsonlines and Wilson loops. We use this formalism to establish the supersymmetricversion of the non-Abelian Stokes Theorem.
Linear Resistivity from Non-Abelian Black Holes
Herzog, Christopher P; Vaz, Ricardo
2014-01-01
Starting with the holographic p-wave superconductor, we show how to obtain a finite DC conductivity through a non-abelian gauge transformation. The translational symmetry is preserved. We obtain phenomenological similarities with high temperature cuprate superconductors. Our results suggest that a lattice or impurities are not essential to produce a finite DC resistivity with a linear temperature dependence.
Metastable Supersymmetry Breaking Vacua on Abelian Brane Models
Halyo, Edi
2009-01-01
We construct Abelian brane models with metastable vacua which are obtained from deformations of ${\\cal N}=2$ supersymmetric brane configurations. One such model lives on a D4 brane stretched between two displaced and rotated NS5 branes. Another one lives on a D5 brane wrapped on a deformed and fibered $A_2$ singularity.
Supersymmetric non-abelian Born-Infeld revisited
Bergshoeff, EA; de Roo, M; Bilal, A; Sevrin, A
2001-01-01
We determine the non-abelian Born-Infeld action, including fermions, as it results from the four-point tree-level open superstring scattering amplitudes at order alpha'(2). We find that, after an appropriate field redefinition all terms at this order can be written as a symmetrised trace. We confron
The Markov-Zariski topology of an abelian group
Dikranjan, Dikran
2010-01-01
According to Markov, a subset of an abelian group G of the form {x in G: nx=a}, for some integer n and some element a of G, is an elementary algebraic set; finite unions of elementary algebraic sets are called algebraic sets. We prove that a subset of an abelian group G is algebraic if and only if it is closed in every precompact (=totally bounded) Hausdorff group topology on G. The family of all algebraic subsets of an abelian group G forms the family of closed subsets of a unique Noetherian T_1 topology on G called the Zariski, or verbal, topology of G. We investigate the properties of this topology. In particular, we show that the Zariski topology is always hereditarily separable and Frechet-Urysohn. For a countable family F of subsets of an abelian group G of cardinality at most the continuum, we construct a precompact metric group topology T on G such that the T-closure of each member of F coincides with its Zariski closure. As an application, we provide a characterization of the subsets of G that are de...
Abelian extensions of algebras in congruence-modular varieties
Rowan, William H.
2000-01-01
We define abelian extensions of algebras in congruence-modular varieties. The theory is sufficiently general that it includes, in a natural way, extensions of R-modules for a ring R. We also define a cohomology theory, which we call clone cohomology, such that the cohomology group in dimension one is the group of equivalence classes of extensions.
Information sets from defining sets in abelian codes
Bernal, José Joaquín
2011-01-01
We describe a technique to construct a set of check positions (and hence an information set) for every abelian code solely in terms of its defining set. This generalizes that given by Imai in \\cite{Imai} in the case of binary TDC codes.
Nonequilibrium formulation of abelian gauge theories
Zoeller, Thorsten
2013-09-01
This work is about a formulation of abelian gauge theories out-of-equilibrium. In contrast to thermal equilibrium, systems out-of-equilibrium are not constant in time, and the interesting questions in such systems refer to time evolution problems. After a short introduction to quantum electrodynamics (QED), the two-particle irreducible (2PI) effective action is introduced as an essential technique for the study of quantum field theories out-of-equilibrium. The equations of motion (EOMs) for the propagators of the theory are then derived from it. It follows a discussion of the physical degrees of freedom (DOFs) of the theory, in particular with respect to the photons, since in covariant formulations of gauge theories unphysical DOFs are necessarily contained. After that the EOMs for the photon propagator are examined more closely. It turns out that they are structurally complicated, and a reformulation of the equations is presented which for the untruncated theory leads to an essential structural simplification of the EOMs. After providing the initial conditions which are necessary in order to solve the EOMs, the free photon EOMs are solved with the help of the reformulated equations. It turns out that the solutions diverge in time, i.e. they are secular. This is a manifestation of the fact that gauge theories contain unphysical DOFs. It is reasoned that these secularities exist only in the free case and are therefore ''artificial''. It is however emphasized that they may not be a problem in principle, but certainly are in practice, in particular for the numerical solution of the EOMs. Further, the origin of the secularities, for which there exists an illustrative explanation, is discussed in more detail. Another characteristic feature of 2PI formulations of gauge theories is the fact that quantities calculated from approximations of the 2PI effective action, which are gauge invariant in the exact theory as well as in an approximated theory at
Non-Abelian Vortex in Four Dimensions as a Critical String on a Conifold
Koroteev, Peter; Yung, Alexei
2016-01-01
Non-Abelian vortex strings supported in a certain four-dimensional N=2 Yang-Mills theory with fundamental matter were shown arXiv:1502.00683 to become critical superstrings. In addition to translational moduli non-Abelian string under consideration carries orientational and size moduli. Their dynamics is described by two-dimensional sigma model whose target space is a tautological bundle over the complex projective space. For the N=2 theory with the $U(2)$ gauge group and four fundamental hypermultiplets there are six orientational and size moduli. After combining with four translational moduli they form a ten-dimensional target space required for a superstring to be critical. For the theory in question the target space of the sigma model is C^2 x Y_6, where Y_6 is a conifold. We study closed string states which emerge in four dimensions (4D) and identify them with hadrons of the 4D bulk N=2 theory. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D...
Non-Abelian vortex in four dimensions as a critical string on a conifold
Koroteev, P.; Shifman, M.; Yung, A.
2016-09-01
Non-Abelian vortex strings supported in a certain four-dimensional N =2 Yang-Mills theory with fundamental matter were shown [1] to become critical superstrings. In addition to translational moduli, the non-Abelian strings under consideration carry orientational and size moduli. Their dynamics is described by the two-dimensional sigma model whose target space is a tautological bundle over the complex projective space. For the N =2 theory with the U (2 ) gauge group and four fundamental hypermultiplets, there are six orientational and size moduli. After combining with four translational moduli, they form a ten-dimensional target space, which is required for a superstring to be critical. For the theory in question, the target space of the sigma model is C2×Y6, where Y6 is a conifold. We study closed string states which emerge in four dimensions (4D) and identify them with hadrons of the 4D bulk N =2 theory. It turns out that most of the states arising from the ten-dimensional graviton spectrum are nondynamical in 4D. We find a single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold. We interpret this degree of freedom as a monopole-monopole baryon of the 4D theory (at strong coupling).
Kinkhabwala, Ali
2013-01-01
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation: Which candidate distribution provides the best fit to the observed data?, (2) Goodness-of-fit: How concordant is this distribution with the observed data?, and (3) Uncertainty: How concordant are other candidate distributions with the observed data? A simple unified approach for univariate data that addresses these traditionally distinct statistical notions is presented called "maximum fidelity". Maximum fidelity is a strict frequentist approach that is fundamentally based on model concordance with the observed data. The fidelity statistic is a general information measure based on the coordinate-independent cumulative distribution and critical yet previously neglected symmetry considerations. An approximation for the null distribution of the fidelity allows its direct conversi...
Coulomb, Landau and Maximally Abelian Gauge Fixing in Lattice QCD with Multi-GPUs
Schröck, Mario
2013-01-01
A lattice gauge theory framework for simulations on graphic processing units (GPUs) using NVIDIA's CUDA is presented. The code comprises template classes that take care of an optimal data pattern to ensure coalesced reading from device memory to achieve maximum performance. In this work we concentrate on applications for lattice gauge fixing in 3+1 dimensional SU(3) lattice gauge field theories. We employ the overrelaxation, stochastic relaxation and simulated annealing algorithms which are perfectly suited to be accelerated by highly parallel architectures like GPUs. The applications support the Coulomb, Landau and maximally Abelian gauges. Moreover, we explore the evolution of the numerical accuracy of the SU(3) valued degrees of freedom over the runtime of the algorithms in single (SP) and double precision (DP). Therefrom we draw conclusions on the reliability of SP and DP simulations and suggest a mixed precision scheme that performs the critical parts of the algorithm in full DP while retaining 80-90% of...
A New Approach to Non-Abelian Hydrodynamics
Fernandez-Melgarejo, Jose J; Surówka, Piotr
2016-01-01
We present a new approach to hydrodynamics carrying non-Abelian macroscopic degrees of freedom. Our derivation is based on the Kaluza-Klein compactification of higher-dimensional neutral dissipative fluid on a group manifold. We obtain colored dissipative fluid coupled to Yang-Mills gauge field in reduced spacetime. The transport coefficients of the new fluid, which show a non-Abelian character, are expressed in terms of the higher-dimensional quantities. In particular, we obtain group-valued terms in the gradient expansions and response quantities such as the conductivity matrix and the chemical potentials. We discuss links between this system and quark-gluon plasma as well as fluid/gravity duality.
Non-Abelian Vortices with an Aharonov-Bohm Effect
Evslin, Jarah; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2014-01-01
The interplay of gauge dynamics and flavor symmetries often leads to remarkably subtle phenomena in the presence of soliton configurations. Non-Abelian vortices -- vortex solutions with continuous internal orientational moduli -- provide an example. Here we study the effect of weakly gauging a U(1)_R subgroup of the flavor symmetry on such BPS vortex solutions. Our prototypical setting consists of an SU(2) x U(1) gauge theory with N_f=2 sets of fundamental scalars that break the gauge symmetry to an "electromagnetic" U(1). The weak U(1)_R gauging converts the well-known CP1 orientation modulus |B| of the non-Abelian vortex into a parameter characterizing the strength of the magnetic field that is responsible for the Aharonov-Bohm effect. As the phase of B remains a genuine zero mode while the electromagnetic gauge symmetry is Higgsed in the interior of the vortex, these solutions are superconducting strings.
Supersymmetry Breaking on Gauged Non-Abelian Vortices
Konishi, Kenichi; Vinci, Walter
2012-01-01
There are a large number of systems characterized by a completely broken gauge symmetry, but with an unbroken global color-flavor diagonal symmetry, i.e., systems in the so-called color-flavor locked phase. If the gauge symmetry breaking supports vortices, the latter develop non-Abelian orientational zero-modes and become non-Abelian vortices, a subject of intense study in the last several years. In this paper we consider the effects of weakly gauging the full exact global flavor symmetry in such systems, deriving an effective description of the light excitations in the presence of a vortex. Surprising consequences are shown to follow. The fluctuations of the vortex orientational modes get diffused to bulk modes through tunneling processes. When our model is embedded in a supersymmetric theory, the vortex is still 1/2 BPS saturated, but the vortex effective action breaks supersymmetry.
Maximal Abelian gauge and a generalized BRST transformation
Deguchi, Shinichi; Mandal, Bhabani Prasad
2016-01-01
We apply a generalized Becchi-Rouet-Stora-Tyutin (BRST) formulation to establish a connection between the gauge-fixed $SU(2)$ Yang-Mills (YM) theories formulated in the Lorenz gauge and in the Maximal Abelian (MA) gauge. It is shown that the generating functional corresponding to the Faddeev-Popov (FP) effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST) transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.
Effective theories of connections and curvature: abelian case
Diaz-Marin, Homero G
2011-01-01
We introduce a notion of measuring scales for quantum abelian gauge systems. At each measuring scale a finite dimensional affine space stores information about the evaluation of the curvature on a discrete family of surfaces. Affine maps from the spaces assigned to finer scales to those assigned to coarser scales play the role of coarse graining maps. This structure induces a continuum limit space which contains information regarding curvature evaluation on all piecewise linear surfaces with boundary. The evaluation of holonomies along contractible loops is also encoded in the spaces introduced here; thus, our framework is closely related to loop quantization and it allows us to discuss effective theories in a sensible way. We develop basic elements of measure theory on the introduced spaces which are essential for the applicability of the framework to the construction of quantum abelian gauge theories.
Non-Abelian 3d Bosonization and Quantum Hall States
Radicevic, Djordje; Turner, Carl
2016-01-01
Bosonization dualities relate two different Chern-Simons-matter theories, with bosonic matter on one side replaced by fermionic matter on the other. We first describe a more general class of non-Abelian bosonization dualities. We then explore the non-relativistic physics of these theories in the quantum Hall regime. The bosonic theory lies in a condensed phase and admits vortices which are known to form a non-Abelian quantum Hall state. We ask how this same physics arises in the fermionic theory. We find that a condensed boson corresponds to a fully filled Landau level of fermions, while bosonic vortices map to fermionic holes. We confirm that the ground state of the two theories is indeed described by the same quantum Hall wavefunction.
Topologically stratified energy minimizers in a product Abelian field theory
Han, Xiaosen; Yang, Yisong
2015-09-01
We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s = 1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1, P2 anti-vortices of two designated species exists if and only if the inequalities
Self-gravitating non-abelian kinks as brane worlds
Melfo, Alejandra; Pantoja, Nelson; Skirzewski, Aureliano; Vasquez, Juan Carlos
2011-01-01
We address the properties of self-gravitating domain walls arising from the breaking of an SU(N) x Z_2- symmetric theory. In the particular case of N=5, we find that the two classes of stable non-abelian kinks possible in flat space have an analogue in the gravitational case, and construct the analytical solutions. Localization of fermion fields in different representations of the gauge group in these branes is investigated. It is also shown that non-abelian gauge fields localization cannot be achieved through interactions with the brane, but that in one of the two classes of kinks this localization can be implemented via the Dvali-Shifman mechanism.
Maximal Abelian gauge and a generalized BRST transformation
Shinichi Deguchi
2016-05-01
Full Text Available We apply a generalized Becchi–Rouet–Stora–Tyutin (BRST formulation to establish a connection between the gauge-fixed SU(2 Yang–Mills (YM theories formulated in the Lorenz gauge and in the Maximal Abelian (MA gauge. It is shown that the generating functional corresponding to the Faddeev–Popov (FP effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.
Statistical dynamics of a non-Abelian anyonic quantum walk
Lehman, Lauri; Brennen, Gavin K; Pachos, Jiannis K; Wang, Zhenghan
2010-01-01
We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.
Kau, Thomas [Klinikum Klagenfurt, General Hospital of Klagenfurt, Institute of Diagnostic and Interventional Radiology, Klagenfurt (Austria); Klinikum Klagenfurt am Worthersee, Radiologie, Klagenfurt (Austria); Eicher, Wolfgang; Reiterer, Christian; Niedermayer, Martin; Rabitsch, Egon; Hausegger, Klaus A. [Klinikum Klagenfurt, General Hospital of Klagenfurt, Institute of Diagnostic and Interventional Radiology, Klagenfurt (Austria); Senft, Birgit [Section of Statistics, Reha Clinic for Mental Health, Klagenfurt (Austria)
2011-08-15
To evaluate the accuracy of dual-energy CT angiography (DE-CTA) maximum intensity projections (MIPs) in symptomatic peripheral arterial occlusive disease (PAOD). In 58 patients, DE-CTA of the lower extremities was performed on dual-source CT. In a maximum of 35 arterial segments, severity of the most stenotic lesion was graded (<10%, 10-49% and 50-99% luminal narrowing or occlusion) independently by two radiologists, with DSA serving as the reference standard. In DSA, 52.3% of segments were significantly stenosed or occluded. Agreement of DE-CTA MIPs with DSA was good in the aorto-iliac and femoro-popliteal regions ({kappa} = 0.72; {kappa} = 0.66), moderate in the crural region ({kappa} = 0.55), slight in pedal arteries ({kappa} = 0.10) and very good in bypass segments ({kappa} = 0.81). Accuracy was 88%, 78%, 74%, 55% and 82% for the respective territories and moderate (75%) overall, with good sensitivity (84%) and moderate specificity (67%). Sensitivity and specificity was 82% and 76% in claudicants and 84% and 61% in patients with critical limb ischaemia. While correlating well with DSA above the knee, accuracy of DE-CTA MIPs appeared to be moderate in the calf and largely insufficient in calcified pedal arteries, especially in patients with critical limb ischaemia. (orig.)
Holomorphic Vector Bundle on Hopf Manifolds with Abelian Fundamental Groups
Xiang Yu ZHOU; Wei Ming LIU
2004-01-01
Let X be a Hopf manifolds with an Abelian fundamental group. E is a holomorphic vector bundle of rank r with trivial pull-back to W = Cn - {0}. We prove the existence of a non-vanishing section of L(×) E for some line bundle on X and study the vector bundles filtration structure of E. These generalize the results of D. Mall about structure theorem of such a vector bundle E.
An Exact Chiral Spin Liquid with Non-Abelian Anyons
Yao, Hong
2010-04-06
We establish the existence of a chiral spin liquid (CSL) as the exact ground state of the Kitaev model on a decorated honeycomb lattice, which is obtained by replacing each site in the familiar honeycomb lattice with a triangle. The CSL state spontaneously breaks time reversal symmetry but preserves other symmetries. There are two topologically distinct CSLs separated by a quantum critical point. Interestingly, vortex excitations in the topologically nontrivial (Chern number {+-}1) CSL obey non-Abelian statistics.
Cohomology of mapping class groups and the abelian moduli space
Andersen, Jørgen Ellegaard; Villemoes, Rasmus
2012-01-01
We consider a surface Σ of genus g≥3 , either closed or with exactly one puncture. The mapping class group Γ of Σ acts symplectically on the abelian moduli space M=Hom(π 1 (Σ),U(1))=Hom(H 1 (Σ),U(1)) , and hence both L 2 (M) and C ∞ (M) are modules over Γ . In this paper, we prove that both the c...
Some Equivalent Multiresolution Conditions on Locally Compact Abelian Groups
R A Kamyabi-Gol; R Raisi Tousi
2010-06-01
Conditions under which a function generates a multiresolution analysis are investigated. The definition of the spectral function of a shift invariant space is generalized from $\\mathbb{R}^n$ to a locally compact abelian group and the union density and intersection triviality properties of a multiresolution analysis are characterized in terms of the spectral functions. Finally, all multiresolution analysis conditions are characterized in terms of the scaling and the spectral functions.
Residual Non-Abelian Dark Matter and Dark Radiation
Ko, P.; Tang, Yong
2016-01-01
We propose a novel particle physics model in which vector dark matter (VDM) and dark radiation (DR) originate from the same non-Abelian dark sector. We show an illustrating example where dark $SU(3)$ is spontaneously broken into $SU(2)$ subgroup by the nonzero vacuum expectation value of a complex scalar in fundamental representation of $SU(3)$. The massless gauge bosons associated with the residual unbroken $SU(2)$ constitute DR and help to relieve the tension in Hubble constant measurements...
Non-Abelian String of a Finite Length
Monin, Sergey; Yung, Alexei
2015-01-01
We consider world-sheet theories for non-Abelian strings assuming compactification on a cylinder with a finite circumference $L$ and periodic boundary conditions. The dynamics of the orientational modes is described by two-dimensional CP$(N-1)$ model. We analyze both non-supersymmetric (bosonic) model and ${\\mathcal N}=(2,2)$ supersymmetric CP$(N-1)$ emerging in the case of 1/2-BPS saturated strings in \
Non Abelian orbifold compactifications of the heterotic string
Konopka, Sebastian J H
2012-01-01
I consider the construction of heterotic orbifold models having a toroidal orbifold with non Abelian point group. I construct an explicit model based on the point group $S_3$ and calculate the spectrum and remnant symmetries. This model provides a simple example of rank reduction of the Yang--Mills gauge group directly in the string theory rather than in the effective field theory. I check consistency of the construction by verifying that all continous and discrete symmetries are non anomalous.
Non-Abelian discrete gauge symmetries in F-theory
Grimm, Thomas W; Regalado, Diego
2015-01-01
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the exp...
Non-Abelian magnetized blackholes and unstable attractors
Mosaffa, A.E. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail: mosaffa@theory.ipm.ac.ir; Randjbar-Daemi, S. [The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11 34014, Trieste (Italy)], E-mail: seif@ictp.trieste.it; Sheikh-Jabbari, M.M. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail: jabbari@theory.ipm.ac.ir
2008-01-21
Fluctuations of non-Abelian gauge fields in a background magnetic charge contain 'tachyonic' modes which as we will show cause an instability of the background. We extend this result to the cases where the background charge (flux) is coupled to four-dimensional Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of (colored) Reissner-Nordstroem blackholes or the AdS{sub 2}xS{sup 2}, are also unstable unless the flux assumes its smallest allowed value, in which case the configuration is stable. We discuss the relevance of these instabilities to several places in string theory including various string compactifications and the attractor mechanism. Our results for the latter imply that the attractor mechanism shown to work for the extremal Abelian charged blackholes, cannot be applied in a straightforward way to the extremal non-Abelian colored blackholes, with the exception of the minimally charged stable ones.
Designer non-Abelian anyon platforms: from Majorana to Fibonacci
Alicea, Jason; Stern, Ady
2015-12-01
The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has evolved from a highly theoretical subject to an active experimental area, particularly following proposals for trapping non-Abelian anyons in ‘engineered’ structures built from well-understood components. In this short overview we briefly tour the impressive progress that has taken place in the quest for the simplest type of non-Abelian anyon—defects binding Majorana zero modes—and then turn to similar strategies for pursuing more exotic excitations. Specifically, we describe how interfacing simple quantum Hall systems with conventional superconductors yields ‘parafermionic’ generalizations of Majorana modes and even Fibonacci anyons—the latter enabling fully fault tolerant universal quantum computation. We structure our treatment in a manner that unifies these topics in a coherent way. The ideas synthesized here spotlight largely uncharted experimental territory in the field of quantum Hall physics that appears ripe for discovery.
The Static Quark Potential from the Gauge Independent Abelian Decomposition
Cundy, Nigel; Lee, Weonjong
2015-01-01
We investigate the relationship between colour confinement and the gauge independent Cho-Duan-Ge Abelian decomposition. The decomposition is defined in terms of a colour field $n$; the principle novelty of our study is that we have defined this field in terms of the eigenvectors of the Wilson Loop. This establishes an equivalence between the path ordered integral of the non-Abelian gauge fields with an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without needing an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field $n$ winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to a area law scaling for the Wilson Loop and ...
Algebra of Observables and States for Quantum Abelian Duality
Capoferri, Matteo
2016-01-01
The study of dualities is a central issue in several modern approaches to quantum field theory, as they have broad consequences on the structure and on the properties of the theory itself. We call Abelian duality the generalisation to arbitrary spacetime dimension of the duality between electric and magnetic field in Maxwell theory. In the present thesis, in the framework of algebraic quantum field theory, the Abelian duality for quantum field theory on globally hyperbolic spacetime with compact Cauchy surface is tackled. Fistly, the algebra of observables is constructed. It is shown that it can be presented as the direct sum of three pre-symplectic Abelian groups, each corresponding to a different sector of the theory. As a consequence, it is possible to provide quantum states for the theory by building separate states on each direct summand. In particular, explicit examples in two and four dimensions are discussed thoroughly; a ground Hadamard state in a suitable sense is proved to exist for both of them. L...
Vortex states in a non-Abelian magnetic field
Nikolić, Predrag
2016-08-01
A type-II superconductor survives in an external magnetic field by admitting an Abrikosov lattice of quantized vortices. This is an imprint of the Aharonov-Bohm effect created by the Abelian U(1) gauge field. The simplest non-Abelian analog of such a gauge field, which belongs to the SU(2) symmetry group, can be found in topological insulators. Here we discover a superconducting ground state with a lattice of SU(2) vortices in a simple two-dimensional model that presents an SU(2) "magnetic" field (invariant under time reversal) to attractively interacting fermions. The model directly captures the correlated topological insulator quantum well, and approximates one channel for instabilities on the Kondo topological insulator surface. Due to its simplicity, the model might become amenable to cold atom simulations in the foreseeable future. The vitality of low-energy vortex states born out of SU(2) magnetic fields is promising for the creation of incompressible vortex liquids with non-Abelian fractional excitations.
Maximum Intensity Projection Based on Visual Perception Enhancement%基于视觉感知增强的最大密度投影算法∗
周志光; 陶煜波; 林海
2013-01-01
This paper proposed a maximum intensity projection method to enhance the depth and shape perception of the internal maximum intensity features, without a sophisticated or time-consuming transfer function specification. On the basis of a traditional maximum intensity projection, the study first searched for the boundary sample with a similar intensity value and the optimal normal in front of the maximum intensity feature. Through by comparing the intensity and gradient norm. Next, the local illumination coefficients were updated according to the depth of boundary structures, the consequential depth-based shading results largely enhanced the depth, and the shape perception of internal feasible structures. A two-threshold region growing scheme was designed to perform and further highlight the features of interest. The seed was selected by users interactively on the rendered image, and the growing process depended on the intensity values and 3D spatial distances of the boundary samples with optimal normal. The comparison results showed that the proposed method provided more depth cues and shape information of the maximum intensity features than traditional methods and had practical applications in medical and engineering fields.% 提出一种基于视觉感知增强的最大密度投影算法，无需调节复杂的传输函数，就可以有效增强体数据内部最大密度特征的深度感知和形状感知。在传统的最大密度投影算法的基础上，利用梯度模属性精确查找特征或相似特征的边界，以确定最佳法向特征；利用最佳法向特征的深度信息自适应地修改局部光照系数，进而对最大密度特征进行光照处理，以获得视觉感知增强的可视化结果；采用基于密度值和三维空间距离的双阈值区域增长策略，动态区分感兴趣区域和背景区域，交互地实现特征突出显示。实验结果表明，该算法在传统算法的基础上
The N = 1 Supersymmetric Wong Equations and the Non-Abelian Landau Problem
Fanuel, Michaël; Avossevou, Gabriel Y H; Dossa, Anselme F
2014-01-01
A Lagrangian formulation is given extending to N = 1 supersymmetry the motion of a charged point particle with spin in a non-abelian external field. The classical formulation is constructed for any external static non-abelian SU(N) gauge potential. As an illustration, a specific gauge is fixed enabling canonical quantization and the study of the supersymmetric non-abelian Landau problem. The spectrum of the quantum Hamiltonian operator follows in accordance with the supersymmetric structure.
Ruiz Fernández, Jesús; Oliva, Marc; Fernández Menéndez, Susana del Carmen; García Hernández, Cristina; Menéndez Duarte, Rosa Ana; Pellitero Ondicol, Ramón; Pérez Alberti, Augusto; Schimmelpfennig, Irene
2017-04-01
CRONOANTAR brings together researchers from Spain, Portugal, France and United Kingdom with the objective of spatially and temporally reconstruct the deglaciation process at the two largest islands in the South Shetlands Archipelago (Maritime Antarctica), since the Global Last Glacial Maximum. Glacier retreat in polar areas has major implications at a local, regional and even planetary scale. Global average sea level rise is the most obvious and socio-economically relevant, but there are others such as the arrival of new fauna to deglaciated areas, plant colonisation or permafrost formation and degradation. This project will study the ice-free areas in Byers and Hurd peninsulas (Livingston Island) and Fildes and Potter peninsulas (King George Island). Ice-cap glacier retreat chronology will be revealed by the use of cosmogenic isotopes (mainly 36Cl) on glacially originated sedimentary and erosive records. Cosmogenic dating will be complemented by other dating methods (C14 and OSL), which will permit the validation of these methods in regions with cold-based glaciers. Given the geomorphological evidences and the obtained ages, a deglaciation calendar will be proposed and we will use a GIS methodology to reconstruct the glacier extent and the ice thickness. The results emerging from this project will allow to assess whether the high glacier retreat rates observed during the last decades were registered in the past, or if they are conversely the consequence (and evidence) of the Global Change in Antarctica. Acknowledgements This work has been funded by the Spanish Ministry of Economy, Industry and Competitiveness (Reference: CTM2016-77878-P).
Li, Xubin, E-mail: lixb@bjmu.edu.cn [Department of Radiology, Tianjin Medical University Cancer Institute and Hospital, National Clinical Reseaech Center for Cancer, Tianjin, Key Laboratory of Cancer Prevention and Therapy, Tianjin 300060 (China); Liu, Xia; Du, Xiangke [Department of Radiology, Peking University People' s Hospital, Beijing 100044 (China); Ye, Zhaoxiang [Department of Radiology, Tianjin Medical University Cancer Institute and Hospital, National Clinical Reseaech Center for Cancer, Tianjin, Key Laboratory of Cancer Prevention and Therapy, Tianjin 300060 (China)
2014-05-15
Purpose: To evaluate the diagnostic performance of three-dimensional (3D) MR maximum intensity projection (MIP) in the assessment of synovitis of the hand and wrist in rheumatoid arthritis (RA) compared to 3D contrast-enhanced magnetic resonance imaging (CE-MRI). Materials and methods: Twenty-five patients with RA underwent MR examinations. 3D MR MIP images were derived from the enhanced images. MR images were reviewed by two radiologists for the presence and location of synovitis of the hand and wrist. The diagnostic sensitivity, specificity and accuracy of 3D MIP were, respectively, calculated with the reference standard 3D CE-MRI. Results: In all subjects, 3D MIP images yielded directly and clearly the presence and location of synovitis with just one image. Synovitis demonstrated high signal intensity on MIP images. The k-values for the detection of articular synovitis indicated excellent interobserver agreements using 3D MIP images (k = 0.87) and CE-MR images (k = 0.91), respectively. 3D MIP demonstrated a sensitivity, specificity and accuracy of 91.07%, 98.57% and 96.0%, respectively, for the detection of synonitis. Conclusion: 3D MIP can provide a whole overview of lesion locations and a reliable diagnostic performance in the assessment of articular synovitis of the hand and wrist in patients with RA, which has potential value of clinical practice.
A Scheme for Simulation of Quantum Gates by Abelian Anyons
沈尧; 艾青; 龙桂鲁
2011-01-01
Anyons can be used to realize quantum computation, because they are two-level systems in two dimensions. In this paper, we propose a scheme to simulate single-qubit gates and CNOT gate using Abelian anyons in the Kitaev model. Two pairs of anyons （six spins） are used to realize single-qubit gates, while ten spins are needed for the CNOT gate. Based on these quantum gates, we show how to realize the Grover algorithm in a two-qubit system.
Semiclassical strings and non-Abelian T-duality
Zacarías, S., E-mail: szacarias@fisica.ugto.mx [Department of Physics, Swansea University, Singleton Park, Swansea SA2 8PP (United Kingdom); Departamento de Física, División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque No. 103 Col. Lomas del Campestre, C.P. 37150, León, Guanajuato, México (Mexico)
2014-10-07
We study semiclassical strings in the Klebanov–Witten and in the non-Abelian T-dual Klebanov–Witten backgrounds. We show that both backgrounds share a subsector of equivalent states up to conditions on the T-dual coordinates. We also analyse string configurations where the strings are stretched along the T-dual coordinates. This semiclassical analysis predicts the existence of (almost) chiral primary operators for the dual superconformal field theory whose (anomalous) bare dimensions depend on the T-dual coordinates. We briefly discuss the Penrose limit of the dualised background.
Primordial Magnetic Fields, Right Electrons, and the Abelian Anomaly
Joyce, M
1997-01-01
In the standard model there are charges with abelian anomaly only (e.g. right-handed electron number) which are effectively conserved in the early universe until some time shortly before the electroweak scale. A state at finite chemical potential of such a charge, possibly arising due to asymmetries produced at the GUT scale, is unstable to the generation of hypercharge magnetic field. We argue that quite large magnetic fields ($\\sim 10^{23}$ gauss at $T\\sim 3$ TeV with typical inhomogeneity scale up to $\\sim interest, potentially acting as seeds for amplification to larger scale magnetic fields through non-linear mechanisms.
Non-abelian T-duality, generalised geometry and holography
Macpherson, Niall T
2013-01-01
Recent progress which relates non-abelian T-duality of $\\mathcal{N}=1$ SuGra solutions to the powerful techniques of Generalised geometry is reviewed. It is shown that SU(3) structure solutions are mapped to SU(2) structures and the transformation rule of the corresponding pure spinors is presented. This constitutes an important step on the road towards the utility of the duality within holography, showing for example, how smeared sources must transform and so how to add flavour to the T-duals.
Abelian Cosmic String in the Starobinsky model of gravity
Graça, J P Morais
2015-01-01
In this paper, I analyze numerically the behaviour of the solutions corresponding to an Abelian string in the framework of the Starobinsky model. The role played by the quadratic term in the Lagrangian density $f(R) = R + \\eta R^2$ of this model is emphasized and the results are compared with the corresponding ones obtained in the framework of Einstein's theory of gravity. I have found that the angular deficit generated by the string is lowered as the $\\eta$ parameter increases, allowing a well-behaved spacetime for a large range of values of the symmetry-breaking scale.
Non-Abelian Magnetized Blackholes and Unstable Attractors
Mosaffa, A. E.; Randjbar-Daemi, S.; Sheikh-Jabbari, M. M.
2006-01-01
Fluctuations of non-Abelian gauge fields in a background magnetic flux contain tachyonic modes and hence the background is unstable. We extend these results to the cases where the background flux is coupled to Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of Reissner-Nordstrom blackholes or the AdS_2xS^2, are also unstable. We discuss the relevance of these instabilities to several places in s...
The group of homomorphisms of abelian torsion groups
M. W. Legg
1979-01-01
Full Text Available Let G and A be abelian torsion groups. In[5], R. S. Pierce develops a complete set of invariants for Hom(G, A. To compute these invariants he introduces, and uses extensively, the group of small homomorphisms of G into A. Also, using some of Pierce's methods, Fuchs characterizes this group in [1]. Our purpose in this paper is to characterize Hom(G, A in what seems to be a more natural manner than either of the treatments just mentioned.
Abelian tensor hierarchy in 4D, N = 1 superspace
Becker, Katrin; Becker, Melanie; Linch, William D.; Robbins, Daniel
2016-03-01
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N =1superspaceandconstructitsChern-Simons-likeinvariants. Whenspecializedtothe case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N = 1 superfields.
Abelian realization of phenomenological two-zero neutrino textures
González Felipe, R., E-mail: ricardo.felipe@ist.utl.pt [Instituto Superior de Engenharia de Lisboa – ISEL, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa (Portugal); Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Serôdio, H., E-mail: hugo.serodio@ific.uv.es [Departament de Física Teòrica and IFIC, Universitat de València-CSIC, E-46100 Burjassot (Spain)
2014-09-15
In an attempt at explaining the observed neutrino mass-squared differences and leptonic mixing, lepton mass matrices with zero textures have been widely studied. In the weak basis where the charged lepton mass matrix is diagonal, various neutrino mass matrices with two zeros have been shown to be consistent with the current experimental data. Using the canonical and Smith normal form methods, we construct the minimal Abelian symmetry realizations of these phenomenological two-zero neutrino textures. The implementation of these symmetries in the context of the seesaw mechanism for Majorana neutrino masses is also discussed.
A theory for non-Abelian superfluid dynamics
Jain, Akash
2016-01-01
We write down a theory for non-Abelian superfluids with a partially broken (semisimple) Lie group. We adapt the offshell formalism of hydrodynamics to superfluids and use it to comment on the superfluid transport compatible with the second law of thermodynamics. We find that the second law can be also used to derive the Josephson equation, which governs dynamics of the Goldstone modes. In the course of our analysis, we derive an alternate and mutually distinct parametrization of the recently proposed classification of hydrodynamic transport and generalize it to superfluids.
Non Abelian TQFT and scattering of self dual field configuration
Gianvittorio, R; Sánchez, J F
1999-01-01
A non-abelian topological quantum field theory describing the scattering of self-dual field configurations over topologically non-trivial Riemann surfaces, arising from the reduction of 4-dim self-dual Yang-Mills fields, is introduced. It is shown that the phase space of the theory can be exactly quantized in terms of the space of holomorphic structures over stable vector bundles of degree zero over Riemann surfaces. The Dirac monopoles are particular static solutions of the field equations. Its relation to topological gravity is discussed.
Remark on non-Abelian classical kinetic theory
Laine, Mikko; Laine, Mikko; Manuel, Cristina
2002-01-01
It is known that non-Abelian classical kinetic theory reproduces the Hard Thermal/Dense Loop (HTL/HDL) effective action of QCD, obtained after integrating out the hardest momentum scales from the system, as well as the first higher dimensional operator beyond the HTL/HDL level. We discuss here its applicability at still higher orders, by comparing the exact classical effective action obtained in the static limit, with the 1-loop quantum effective potential. We remark that while correct types of operators arise, the classical colour algebra reproduces correctly the prefactor of the 4-point function $tr A_0^4$ only for matter in asymptotically high dimensional colour representations.
Multiple conjugay problem in graphs of free abelian groups
Beeker, Benjamin
2011-01-01
A group G is a vGBS group if it admits a decomposition as a finite graph of groups with all edge and vertex groups finitely generated and free abelian. We prove that the multiple conjugacy problem is solvable between two n-tuples A and B of elements of G whenever the elements of A does not generate an elliptic subgroup. When the edge and vertex groups are infinite cyclic, i.e. G is a Generalized Baumslag-Solitar group, we prove that the multiple conjugacy problem is fully solvable.
Automatic structures and growth functions for finitely generated abelian groups
Kamei, Satoshi
2011-01-01
In this paper, we consider the formal power series whose n-th coefficient is the number of copies of a given finite graph in the ball of radius n centred at the identity element in the Cayley graph of a finitely generated group and call it the growth function. Epstein, Iano-Fletcher and Uri Zwick proved that the growth function is a rational function if the group has a geodesic automatic structure. We compute the growth function in the case where the group is abelian and see that the denominator of the rational function is determined from the rank of the group.
Rotating black holes with non-Abelian hair
Kleihaus, Burkhard; Navarro-Lerida, Francisco
2016-01-01
We here review asymptotically flat rotating black holes in the presence of non-Abelian gauge fields. Like their static counterparts these black holes are no longer uniquely determined by their global charges. In the case of pure SU(2) Yang-Mills fields, the rotation generically induces an electric charge, while the black holes do not carry a magnetic charge. When a Higgs field is coupled, rotating black holes with monopole hair arise in the case of a Higgs triplet, while in the presence of a complex Higgs doublet the black holes carry sphaleron hair. The inclusion of a dilaton allows for Smarr type mass formulae.
Towards a Gravitational Analog to S-duality in Non-abelian Gauge Theories
García-Compéan, H; Plebanski, J F; Ramírez, C
1998-01-01
It is well known that Yang-Mills theories do possess a phase of non-Abelian strong-weak duality invariance. Moreover, dual theories, with inverted couplings, to non-Abelian, non-supersymmetric gauge theories have been constructed. Following a similar procedure we propose a non-dynamical gravitational analog to this kind of theories.
Quadri, A
2006-01-01
We elucidate the geometry of the polynomial formulation of the non-abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent BRST differential exists allowing to implement the constraint on the sigma field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-abelian gauge fields. As all versions of the Stueckelberg theory, also the abelian embedding formulation yields a non power-counting renormalizable theory in D=4. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the abelian embedding formalism.
An "almost" full embedding of the category of graphs into the category of abelian groups
Przezdziecki, Adam J
2011-01-01
We construct an embedding G of the category of graphs into the category of abelian groups such that for graphs X and Y we have Hom(GX,GY)=Z[Hom(X,Y)], the free abelian group whose basis is the set Hom(X,Y). The isomorphism is functorial in X and Y. The existence of such an embedding implies that, contrary to a common belief, the category of abelian groups is as complex and comprehensive as any other concrete category. We use this embedding to settle an old problem of Isbell whether every full subcategory of the category of abelian groups, which is closed under limits, is reflective. A positive answer turns out to be equivalent to weak Vopenka's principle, a large cardinal axiom which is not provable but believed to be consistent with standard set theory. Several known constructions in the category of abelian groups are obtained as quick applications of the embedding.
Orbifold groups, quasi-projectivity and covers
Bartolo, Enrique Artal; Matei, Daniel
2012-01-01
We discuss properties of complex algebraic orbifold groups, their characteristic varieties, and their abelian covers. In particular, we deal with the question of (quasi)-projectivity of orbifold groups. We also prove a structure theorem for the variety of characters of normal-crossing quasi-projective orbifold groups. Finally, we extend Sakuma's formula for the first Betti number of abelian covers of orbifold fundamental groups. Several examples are presented, including a compact orbifold group which is not projective and a Zariski pair of plane projective curves that can be told by considering an unbranched cover of the projective plane with an orbifold structure.
On projective space bundle with nef normalized tautological line bundle
Yasutake, Kazunori
2011-01-01
In this paper, we study the structure of projective space bundles whose relative anti-canonical line bundle is nef. As an application, we get a characterization of abelian varieties up to finite etale covering.
Harrington, G.; Jardine, P.
2012-12-01
The early Palaeogene hyperthermals provide an unprecedented opportunity to investigate the biotic responses to rapid and transient global warming events. As part of the Bighorn Basin Coring Project (BBCP), we have analyzed 182 sporomorph (pollen and spore) samples from three newly cored sites in the Bighorn Basin of Wyoming. Two sites, Basin Substation (121 samples) and Polecat Bench (41 samples), contain the Paleocene-Eocene Thermal Maximum (PETM, ETM1), and one early Eocene site, Gilmore Hill (20 samples), contains the ELMO (ETM2) event. We have focused initially on the Basin Substation section, because it is more organic rich, has demonstrated higher sporomorph recovery potential than the other two sites, and is the main focus of complementary geochemical analyses. Below 90 m core depth sporomorph concentrations are typically 1000 - 10 000 grains/gram, but between 90 and 60 m these decline to gymnosperms Cupressacites hiatipites (cypress, Cupressaceae) and bisaccate pollen (Pinaceae and/or Podocarpaceae), and the angiosperm taxa Polyatriopollenites vermontensis (wingnut or wheel wingnut, Juglandaceae), Caryapollenites spp. (hickory, Juglandaceae), and Alnipollenites spp. (alder, Betulaceae). However, samples are heterogeneous in terms of the dominant taxon, with different taxa having the highest relative abundance in different samples. In the upper part of the core, the assemblage is similar to that in the lower part, but with a more consistent dominance of gymnosperm taxa, and with the addition of Eocene marker taxa Intratriporopollenites instructus (linden, Tilioideae) and Celtis spp. (hackberry, Cannabaceae). These both have their first appearance at 56.14 m in the core, just above the zone of low sporomorph recovery. These results point to (a) a decrease in sporomorph preservation that is linked to environmental change during the PETM event, and (b) repeated reorganizations of plant relative abundances prior to the PETM. Current research is focusing on the
Liu Jin
2012-01-01
Full Text Available Abstract Background To evaluate the accuracy of the combined maximum and minimum intensity projection-based internal target volume (ITV delineation in 4-dimensional (4D CT scans for liver malignancies. Methods 4D CT with synchronized IV contrast data were acquired from 15 liver cancer patients (4 hepatocellular carcinomas; 11 hepatic metastases. We used five approaches to determine ITVs: (1. ITVAllPhases: contouring gross tumor volume (GTV on each of 10 respiratory phases of 4D CT data set and combining these GTVs; (2. ITV2Phase: contouring GTV on CT of the peak inhale phase (0% phase and the peak exhale phase (50% and then combining the two; (3. ITVMIP: contouring GTV on MIP with modifications based on physician's visual verification of contours in each respiratory phase; (4. ITVMinIP: contouring GTV on MinIP with modification by physician; (5. ITV2M: combining ITVMIP and ITVMinIP. ITVAllPhases was taken as the reference ITV, and the metrics used for comparison were: matching index (MI, under- and over-estimated volume (Vunder and Vover. Results 4D CT images were successfully acquired from 15 patients and tumor margins were clearly discernable in all patients. There were 9 cases of low density and 6, mixed on CT images. After comparisons of metrics, the tool of ITV2M was the most appropriate to contour ITV for liver malignancies with the highest MI of 0.93 ± 0.04 and the lowest proportion of Vunder (0.07 ± 0.04. Moreover, tumor volume, target motion three-dimensionally and ratio of tumor vertical diameter over tumor motion magnitude in cranio-caudal direction did not significantly influence the values of MI and proportion of Vunder. Conclusion The tool of ITV2M is recommended as a reliable method for generating ITVs from 4D CT data sets in liver cancer.
Kye, Heewon; Sohn, Bong-Soo; Lee, Jeongjin
2012-07-01
Maximum intensity projection (MIP) is an important visualization method that has been widely used for the diagnosis of enhanced vessels or bones by rotating or zooming MIP images. With the rapid spread of multidetector-row computed tomography (MDCT) scanners, MDCT scans of a patient generate a large data set. However, previous acceleration methods for MIP rendering of such a data set failed to generate MIP images at interactive rates. In this paper, we propose novel culling methods in both object and image space for interactive MIP rendering of large medical data sets. In object space, for the visibility test of a block, we propose the initial occluder resulting from a preceding image to utilize temporal coherence and increase the block culling ratio a lot. In addition, we propose the hole filling method using the mesh generation and rendering to improve the culling performance during the generation of the initial occluder. In image space, we find out that there is a trade-off between the block culling ratio in object space and the culling efficiency in image space. In this paper, we classify the visible blocks into two types by their visibility. And we propose a balanced culling method by applying a different culling algorithm in image space for each type to utilize the trade-off and improve the rendering speed. Experimental results on twenty CT data sets showed that our method achieved 3.85 times speed up in average without any loss of image quality comparing with conventional bricking method. Using our visibility culling method, we achieved interactive GPU-based MIP rendering of large medical data sets.
Taniguchi, Daigo; Tokunaga, Daisaku; Oda, Ryo; Fujiwara, Hiroyoshi; Ikeda, Takumi; Ikoma, Kazuya; Kishida, Aiko; Yamasaki, Tetsuro; Kawahito, Yutaka; Seno, Takahiro; Ito, Hirotoshi; Kubo, Toshikazu
2014-07-01
Magnetic resonance imaging (MRI) with maximum intensity projection (MIP) is used to evaluate the hand in rheumatoid arthritis (RA). MIP yields clear visualization of synovitis over the entirety of the bilateral hands with a single image. In this study, we assessed synovitis with MIP images, clinical findings, and power Doppler (PD) findings to examine the clinical usefulness of MIP images for RA in the hand. Thirty RA patients were assessed for swelling and tenderness in the joints included in the DAS28, and both contrast-enhanced MRI for bilateral hands and ultrasonography for bilateral wrist and metacarpophalangeal (MCP) joints were performed. Articular synovitis was scored in MIP images, and the scores were compared with those for PD. The agreement on synovitis between MIP and conventional MR images was excellent. Palpation showed low sensitivity and high specificity compared with both MIP and PD images. There were joints that were positive in MIP images only, but there were no joints that were positive in PD images only. A statistically significant correlation between the scores of MIP and PD images was found. Furthermore, the agreement between grade 2 on MIP images and positive on PD images was 0.87 (κ = 0.73) for the wrist and 0.92 (κ = 0.57) for MCP joints. Using MIP images together with palpation makes detailed evaluation of synovitis of the hand in RA easy. MIP images may predict further joint damage, since they allow semiquantitative estimation of the degree of thickening of the synovial membrane.
Non-Abelian vortices with an Aharonov-Bohm effect
Evslin, Jarah [TPCSF, IHEP, Chinese Academy of Sciences,Beijing (China); Theoretical physics division, IHEP, Chinese Academy of Sciences,Beijing (China); Konishi, Kenichi [Department of Physics “Enrico Fermi”, University of Pisa,Largo Pontecorvo 3, 56127, Pisa (Italy); INFN, Sezione di Pisa,Largo Pontecorvo 3, 56127, Pisa (Italy); Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University,4-1-1 Hiyoshi, Yokohama, Kanagawa 223-8521 (Japan); Ohashi, Keisuke [Department of Physics, Osaka City University,Osaka (Japan); Vinci, Walter [London Centre for Nanotechnology and Computer Science, University College London,17-19 Gordon Street, London, WC1H 0AH (United Kingdom)
2014-01-16
The interplay of gauge dynamics and flavor symmetries often leads to remarkably subtle phenomena in the presence of soliton configurations. Non-Abelian vortices — vortex solutions with continuous internal orientational moduli — provide an example. Here we study the effect of weakly gauging a U(1){sub R} subgroup of the flavor symmetry on such BPS vortex solutions. Our prototypical setting consists of an SU(2)×U(1) gauge theory with N{sub f}=2 sets of fundamental scalars that break the gauge symmetry to an “electromagnetic' U(1). The weak U(1){sub R} gauging converts the well-known CP{sup 1} orientation modulus |B| of the non-Abelian vortex into a parameter characterizing the strength of the magnetic field that is responsible for the Aharonov-Bohm effect. As the phase of B remains a genuine zero mode while the electromagnetic gauge symmetry is Higgsed in the interior of the vortex, these solutions are superconducting strings.
Functional integration and gauge ambiguities in generalized abelian gauge theories
Kelnhofer, Gerald
2007-01-01
We consider the covariant quantization of generalized abelian gauge theories on a closed and compact n-dimensional manifold whose space of gauge invariant fields is the abelian group of Cheeger-Simons differential characters. The space of gauge fields is shown to be a non-trivial bundle over the orbits of the subgroup of smooth Cheeger-Simons differential characters. Furthermore each orbit itself has the structure of a bundle over a multi-dimensional torus. As a consequence there is a topological obstruction to the existence of a global gauge fixing condition. A functional integral measure is proposed on the space of gauge fields which takes this problem into account and provides a regularization of the gauge degrees of freedom. For the generalized p-form Maxwell theory closed expressions for all physical observables are obtained. The Greens functions are shown to be affected by the non-trivial bundle structure. Finally the vacuum expectation values of circle-valued homomorphisms, including the Wilson operato...
Topologically stratified energy minimizers in a product Abelian field theory
Xiaosen Han
2015-09-01
Full Text Available We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s=1,2 realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1,P2 anti-vortices of two designated species exists if and only if the inequalities |N1+N2−(P1+P2|<|S|π,|N1+2N2−(P1+2P2|<|S|π, hold simultaneously, which give bounds for the ‘differences’ of the vortex and anti-vortex numbers in terms of the total surface area of S. The minimum energy of these solutions is shown to assume the explicit value E=4π(N1+N2+P1+P2, given in terms of several topological invariants, measuring the total tension of the vortex-lines.
Charged isotropic non-Abelian dyonic black branes
Yves Brihaye
2015-05-01
Full Text Available We construct black holes with a Ricci-flat horizon in Einstein–Yang–Mills theory with a negative cosmological constant, which approach asymptotically an AdSd spacetime background (with d≥4. These solutions are isotropic, i.e. all space directions in a hypersurface of constant radial and time coordinates are equivalent, and possess both electric and magnetic fields. We find that the basic properties of the non-Abelian solutions are similar to those of the dyonic isotropic branes in Einstein–Maxwell theory (which, however, exist in even spacetime dimensions only. These black branes possess a nonzero magnetic field strength on the flat boundary metric, which leads to a divergent mass of these solutions, as defined in the usual way. However, a different picture is found for odd spacetime dimensions, where a non-Abelian Chern–Simons term can be incorporated in the action. This allows for black brane solutions with a magnetic field which vanishes asymptotically.
Flavored Gauge Mediation with Discrete Non-Abelian Symmetries
Everett, Lisa L
2016-01-01
We explore the model-building and phenomenology of flavored gauge mediation models of supersymmetry breaking in which the electroweak Higgs doublets and the SU(2) messenger doublets are connected by a discrete non-Abelian symmetry. The embedding of the Higgs and messenger fields into representations of this non-Abelian Higgs-messenger symmetry results in specific relations between the Standard Model Yukawa couplings and the messenger-matter Yukawa interactions. Taking the concrete example of an S(3) Higgs-messenger symmetry, we demonstrate that while the minimal implementation of this scenario suffers from a severe mu/B_mu problem that is well-known from ordinary gauge mediation, expanding the Higgs-messenger field content allows for the possibility that mu and B_mu can be separately tuned, allowing for the possibility of phenomenologically viable models of the soft supersymmetry breaking terms. We construct toy examples of this type that are consistent with the observed 125 GeV Higgs boson mass.
The Non-Abelian Exponentiation theorem for multiple Wilson lines
Gardi, Einan; White, Chris D
2013-01-01
We study the structure of soft gluon corrections to multi-leg scattering amplitudes in a non-Abelian gauge theory by analysing the corresponding product of semi-infinite Wilson lines. We prove that diagrams exponentiate such that the colour factors in the exponent are fully connected. This completes the generalisation of the non-Abelian exponentiation theorem, previously proven in the case of a Wilson loop, to the case of multiple Wilson lines in arbitrary representations of the colour group. Our proof is based on the replica trick in conjunction with a new formalism where multiple emissions from a Wilson line are described by effective vertices, each having a connected colour factor. The exponent consists of connected graphs made out of these vertices. We show that this readily provides a general colour basis for webs. We further discuss the kinematic combinations that accompany each connected colour factor, and explicitly catalogue all three-loop examples, as necessary for a direct computation of the soft a...
The non-Abelian exponentiation theorem for multiple Wilson lines
Gardi, Einan; Smillie, Jennifer M.; White, Chris D.
2013-06-01
We study the structure of soft gluon corrections to multi-leg scattering amplitudes in a non-Abelian gauge theory by analysing the corresponding product of semi-infinite Wilson lines. We prove that diagrams exponentiate such that the colour factors in the exponent are fully connected. This completes the generalisation of the non-Abelian exponentiation theorem, previously proven in the case of a Wilson loop, to the case of multiple Wilson lines in arbitrary representations of the colour group. Our proof is based on the replica trick in conjunction with a new formalism where multiple emissions from a Wilson line are described by effective vertices, each having a connected colour factor. The exponent consists of connected graphs made out of these vertices. We show that this readily provides a general colour basis for webs. We further discuss the kinematic combinations that accompany each connected colour factor, and explicitly catalogue all three-loop examples, as necessary for a direct computation of the soft anomalous dimension at this order.
On spectral synthesis on element-wise compact Abelian groups
Platonov, S. S.
2015-08-01
Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ_y\\colon f(x)\\mapsto f(xy), y\\in G. By definition, an invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis if \\mathscr H coincides with the closure in C(G) of the linear span of all characters of G belonging to \\mathscr H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.
2D Non-Abelian Theory: Some Novel Features
Srinivas, N; Kureel, B K; Malik, R P
2016-01-01
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss some novel features of a two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations for this specific 2D theory. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci-Ferrari (CF) type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities respect some precise and perf...
Topologically Stratified Energy Minimizers in a Product Abelian Field Theory
Han, Xiaosen
2015-01-01
The recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities is reformulated into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from $N_s$ vortices and $P_s$ anti-vortices ($s=1,2$) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface $S$ which states that a solution with prescribed $N_1, N_2$ vortices and $P_1,P_2$ anti-vortices of two designated species exists if and only if the inequalities \\[ \\left|N_1+N_2-(P_1+P_2)\\right|<\\frac{|S|}{\\pi},\\quad \\left|N_1+2N_2-(P_1+2P_2)\\right|<\\frac{|S|}{\\pi}, \\] hold simultaneously, which give bounds for the `differences' of the vortex and anti-vortex numbers in terms of the total surface area of $S$. The minimum energy of these solutions is shown to assume the explicit value \\...
Mass inflation inside non-Abelian black holes
Breitenlohner, P; Maison, D; Breitenlohner, Peter; Lavrelashvili, George; Maison, Dieter
1997-01-01
The interior geometry of static, spherically symmetric black holes of the Einstein-Yang-Mills-Higgs theory is analyzed. It is found that in contrast to the Abelian case generically no inner (Cauchy) horizon is formed inside non-Abelian black holes. Instead the solutions come close to a Cauchy horizon but then undergo an enormous growth of the mass function, a phenomenon which can be termed `mass inflation' in analogy to what is observed for perturbations of the Reissner-Nordstr{ø}m solution. A significant difference between the theories with and without a Higgs field is observed. Without a Higgs field the YM field induces repeated cycles of mass inflation -- taking the form of violent `explosions' -- interrupted by quiescent periods and subsequent approaches to an almost Cauchy horizon. With the Higgs field no such cycles occur. Besides the generic solutions there are non-generic families with a Schwarzschild, Reissner-Nordstr{ø}m and a pseudo Reissner-Nordstr{ø}m type singularity at $r=0$
Matrix product states and the non-Abelian rotor model
Milsted, Ashley
2016-04-01
We use uniform matrix product states to study the (1 +1 )D O (2 ) and O (4 ) rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free non-Abelian lattice gauge theory on a "Hawaiian earring" graph for U (1 ) and S U (2 ), respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the β function, we find excellent agreement with known results, locating the Berezinskii-Kosterlitz-Thouless transition for O (2 ) and successfully entering the asymptotic weak-coupling regime for O (4 ). To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the non-Abelian theory, where entanglement also suddenly increases. This could have important consequences for tensor network state studies of Yang-Mills on higher-dimensional graphs.
Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
Nitta, Muneto
2015-01-01
Non-Abelian Josephson junction is a junction of non-Abelian color superconductors sandwiching an insulator, or non-Abelian domain wall if flexible, whose low-energy dynamics is described by a $U(N)$ principal chiral model with the conventional pion mass. A non-Abelian Josephson vortex is a non-Abelian vortex (color magnetic flux tube) residing inside the junction, that is described as a non-Abelian sine-Gordon soliton. In this paper, we propose Josephson instantons and Josephson monopoles, that is, Yang-Mills instantons and monopoles inside a non-Abelian Josephson junction, respectively, and show that they are described as $SU(N)$ Skyrmions and $U(1)^{N-1}$ vortices in the $U(N)$ principal chiral model without and with a twisted mass term, respectively. Instantons with a twisted boundary condition are reduced (or T-dual) to monopoles, implying that ${\\mathbb C}P^{N-1}$ lumps are T-dual to ${\\mathbb C}P^{N-1}$ kinks inside a vortex. Here we find $SU(N)$ Skyrmions are T-dual to $U(1)^{N-1}$ vortices inside a wa...
Lu, Wei, E-mail: wlu@umm.edu [Department of Radiation Oncology, University of Maryland School of Medicine, Baltimore, Maryland (United States); Neuner, Geoffrey A.; George, Rohini; Wang, Zhendong; Sasor, Sarah [Department of Radiation Oncology, University of Maryland School of Medicine, Baltimore, Maryland (United States); Huang, Xuan [Research and Development, Care Management Department, Johns Hopkins HealthCare LLC, Glen Burnie, Maryland (United States); Regine, William F.; Feigenberg, Steven J.; D' Souza, Warren D. [Department of Radiation Oncology, University of Maryland School of Medicine, Baltimore, Maryland (United States)
2014-01-01
Purpose: To investigate whether coaching patients' breathing would improve the match between ITV{sub MIP} (internal target volume generated by contouring in the maximum intensity projection scan) and ITV{sub 10} (generated by combining the gross tumor volumes contoured in 10 phases of a 4-dimensional CT [4DCT] scan). Methods and Materials: Eight patients with a thoracic tumor and 5 patients with an abdominal tumor were included in an institutional review board-approved prospective study. Patients underwent 3 4DCT scans with: (1) free breathing (FB); (2) coaching using audio-visual (AV) biofeedback via the Real-Time Position Management system; and (3) coaching via a spirometer system (Active Breathing Coordinator or ABC). One physician contoured all scans to generate the ITV{sub 10} and ITV{sub MIP}. The match between ITV{sub MIP} and ITV{sub 10} was quantitatively assessed with volume ratio, centroid distance, root mean squared distance, and overlap/Dice coefficient. We investigated whether coaching (AV or ABC) or uniform expansions (1, 2, 3, or 5 mm) of ITV{sub MIP} improved the match. Results: Although both AV and ABC coaching techniques improved frequency reproducibility and ABC improved displacement regularity, neither improved the match between ITV{sub MIP} and ITV{sub 10} over FB. On average, ITV{sub MIP} underestimated ITV{sub 10} by 19%, 19%, and 21%, with centroid distance of 1.9, 2.3, and 1.7 mm and Dice coefficient of 0.87, 0.86, and 0.88 for FB, AV, and ABC, respectively. Separate analyses indicated a better match for lung cancers or tumors not adjacent to high-intensity tissues. Uniform expansions of ITV{sub MIP} did not correct for the mismatch between ITV{sub MIP} and ITV{sub 10}. Conclusions: In this pilot study, audio-visual biofeedback did not improve the match between ITV{sub MIP} and ITV{sub 10}. In general, ITV{sub MIP} should be limited to lung cancers, and modification of ITV{sub MIP} in each phase of the 4DCT data set is recommended.
Ding, Wen Quan, E-mail: dingwenquan1982@163.com [Department of Hand Surgery, Hand Surgery Research Center, Affiliated Hospital of Nantong University, Nantong, Jiangsu (China); Zhou, Xue Jun, E-mail: zxj0925101@sina.com [Department of Radiology, Affiliated Hospital of Nantong University, Nantong, Jiangsu (China); Tang, Jin Bo, E-mail: jinbotang@yahoo.com [Department of Hand Surgery, Hand Surgery Research Center, Affiliated Hospital of Nantong University, Nantong, Jiangsu (China); Gu, Jian Hui, E-mail: gujianhuint@163.com [Department of Hand Surgery, Hand Surgery Research Center, Affiliated Hospital of Nantong University, Nantong, Jiangsu (China); Jin, Dong Sheng, E-mail: jindongshengnj@aliyun.com [Department of Radiology, Jiangsu Province Official Hospital, Nanjing, Jiangsu (China)
2015-06-15
Highlights: • 3D displays of peripheral nerves can be achieved by 2 MIP post-processing methods. • The median nerves’ FA and ADC values can be accurately measured by using DTI6 data. • Adopting 6-direction DTI scan and MIP can evaluate peripheral nerves efficiently. - Abstract: Objectives: To achieve 3-dimensional (3D) display of peripheral nerves in the wrist region by using maximum intensity projection (MIP) post-processing methods to reconstruct raw images acquired by a diffusion tensor imaging (DTI) scan, and to explore its clinical applications. Methods: We performed DTI scans in 6 (DTI6) and 25 (DTI25) diffusion directions on 20 wrists of 10 healthy young volunteers, 6 wrists of 5 patients with carpal tunnel syndrome, 6 wrists of 6 patients with nerve lacerations, and one patient with neurofibroma. The MIP post-processing methods employed 2 types of DTI raw images: (1) single-direction and (2) T{sub 2}-weighted trace. The fractional anisotropy (FA) and apparent diffusion coefficient (ADC) values of the median and ulnar nerves were measured at multiple testing sites. Two radiologists used custom evaluation scales to assess the 3D nerve imaging quality independently. Results: In both DTI6 and DTI25, nerves in the wrist region could be displayed clearly by the 2 MIP post-processing methods. The FA and ADC values were not significantly different between DTI6 and DTI25, except for the FA values of the ulnar nerves at the level of pisiform bone (p = 0.03). As to the imaging quality of each MIP post-processing method, there were no significant differences between DTI6 and DTI25 (p > 0.05). The imaging quality of single-direction MIP post-processing was better than that from T{sub 2}-weighted traces (p < 0.05) because of the higher nerve signal intensity. Conclusions: Three-dimensional displays of peripheral nerves in the wrist region can be achieved by MIP post-processing for single-direction images and T{sub 2}-weighted trace images for both DTI6 and DTI25
The free abelian topological group and the free locally convex space on the unit interval
Leiderman, A G; Pestov, V G
1992-01-01
We give a complete description of the topological spaces $X$ such that the free abelian topological group $A(X)$ embeds into the free abelian topological group $A(I)$ of the closed unit interval. In particular, the free abelian topological group $A(X)$ of any finite-dimensional compact metrizable space $X$ embeds into $A(I)$. The situation turns out to be somewhat different for free locally convex spaces. Some results for the spaces of continuous functions with the pointwise topology are also obtained. Proofs are based on the classical Kolmogorov's Superposition Theorem.
The free abelian topological group and the free locally convex space on the unit interval
Leiderman, A. G.; Morris, S. A.; Pestov, V. G.
1992-01-01
We give a complete description of the topological spaces $X$ such that the free abelian topological group $A(X)$ embeds into the free abelian topological group $A(I)$ of the closed unit interval. In particular, the free abelian topological group $A(X)$ of any finite-dimensional compact metrizable space $X$ embeds into $A(I)$. The situation turns out to be somewhat different for free locally convex spaces. Some results for the spaces of continuous functions with the pointwise topology are also...
Non-Abelian Born-Infeld theory without the square root
Obregón, O
2005-01-01
A non-Abelian Born-Infeld theory is presented. The square root structure that characterizes the Dirac-Born-Infeld (DBI) action does not appear. The procedure is based on an Abelian theory proposed by Erwin Schr\\"{o}dinger that, as he showed, is equivalent to Born-Infeld theory. We briefly mention other possible similar proposals. Our results could be of interest in connection with string theory and possible extensions of well known physical results in the usual Born-Infeld Abelian case.
Non-abelian representations of the slim dense near hexagons on 81 and 243 points
De Bruyn, B; Sastry, N S N
2010-01-01
We prove that the near hexagon $Q(5,2) \\times \\mathbb{L}_3$ has a non-abelian representation in the extra-special 2-group $2^{1+12}_+$ and that the near hexagon $Q(5,2) \\otimes Q(5,2)$ has a non-abelian representation in the extra-special 2-group $2^{1+18}_-$. The description of the non-abelian representation of $Q(5,2) \\otimes Q(5,2)$ makes use of a new combinatorial construction of this near hexagon.
Detecting non-Abelian geometric phases with three-level {Lambda} systems
Du Yanxiong; Xue Zhengyuan; Zhang Xinding; Yan Hui [Laboratory of Quantum Information Technology, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006 (China)
2011-09-15
We show that a non-Abelian gauge potential in two nearly degenerated dressed states may be induced by two laser beams interacting with a three-level {Lambda} atomic system. We demonstrate that the populations of the atomic states at the end of a composed path formed by two closed loops are dependent on the order of those two loops, showing an unambiguous signature of the non-Abelian geometric phase. Through numerical calculations, we show that the non-Abelian feature of the geometric phases can be tested under realistic conditions.
Nonrelativistic limit of the abelianized ABJM model and the ADS/CMT correspondence
Lopez-Arcos, Cristhiam; Murugan, Jeff; Nastase, Horatiu
2016-05-01
We consider the nonrelativistic limit of the abelian reduction of the massive ABJM model proposed in [1], obtaining a supersymmetric version of the Jackiw-Pi model. The system exhibits an mathcal{N}=2 Super-Schrödinger symmetry with the Jackiw-Pi vortices emerging as BPS solutions. We find that this (2 + 1)-dimensional abelian field theory is dual to a certain (3+1)-dimensional gravity theory that differs somewhat from previously considered abelian condensed matter stand-ins for the ABJM model. We close by commenting on progress in the top-down realization of the AdS/CMT correspondence in a critical string theory.
Abelian symmetries in multi-Higgs-doublet models
Ivanov, Igor P; Vdovin, Evgeny
2011-01-01
N-Higgs-doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.
Abelian cosmic string in the extended Starobinsky model of gravity
Graça, J P Morais
2016-01-01
We analyze numerically the behaviour of the solutions corresponding to an Abelian cosmic string taking into account an extension of the Starobinsky model, where the action of general relativity is replaced by $f(R) = R - 2\\Lambda + \\eta R^2 + \\rho R^m$, with $m > 2$. As an interesting result, we find that the angular deficit which characterizes the cosmic string decreases as the parameters $\\eta$ and $\\rho$ increase. We also find that the cosmic horizon due to the presence of a cosmological constant is affected in such a way that it can grows or shrinks, depending on the vacuum expectation value of the scalar field and on the value of the cosmological constant
Symplectic quantization of three dimensional Abelian topological gravity
Cartas-Fuentevilla, R; Herrera-Aguilar, Alfredo
2016-01-01
A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is performed; we show that this formalism is equivalent and more economical than Dirac's method. In particular, we identify the complete set of constraints of the theory, from which the number of physical degrees of freedom is explicitly computed. We prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide to each other. Moreover, we perform the Faddeev-Jackiw analysis of the theory under study by working at the chiral point, we report the full set of constraints and the generalized Faddeev-Jackiw brackets are constructed. Finally we compare our results with those found in the literature and we discuss some remarks and prospects.
Abelian tensor hierarchy in 4D, N=1 superspace
Becker, Katrin; Becker, Melanie; III, William D. Linch; Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University, College Station, TX 77843 (United States)
2016-03-09
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
Schwinger-Fronsdal Theory of Abelian Tensor Gauge Fields
Sebastian Guttenberg
2008-09-01
Full Text Available This review is devoted to the Schwinger and Fronsdal theory of Abelian tensor gauge fields. The theory describes the propagation of free massless gauge bosons of integer helicities and their interaction with external currents. Self-consistency of its equations requires only the traceless part of the current divergence to vanish. The essence of the theory is given by the fact that this weaker current conservation is enough to guarantee the unitarity of the theory. Physically this means that only waves with transverse polarizations are propagating very far from the sources. The question whether such currents exist should be answered by a fully interacting theory. We also suggest an equivalent representation of the corresponding action.
Interactions and excitations of non-Abelian vortices
Alford, M.G.; Benson, K.; Coleman, S.; March-Russell, J. (Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138 (USA)); Wilczek, F. (Institute for Advanced Study, Princeton, New Jersey 08540 (USA))
1990-04-02
We examine bosonic zero modes of vortices formed in the gauge breaking {ital G}{r arrow}{ital H}. For non-Abelian {ital G}, zero modes are generic. Their solutions depend on global symmetry structure. Vortices render the embedding {ital H}{contained in}{ital G} space dependent, with a dynamically determined subgroup {ital {tilde H}} single valued. They Aharonov-Bohm scatter gauge bosons associated with multivalued generators. Alice strings ({ital H}=O(2), {ital {tilde H}}={ital openZ}{sub 2}) attract charges and scatter SO(2) photons,'' and a two-string system has zero modes with unlocalizable Cheshire'' charge. The resulting superconductivity has novel electrodynamics.
Evolution of a Non-Abelian Cosmic String Network
McGraw, P N
1998-01-01
We describe a numerical simulation of the evolution of an $S_3$ cosmic string network which takes fully into account the non-commutative nature of the cosmic string fluxes and the topological obstructions which hinder strings from moving past each other or intercommuting. The influence of initial conditions, string tensions, and other parameters on the network's evolution is explored. In a broad range of regimes, the total energy density as a function of time exhibits a familiar power-law behavior, and we do not find strong support for a string-dominated cosmological scenario. However, the speed of the network's collapse (coefficient of the power law) can vary quite a bit, as can the qualitative features of the network. There is a surprisingly strong dependence on the statistical properties of the initial conditions. The results give some insight as to which processes play the most important roles in the evolution of a non-Abelian network.
Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups
Mubeena, T
2011-01-01
Given an automorphism $\\phi:\\Gamma\\lr \\Gamma$, one has an action of $\\Gamma$ on itself by $\\phi$-twisted conjugacy, namely, $g.x=gx\\phi(g^{-1})$. The orbits of this action are called $\\phi$-twisted conjugacy classes. One says that $\\Gamma$ has the $R_\\infty$-property if there are infinitely many $\\phi$-twisted conjugacy classes for every automorphism $\\phi$ of $\\Gamma$. In this paper we show that $\\SL(n,\\bz)$ and its congruence subgroups have the $R_\\infty$-property. Further we show that any (countable) abelian extension of $\\Gamma$ has the $R_\\infty$-property where $\\Gamma$ is a torsion free non-elementary hyperbolic group, or $\\SL(n,\\bz), \\Sp(2n,\\bz)$ or a principal congruence subgroup of $\\SL(n,\\bz)$ or the fundamental group of a complete Riemannian manifold of constant negative curvature.
Do Large Abelian Monopole Loops Survive the Continuum Limit?
Grady, M
1999-01-01
An analysis of the monopole loop length distribution is performed in Wilson-action SU(2) lattice gauge theory. A pure power law in the inverse length is found, at least for loops of length, $l$, less than the linear lattice size $N$. This power shows a definite $\\beta$ dependence, passing 5 around $\\beta =2.9$, and appears to have very little finite lattice size dependence. It is shown that when this power exceeds 5, no loops any finite fraction of the lattice size will survive the infinite lattice limit. This is true for any reasonable size distribution for loops larger than N. The apparent lack of finite size dependence in this quantity would seem to indicate that abelian monopole loops large enough to cause confinement do not survive the continuum limit. Indeed they are absent for all $\\beta > 2.9$.
Abelian Hidden Sectors at a GeV
Morrissey, David E.; Poland, David; /Harvard U.; Zurek, Kathryn; /Fermilab /Michigan U.
2009-04-16
We discuss mechanisms for naturally generating GeV-scale hidden sectors in the context of weak-scale supersymmetry. Such low mass scales can arise when hidden sectors are more weakly coupled to supersymmetry breaking than the visible sector, as happens when supersymmetry breaking is communicated to the visible sector by gauge interactions under which the hidden sector is uncharged, or if the hidden sector is sequestered from gravity-mediated supersymmetry breaking. We study these mechanisms in detail in the context of gauge and gaugino mediation, and present specific models of Abelian GeV-scale hidden sectors. In particular, we discuss kinetic mixing of a U(1){sub x} gauge force with hypercharge, singlets or bi-fundamentals which couple to both sectors, and additional loop effects. Finally, we investigate the possible relevance of such sectors for dark matter phenomenology, as well as for low- and high-energy collider searches.
Non-Abelian gerbes and enhanced Leibniz algebras
Strobl, Thomas
2016-07-01
We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e., dropping eventual contributions that can be added in particular space-time dimensions only such as higher Chern-Simons terms. After appropriate field redefinitions it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the process one sees explicitly how the existence of a gauge-invariant functional enforces that the most general semistrict Lie 2-algebra describing the bundle of a non-Abelian gerbe gets reduced to a very particular structure, which, after the field redefinition, can be identified with the one of an enhanced Leibniz algebra. This is the first step towards a systematic construction of such functionals for higher gauge theories, with kinetic terms for a tower of gauge fields up to some highest form degree p , solved here for p =2 .
Non-abelian Gerbes and Enhanced Leibniz Algebras
Strobl, Thomas
2016-01-01
We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping eventual contributions that can be added in particular space-time dimensions only such as higher Chern-Simons terms. After appropriate field redefinitions it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the process one sees explicitly how the existence of a gauge invariant functional enforces that the most general semi-strict Lie 2-algebra describing the bundle of a non-abelian gerbe gets reduced to a very particular structure, which, after the field redefinition, can be identified with the one of an enhanced Leibniz algebra. This is the first step towards a systematic construction of such functionals for higher gauge theories, with kinetic terms for a tower of gauge fields up to some highest form degree p, solved here for p = 2.
Oscillons and oscillating kinks in the Abelian-Higgs model
Tsagkarakis, C E; Diakonos, F K; Frantzeskakis, D J; Katsimiga, G C; Maintas, X N; Manousakis, E; Tsapalis, A
2015-01-01
We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schr\\"{o}dinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of numerical simulations are found to be in very good agreement with the analytical findings, and show that the oscillons are robust, while kinks are unstable. It is also demonstrated that oscillons emerge spontaneously as a result of the onset of the modulational instability of plane wave solutions of the model. Connections of the obtained solutions with the phenomenology of superconductors is discussed.
The static quark potential from the gauge independent Abelian decomposition
Nigel Cundy
2015-06-01
We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are responsible for confinement.
Abelian Tensor Hierarchy in 4D, N=1 Superspace
Becker, Katrin; Linch, William D; Robbins, Daniel
2016-01-01
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.
Oscillatory and Power-law Mass Inflation in Non-Abelian Black Holes
Galtsov, D V; Zotov, M Yu
1997-01-01
Interior structure of non-Abelian black holes is shown to exhibit in a general case either an oscillating mass-inflationary behavior, or power-law behavior with a divergent mass function. In both cases no Cauchy horizon forms.
Six-dimensional superconformal couplings of non-abelian tensor and hypermultiplets
Samtleben, Henning; Wimmer, Robert
2012-01-01
We construct six-dimensional superconformal models with non-abelian tensor and hypermultiplets. They describe the field content of (2,0) theories, coupled to (1,0) vector multiplets. The latter are part of the non-abelian gauge structure that also includes non-dynamical three- and four-forms. The hypermultiplets are described by gauged nonlinear sigma models with a hyper-Kaehler cone target space. We also address the question of constraints in these models and show that their resolution requires the inclusion of abelian factors. These provide couplings that were previously considered for anomaly cancellations with abelian tensor multiplets and resulted in the selection of ADE gauge groups.
Free energy for a damped cold atom in SU(2) non-Abelian gauge potentials
Guingarey, Issoufou; Avossevou, Gabriel Y. H.
2017-03-01
Our main aim in this work is to find out the exact formula of the equilibrium free energy for a cold atom subjected to a harmonic potential in the background of an artificial non-Abelian uniform magnetic field and linearly coupled to a heat bath. The heat bath consists of a collection of independent quantum harmonic oscillators, while its interaction with the cold atom is modeled in terms of bilinear coupling between the coordinate variables of the cold atom and the oscillators. The main thermodynamic properties of such a system are modified in comparison with the Abelian case. For a non-Abelian magnetic field generated from the laser methods employing degenerate dark states, we evaluate the effect of the non-Abelian dynamics on the magnetic moment of the cold atom.
Field Theory Aspects of non-Abelian T-duality and N=2 Linear Quivers
Lozano, Yolanda
2016-01-01
In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS_5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d N=2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Nunez. This suggests different completions of the long quiver describing the CFT dual to the non-Abelian T-dual background that match different observables.
Field theory aspects of non-Abelian T-duality and {N} =2 linear quivers
Lozano, Yolanda; Núñez, Carlos
2016-05-01
In this paper we propose a linear quiver with gauge groups of increasing rank as field theory dual to the AdS 5 background constructed by Sfetsos and Thompson through non-Abelian T-duality. The formalism to study 4d {N} = 2 SUSY CFTs developed by Gaiotto and Maldacena is essential for our proposal. We point out an interesting relation between (Hopf) Abelian and non-Abelian T-dual backgrounds that allows to see both backgrounds as different limits of a solution constructed by Maldacena and Núñez. This suggests different completions of the long quiver describing the CFT dual to the nonAbelian T-dual background that match different observables.
Marginal and non-commutative deformations via non-abelian T-duality
Hoare, Ben; Thompson, Daniel C.
2017-02-01
In this short article we develop recent proposals to relate Yang-Baxter sigmamodels and non-abelian T-duality. We demonstrate explicitly that the holographic spacetimes associated to both (multi-parameter)- β-deformations and non-commutative deformations of N = 4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.
Marginal and non-commutative deformations via non-abelian T-duality
Hoare, Ben
2016-01-01
In this short article we develop recent proposals to relate Yang-Baxter sigma-models and non-abelian T-duality. We demonstrate explicitly that the holographic space-times associated to both (multi-parameter)-$\\beta$-deformations and non-commutative deformations of ${\\cal N}=4$ super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.
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.
Abelian gauge invariance of the WZ-type coupling in ABJM theory
Dongmin Jang
2015-09-01
Full Text Available We construct the interaction terms between the worldvolume fields of multiple M2-branes and 3-form gauge field of 11-dimensional supergravity, in the context of ABJM theory. The obtained Wess–Zumino-type coupling is simultaneously invariant under the UL(N×UR(N non-Abelian gauge transformation of the ABJM theory and the Abelian gauge transformation of the 3-form field in 11-dimensional supergravity.
On abelianizations of the ABJM model and applications to condensed matter
Murugan, Jeff, E-mail: jeff@nassp.uct.ac.za [The Laboratory for Quantum Gravity and Strings, Department of Mathematics and Applied Mathematics, University of Cape Town (South Africa); Nastase, Horatiu, E-mail: nastase@ift.unesp.br [Universidade Estadual Paulista Julio de Mesquita Filho (UNESP), Sao Paulo, SP (Brazil). Instituto de Fisica Teorica
2015-08-15
In applications of AdS/CFT to condensed matter systems in 2+1 dimensions, the ABJM model is often used; however, the condensed matter models are usually abelian and contain charged fields. We show that a naive reduction of the ABJM model to N = 1 does not have the desired features, but we can find an abelian reduction that has most features, and we can also add fundamental fields to the ABJM model to obtain other models with similar properties. (author)
On abelian and discrete symmetries in F-theory
Piragua, Hernan Augusto
In this dissertation, we systematically construct and study global F-theory compactifications with abelian and discrete gauge groups. These constructions are of fundamental relevance for both conceptual and phenomenological reasons. In the case of abelian symmetries, we systematically engineer compactifications that support U(1)xU(1) and U(1)xU(1)xU(1) gauge groups. The engineered geometries are elliptic fibrations with Mordell-Weil group rank two and three respectively. The bases of the fibrations are arbitrary, but as proofs of concept, we explicit create examples with bases P 2 and P3. We study the low energy physics of these compactifications, we calculate the matter spectrum and confirm that it is anomaly free. In 4D compactifications, the G4 flux is designed and the existence of Yukawa couplings is verified. We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. The discrete gauge groups Z3 and U(1) x Z2 are naturally found when P2 and P1 x P1 are used as fiber ambient spaces. We also find the first realization of matter with U(1) charge three. Finally, we study the discrete gauge group Z 3 in detail. We find the three elements of the Tate-Shafarevich (TS) group. We make use of the Higgs mechanism with the charge three hypermultiplets and the Kaluza-Klein reduction from 6D to 5D. The results are interpreted from the F- M- theory duality perspective. In F-theory, compactifications over any of the three elements of the TS groups yield the same low energy physics, however, M-theory compactifications over the same elements give rise to different
2+1 Abelian `Gauge Theory' Inspired by Ideal Hydrodynamics
Krishnaswami, G S
2005-01-01
We study a theory of abelian gauge fields on a two-manifold M with volume form mu. The phase space coincides with that of incompressible hydrodynamics: a coadjoint orbit of the volume-preserving diffeomorphism group of M. Gauge fields satisfy a Poisson algebra different from the Heisenberg algebra of electrodynamics, but reminiscent of Yang-Mills theory on a null surface. Enstrophy invariants are Casimirs. Some symplectic leaves are identified. The magnetic energy depends on a metric unrelated to mu. The magnetic field evolves by a quadratically non-linear `Euler' equation, which may also be regarded as describing geodesic flow on SDiff(M,mu). Some static solutions are found. For uniform mu, we find infinitely many conserved charges in involution, suggesting integrability. This is a toy-model for ordinary Yang-Mills theory and matrix field theories, whose gauge-invariant phase space is conjectured to be a coadjoint orbit of a diffeomorphism group of a non-commutative space.
Non-abelian higher gauge theory and categorical bundle
Viennot, David
2012-01-01
A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is an attempt to generalize the bundle structure in order to describe horizontal lifts of surfaces. A such attempt is particularly difficult for the non-abelian case. Some structures have been proposed to realize this goal (twisted bundle, gerbes with connection, bundle gerbe, 2-bundle). Each of them uses a category in place of the total space manifold of the usual principal bundle structure. Some of them replace also the structure group by a category (more precisely a Lie crossed module viewed as a category). But the base space remains still a simple manifold (possibly viewed as a trivial category with only identity arrows). We propose a new principal categorical bundle structure, with a Lie crossed module as structure groupoid, but with a base space belonging to a bigger clas...
Abelian Higgs Cosmic Strings: Small Scale Structure and Loops
Hindmarsh, Mark; Bevis, Neil
2008-01-01
Classical lattice simulations of the Abelian Higgs model are used to investigate small scale structure and loop distributions in cosmic string networks. Use of the field theory ensures that the small-scale physics is captured correctly. The results confirm analytic predictions of Polchinski & Rocha [1] for the two-point correlation function of the string tangent vector, with a power law from length scales of order the string core width up to horizon scale with evidence to suggest that the small scale structure builds up from small scales. An analysis of the size distribution of string loops gives a very low number density, of order 1 per horizon volume, in contrast with Nambu-Goto simulations. Further, our loop distribution function does not support the detailed analytic predictions for loop production derived by Dubath et al. [2]. Better agreement to our data is found with a model based on loop fragmentation [3], coupled with a constant rate of energy loss into massive radiation. Our results show a stron...
Strongly coupled non-Abelian plasmas in a magnetic field
Critelli, Renato
2016-01-01
In this dissertation we use the gauge/gravity duality approach to study the dynamics of strongly coupled non-Abelian plasmas. Ultimately, we want to understand the properties of the quark-gluon plasma (QGP), whose scientifc interest by the scientific community escalated exponentially after its discovery in the 2000's through the collision of ultrarelativistic heavy ions. One can enrich the dynamics of the QGP by adding an external field, such as the baryon chemical potential (needed to study the QCD phase diagram), or a magnetic field. In this dissertation, we choose to investigate the magnetic effects. Indeed, there are compelling evidences that strong magnetic fields of the order $eB\\sim 10 m_\\pi^2$ are created in the early stages of ultrarelativistic heavy ion collisions. The chosen observable to scan possible effects of the magnetic field on the QGP was the viscosity, due to the famous result $\\eta/s=1/4\\pi$ obtained via holography. In a first approach we use a caricature of the QGP, the $\\mathcal{N}=4$ s...
New Solutions for Non-Abelian Cosmic Strings
Hindmarsh, Mark; Rummukainen, Kari; Weir, David J.
2016-12-01
We study the properties of classical vortex solutions in a non-Abelian gauge theory. A system of two adjoint Higgs fields breaks the SU(2) gauge symmetry to Z2 , producing 't Hooft-Polyakov monopoles trapped on cosmic strings, termed beads; there are two charges of monopole and two degenerate string solutions. The strings break an accidental discrete Z2 symmetry of the theory, explaining the degeneracy of the ground state. Further symmetries of the model, not previously appreciated, emerge when the masses of the two adjoint Higgs fields are degenerate. The breaking of the enlarged discrete symmetry gives rise to additional string solutions and splits the monopoles into four types of "semipole": kink solutions that interpolate between the string solutions, classified by a complex gauge-invariant magnetic flux and a Z4 charge. At special values of the Higgs self-couplings, the accidental symmetry broken by the string is continuous, giving rise to supercurrents on the strings. The SU(2) theory can be embedded in a wide class of grand unified theories (GUTs), including SO(10). We argue that semipoles and supercurrents are generic on GUT strings.
Evolution of a non-Abelian cosmic string network
McGraw, P. [California Institute of Technology, Pasadena, California 91125 (United States)]|[Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599 (United States)
1998-03-01
We describe a numerical simulation of the evolution of an S{sub 3} cosmic string network which takes fully into account the noncommutative nature of the cosmic string fluxes and the topological obstructions which hinder strings from moving past each other or intercommuting. The influence of initial conditions, string tensions, and other parameters on the network{close_quote}s evolution is explored. Contrary to some previous suggestions, we find no strong evidence of the {open_quotes}freezing{close_quotes} required for a string-dominated cosmological scenario. Instead, the results in a broad range of regimes are consistent with the familiar scaling law, i.e., a constant number of strings per horizon volume. The size of this number, however, can vary quite a bit, as can other overall features. There is a surprisingly strong dependence on the statistical properties of the initial conditions. We also observe a rich variety of interesting new structures, such as light string webs stretched between heavier strings, which are not seen in Abelian networks. {copyright} {ital 1998} {ital The American Physical Society}
Non-abelian higher gauge theory and categorical bundle
Viennot, David
2016-12-01
A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is an attempt to generalize the bundle structure in order to describe horizontal lifts of surfaces. A such attempt is particularly difficult for the non-abelian case. Some structures have been proposed to realize this goal (twisted bundle, gerbes with connection, bundle gerbe, 2-bundle). Each of them uses a category in place of the total space manifold of the usual principal bundle structure. Some of them replace also the structure group by a category (more precisely a Lie crossed module viewed as a category). But the base space remains still a simple manifold (possibly viewed as a trivial category with only identity arrows). We propose a new principal categorical bundle structure, with a Lie crossed module as structure groupoid, but with a base space belonging to a bigger class of categories (which includes non-trivial categories), that we called affine 2-spaces. We study the geometric structure of the categorical bundles built on these categories (which are a more complicated structure than the 2-bundles) and the connective structures on these bundles. Finally we treat an example interesting for quantum dynamics which is associated with the Bloch wave operator theory.
Non-Abelian dark matter and dark radiation
Buen-Abad, Manuel A; Schmaltz, Martin
2015-01-01
We propose a new class of dark matter models with unusual phenomenology. What is ordinary about our models is that dark matter particles are WIMPs, they are weakly coupled to the Standard Model and have weak scale masses. What is unusual is that they come in multiplets of a new "dark" non-Abelian gauge group with milli-weak coupling. The massless dark gluons of this dark gauge group contribute to the energy density of the universe as a form of weakly self-interacting dark radiation. In this paper we explore the consequences of having i.) dark matter in multiplets ii.) self-interacting dark radiation and iii.) dark matter which is weakly coupled to dark radiation. We find that i.) dark matter cross sections are modified by multiplicity factors which have significant consequences for collider searches and indirect detection, ii.) dark gluons have thermal abundances which affect the CMB as dark radiation. Unlike additional massless neutrino species the dark gluons are interacting and have vanishing viscosity and...
Nonlocal wave turbulence in non-Abelian plasmas
Mehtar-Tani, Yacine
2016-01-01
We investigate driven wave turbulence in non-Abelian plasmas, in the framework of kinetic theory where both elastic and inelastic processes are considered in the small angle approximation. The gluon spectrum, that forms in the presence of a steady source, is shown to be controlled by nonlocal interactions in momentum space, in contrast to the universal Kolmogorov-Zakharov spectra. Assuming strongly nonlocal interactions, we show that inelastic processes are dominant in the IR and cause a thermal bath to form below the forcing scale, as a result of a detailed balance between radiation and absorption of soft gluons by the hard ones. Above the forcing scale, the inelastic collision term reduces to an inhomogeneous diffusion-like equation yielding a spectrum that spreads to the UV as $t^{1/2}$, similarly to elastic processes. Due to nonlocal interactions the non-universal turbulent spectrum is not steady and flattens when time goes on toward the thermal distribution. This analysis is complemented by numerical sim...
Topological Nematic States and Non-Abelian Lattice Dislocations
Maissam Barkeshli
2012-08-01
Full Text Available An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number N, which can be mapped to an N-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Consequently, lattice dislocations become defects with a nontrivial quantum dimension, even when the fractional quantum Hall state being realized is, by itself, Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high-genus surfaces in the lab even though the sample has only the disk geometry.
AGT relations for abelian quiver gauge theories on ALE spaces
Pedrini, Mattia; Sala, Francesco; Szabo, Richard J.
2016-05-01
We construct level one dominant representations of the affine Kac-Moody algebra gl̂k on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution Xk of the Ak-1 toric singularity C2 /Zk. We show that the direct sum of the fundamental classes of these moduli spaces is a Whittaker vector for gl̂k, which proves the AGT correspondence for pure N = 2 U(1) gauge theory on Xk. We consider Carlsson-Okounkov type Ext-bundles over products of the moduli spaces and use their Euler classes to define vertex operators. Under the decomposition gl̂k ≃ h ⊕sl̂k, these vertex operators decompose as products of bosonic exponentials associated to the Heisenberg algebra h and primary fields of sl̂k. We use these operators to prove the AGT correspondence for N = 2 superconformal abelian quiver gauge theories on Xk.
New CMB constraints for Abelian Higgs cosmic strings
Lizarraga, Joanes; Daverio, David; Hindmarsh, Mark; Kunz, Martin
2016-01-01
We present cosmic microwave background (CMB) power spectra from recent numerical simulations of cosmic strings in the Abelian Higgs model and compare them to CMB power spectra measured by Planck. We obtain revised constraints on the cosmic string tension parameter $G\\mu$. For example, in the $\\Lambda$CDM model with the addition of strings and no primordial tensor perturbations, we find $G\\mu < 2.0 \\times 10^{-7}$ at 95% confidence, about 20% lower than the value obtained from previous simulations, which had 1/64 of the spatial volume. We investigate the source of the difference, showing that the main cause is an improved treatment of the string evolution across the radiation-matter transition. The increased computational volume also makes possible to simulate fully the physical equations of motion, in which the string cores shrink in comoving coordinates. This, and the larger dynamic range, changes the amplitude of the power spectra by only about 10%, demonstrating that field theory simulations of cosmic s...
Extending Topological Abelian Groups by the Unit Circle
Hugo J. Bello
2013-01-01
Full Text Available A twisted sum in the category of topological Abelian groups is a short exact sequence 0→Y→X→Z→0 where all maps are assumed to be continuous and open onto their images. The twisted sum splits if it is equivalent to 0→Y→Y×Z→Z→0. We study the class STG of topological groups G for which every twisted sum 0→→X→G→0 splits. We prove that this class contains Hausdorff locally precompact groups, sequential direct limits of locally compact groups, and topological groups with ℒ∞ topologies. We also prove that it is closed by taking open and dense subgroups, quotients by dually embedded subgroups, and coproducts. As means to find further subclasses of STG, we use the connection between extensions of the form 0→→X→G→0 and quasi-characters on G, as well as three-space problems for topological groups. The subject is inspired on some concepts known in the framework of topological vector spaces such as the notion of -space, which were interpreted for topological groups by Cabello.
Heterotic Non-Abelian String of a Finite Length
Monin, S; Yung, A
2016-01-01
We consider non-Abelian strings in N=2 supersymmetric QCD with the U$(N)$ gauge group and $N_f=N$ quark flavors deformed by a mass term for the adjoint matter. This deformation breaks N=2 supersymmetry down to N=1. Dynamics of orientational zero modes on the string world sheet are described then by CP$(N-1)$ model with N=(0,2) supersymmetry. We study the string of a finite length $L$ assuming compactification on a cylinder (periodic boundary conditions). The world-sheet theory is solved in the large-$N$ approximation. We find a rich phase structure in the $(L, \\,u)$ plane where $u$ is a deformation parameter. At large $L$ and intermediate $u$ we find a phase with broken $Z_{2N}$ symmetry, $N$ vacua and a mass gap. At large values of $L$ and $u$ still larger we have the $Z_{2N}$-symmetric phase with a single vacuum and massless fermions. In both phases N=(0,2) supersymmetry is spontaneously broken. We also observe a phase with broken SU$(N)\\;$ symmetry at small $L$. In the latter phase the mass gap vanishes an...
New solutions for non-Abelian cosmic strings
Hindmarsh, Mark; Weir, David J
2016-01-01
We study the properties of classical vortex solutions in a non-Abelian gauge theory. A system of two adjoint Higgs fields breaks the SU(2) gauge symmetry to $Z_2$, producing 't Hooft-Polyakov monopoles trapped on cosmic strings, termed beads; there are two charges of monopole and two degenerate string solutions. The strings break an accidental discrete $Z_2$ symmetry of the theory, explaining the degeneracy of the ground state. Further symmetries of the model, not previously appreciated, emerge when the masses of the two adjoint Higgs fields are degenerate. The breaking of the enlarged discrete symmetry gives rise to additional string solutions and splits the monopoles into four types of `semipole': kink solutions that interpolate between the string solutions, classified by a complex gauge invariant magnetic flux and a $Z_4$ charge. At special values of the Higgs self-couplings, the accidental symmetry broken by the string is continuous, giving rise to supercurrents on the strings. The SU(2) theory can be emb...
Fainberg, V Ya; Shikakhwa, M S
1996-01-01
The cvariant path integral quantization of the theory of the scalar and spinor particles interacting through the abelian and non-Abelian Chern-Simons gauge fields is carried out and is shown to be mathematically ill defined due to the absence of the transverse components of these gauge fields. This is remedied by the introduction of the Maxwell or the Maxwell-type (in the non-Abelian case)term which makes the theory superrenormalizable and guarantees its gauge-invariant regularization and renormalization. The generating functionals are constructed and shown to be formally the same as those of QED (or QCD) in 2+1 dimensions with the substitution of the Chern-Simons propagator for the photon (gluon) propagator. By constructing the propagator in the general case, the existence of two limits; pure Chern-Simons and QED (QCD) after renormalization is demonstrated. By carrying out carefully the path integral quantization of the non-Abelian Chern-Simons theories using the De Witt-Fadeev-Popov and the Batalin-Fradkin-...
Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase
Zhu, W.; Liu, Zhao; Haldane, F. D. M.; Sheng, D. N.
2016-12-01
Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here, we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil "fingerprint" evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian (331) Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a "proof-of-principle" demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral p -wave pairing states.
Duality Equivalence Between Self-Dual And Topologically Massive Non-Abelian Models
Ilha, A
2001-01-01
The non-abelian version of the self-dual model proposed by Townsend, Pilch and van Nieuwenhuizen presents some well known difficulties not found in the abelian case, such as well defined duality operation leading to self-duality and dual equivalence with the Yang-Mills-Chern-Simons theory, for the full range of the coupling constant. These questions are tackled in this work using a distinct gauge lifting technique that is alternative to the master action approach first proposed by Deser and Jackiw. The master action, which has proved useful in exhibiting the dual equivalence between theories in diverse dimensions, runs into trouble when dealing with the non-abelian case apart from the weak coupling regime. This new dualization technique on the other hand, is insensitive of the non-abelian character of the theory and generalize straightforwardly from the abelian case. It also leads, in a simple manner, to the dual equivalence for the case of couplings with dynamical fermionic matter fields. As an application, ...
Phase structure and critical properties of an abelian gauge theory
Mo, Sjur
2001-12-01
The main new results are presented in the form of three papers at the end of this thesis. The main topic is Monte-Carlo studies of the phase structure and critical properties of the phenomenological Ginzburg-Landau model, i.e. an abelian gauge theory. However, the first paper is totally different and deals with microscopic theory for lattice-fermions in a magnetic field. Paper I is about ''Fermion-pairing on a square lattice in extreme magnetic fields''. We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest neighbor interactions is transformed to ''k-space'', or more precisely, to the space of eigenfunctions of Harper's equation, which constitute basis functions of the magnetic translation group for the lattice. A BCS-like truncation of the interaction term is performed. Expanding the interactions in the basis functions of the irreducible representations of the point group C{sub 4{nu}} of the square lattice simplify calculations. The numerical results indicate enhanced binding compared to zero magnetic field, and thus re-entrant superconducting pairing at extreme magnetic fields, well beyond the point where the usual semi-classical treatment of the magnetic field breaks down. Paper II is about the ''Hausdorff dimension of critical fluctuations in abelian gauge theories''. Here we analyze the geometric properties of the line-like critical fluctuations (vortex loops) in the Ginzburg-Landau model in zero magnetic background field. By using a dual description, we obtain scaling relations between exponents of geometric arid thermodynamic nature. In particular we connect the anomalous scaling dimension {eta} of the dual matter field to the Hausdorff or fractal dimension D{sub H} of the critical fluctuations, in the original model
The Question of Abelian Higgs Hair Expulsion from Extremal Dilaton Black Holes
Moderski, R; Moderski, Rafal; Rogatko, Marek
1999-01-01
It has been argued that the extremal dilaton black holes exhibit a flux expulsion of Abelian-Higgs vortices. We re-examine carefully the problem and give analytic proofs for the flux expulsion always takes place. We also conduct numerical analysis of the problem using three initial data sets on the horizon of an extreme dilatonic black hole, namely, core, vacuum and sinusoidal initial conditions. We also show that an Abelian-Higgs vortex can end on the extremal dilaton black hole. Concluding, we calculate the backreaction of the Abelian-Higgs vortex on the geometry of the extremal black hole and drew a conclusion that a straight cosmic string and the extreme dilaton black hole hardly knew their presence.
Propagating modes of non-Abelian tensor gauge field of second rank
Konitopoulos, Spyros
2007-01-01
In the recently proposed extension of the YM theory, non-Abelian tensor gauge field of the second rank is represented by a general tensor whose symmetric part describes the propagation of charged gauge boson of helicity two and its antisymmetric part - the helicity zero charged gauge boson. On the non-interacting level these polarizations are similar to the polarizations of the graviton and of the Abelian antisymmetric B field, but the interaction of these gauge bosons carrying non-commutative internal charges cannot be directly identified with the interaction of gravitons or B field. Our intention here is to illustrate this result from different perspectives which would include Bianchi identity for the corresponding field strength tensor and the analysis of the second-order partial differential equation which describes in this theory the propagation of non-Abelian tensor gauge field of the second rank.
Reissner-Nordström black holes with non-Abelian hair
Herdeiro, Carlos; Paturyan, Vanush; Radu, Eugen; Tchrakian, D. H.
2017-09-01
We consider d ⩾ 4 Einstein-(extended-)Yang-Mills theory, where the gauge sector is augmented by higher order terms. Linearising the (extended) Yang-Mills equations on the background of the electric Reissner-Nordström (RN) black hole, we show the existence of normalisable zero modes, dubbed non-Abelian magnetic stationary clouds. The non-linear realisation of these clouds bifurcates the RN family into a branch of static, spherically symmetric, electrically charged and asymptotically flat black holes with non-Abelian hair. Generically, the hairy black holes are thermodynamically preferred over the RN solution, which, in this model, becomes unstable against the formation of non-Abelian hair, for sufficiently large values of the electric charge.
On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
Delcamp, Clement; Riello, Aldo
2016-01-01
Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non--Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non--Abelian analogue of the `magnetic centre choice', as obtained through an extended--Hilbert--space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. W...
Interacting D2-branes in 10 dimensions and non abelian Born-Infeld theory
Gianvittorio, R; Stephany, J
2006-01-01
In this paper we extend the bosonic $D$-brane action in D=10 obtained by duality from the D=11 membrane wrapped on $S^1$ to an SU(2) non abelian system. This system presents only first class constraints, whose algebra closes off-shell and generalizes the algebra of diffeomorphisms of the $D2$-brane to include non abelian symmetry generators. From the SU(2) $D$-brane action, we also obtain the SU(2) Born-Infeld theory by performing a covariant reduction to a flat background. This calculation agrees up to fourth order with the result obtained from the superstring amplitudes and gives an alternative approach to analyze non-abelian Born-Infeld theories.
Nonrelativistic limit of the abelianized ABJM model and the ADS/CMT correspondence
Lopez-Arcos, Cristhiam; Nastase, Horatiu
2015-01-01
We consider the nonrelativistic limit of the abelian reduction of the massive ABJM model proposed in \\cite{Mohammed:2012gi}, obtaining a supersymmetric version of the Jackiw-Pi model. The system exhibits an ${\\cal N}=2$ Super-Schr\\"odinger symmetry with the Jackiw-Pi vortices emerging as BPS solutions. We find that this $(2+1)$-dimensional abelian field theory is dual to a certain (3+1)-dimensional gravity theory that differs somewhat from previously considered abelian condensed matter stand-ins for the ABJM model. We close by commenting on progress in the top-down realization of the AdS/CMT correspondence in a critical string theory.
On non-abelian T-dual geometries with Ramond fluxes
Sfetsos, Konstadinos
2010-01-01
We show how to implement T-duality along non-abelian isometries in backgrounds with non-vanishing Ramond fields. When the dimension of the isometry group is odd (even) the duality swaps (preserves) the chirality of the theory. In certain cases a non-abelian duality can result in a massive type-IIA background. We provide two examples by dualising SU(2) isometry subgroups in $AdS_5\\times S^5$ and $AdS_3\\times S^3\\times T^4$. The resultant dual geometries inherit the original AdS factors but have transverse spaces with reduced isometry and preserve only half of the original supersymmetry. The non-abelian dual of $AdS_5\\times S^5$ has an M-theory lift which is related to the gravity duals of N=2 superconformal theories. We comment on a possible interpretation of this as a high spin limit.
On non-abelian T-dual geometries with Ramond fluxes
Sfetsos, Konstadinos; Thompson, Daniel C.
2011-05-01
We show how to implement T-duality along non-abelian isometries in backgrounds with non-vanishing Ramond fields. When the dimension of the isometry group is odd (even) the duality swaps (preserves) the chirality of the theory. In certain cases a non-abelian duality can result in a massive type-IIA background. We provide two examples by dualising SU(2) isometry subgroups in AdS×S and AdS×S×T. The resultant dual geometries inherit the original AdS factors but have transverse spaces with reduced isometry and preserve only half of the original supersymmetry. The non-abelian dual of AdS×S has an M-theory lift which is related to the gravity duals of N=2 superconformal theories. We comment on a possible interpretation of this as a high spin limit.
Non-Abelian Geometrical Phase for General Three-Dimensional Quantum Systems
Mostafazadeh, A
1996-01-01
Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually solving the full eigenvalue problem for the instantaneous Hamiltonian. The parameter space of such systems which has the structure of $\\xC P^2$ is explicitly constructed. The results of this article are applicable for arbitrary multipole interaction Hamiltonians $H=Q^{i_1,\\cdots i_n}J_{i_1}\\cdots J_{i_n}$ and their linear combinations for spin $j=1$ systems. In particular it is shown that the nuclear quadrupole Hamiltonian $H=Q^{ij}J_iJ_j$ does actually lead to non-Abelian geometric phases for $j=1$. This system, being bosonic, is time-reversal-invariant. Therefore it cannot support Abelian adiabatic geometrical phases.
Some Sufficient Conditions on the Number of Non-abelian Subgroups of a Finite Group to be Solvable
Jiang Tao SHI; Cui ZHANG
2011-01-01
Thompson's theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson's theorem, a finite group is solvable if it has an abelian .maximal subgroup. In this paper, we give some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable.
Johnston, James D. [University of Saskatchewan, Department of Mechanical Engineering, Saskatoon, SK (Canada); University of British Columbia, Department of Mechanical Engineering, Vancouver, BC (Canada); Kontulainen, Saija A. [University of Saskatchewan, College of Kinesiology, Saskatoon, SK (Canada); Masri, Bassam A.; Wilson, David R. [University of British Columbia, Department of Orthopaedics, Vancouver, BC (Canada)
2010-09-15
The objective was to identify subchondral bone density differences between normal and osteoarthritic (OA) proximal tibiae using computed tomography osteoabsorptiometry (CT-OAM) and computed tomography topographic mapping of subchondral density (CT-TOMASD). Sixteen intact cadaver knees from ten donors (8 male:2 female; mean age:77.8, SD:7.4 years) were categorized as normal (n = 10) or OA (n = 6) based upon CT reconstructions. CT-OAM assessed maximum subchondral bone mineral density (BMD). CT-TOMASD assessed average subchondral BMD across three layers (0-2.5, 2.5-5 and 5-10 mm) measured in relation to depth from the subchondral surface. Regional analyses of CT-OAM and CT-TOMASD included: medial BMD, lateral BMD, and average BMD of a 10-mm diameter area that searched each medial and lateral plateau for the highest ''focal'' density present within each knee. Compared with normal knees, both CT-OAM and CT-TOMASD demonstrated an average of 17% greater whole medial compartment density in OA knees (p < 0.016). CT-OAM did not distinguish focal density differences between OA and normal knees (p > 0.05). CT-TOMASD focal region analyses revealed an average of 24% greater density in the 0- to 2.5-mm layer (p = 0.003) and 36% greater density in the 2.5- to 5-mm layer (p = 0.034) in OA knees. Both CT-OAM and TOMASD identified higher medial compartment density in OA tibiae compared with normal tibiae. In addition, CT-TOMASD indicated greater focal density differences between normal and OA knees with increased depth from the subchondral surface. Depth-specific density analyses may help identify and quantify small changes in subchondral BMD associated with OA disease onset and progression. (orig.)
Abelian surfaces, Kummer surfaces and the non-Archimedean Hodge-D-conjecture
Sreekantan, Ramesh
2011-01-01
We construct new elements in the higher Chow group CH2(A,1) of a principally polarized Abelian surface over a non Archimedean local field, which generalize an element constructed by Collino. These elements are constructed using a generalization, due to Birkenhake and Wilhelm, of a classical construction of Humbert. They can be used to prove the non-Archimedean Hodge-D-conjecture - namely, the surjectivity of the boundary map in the localization sequence - in the case when the Abelian surface has good and ordinary reduction.
Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields
Volkov, M S; Volkov, Mikhail S.; Galtsov, Dmitri V.
1999-01-01
We present a review of gravitating particle-like and black hole solutions with non-Abelian gauge fields. The emphasis is given to the description of the structure of the solutions and to the connection with the results of flat space soliton physics. We describe the Bartnik-McKinnon solitons and the non-Abelian black holes arising in the Einstein-Yang-Mills theory, and consider their various generalizations. These include axially symmetric and slowly rotating configurations, solutions with higher gauge groups, $\\Lambda$-term, dilaton, and higher curvature corrections. The stability issue is discussed as well. We also describe the gravitating generalizations for flat space monopoles, sphalerons, and Skyrmions.
Supersymmetry and non-Abelian T-duality in type II supergravity
Kelekci, Özgür; Macpherson, Niall T; Colgáin, Eoin Ó
2014-01-01
We study the effect of T-duality on supersymmetry in the context of type II supergravity. For both U(1) Abelian and SU(2) non-Abelian T-duality, we demonstrate that the Killing spinor equations before and after T-duality can be mapped up to the Kosmann spinorial Lie derivative, which guarantees supersymmetry is preserved upon vanishing. As a byproduct, we give closed expressions for SU(2) T-duality in a class of spacetimes with diagonal Bianchi IX symmetry and comment on specific examples of T-dual geometries, including a novel AdS3 geometry with large N = (4,4) superconformal symmetry.
Quillen Bundle and Geometric Prequantization of Non-Abelian Vortices on a Riemann Surface
Rukmini Dey; Samir K Paul
2011-02-01
In this paper we prequantize the moduli space of non-abelian vortices. We explicitly calculate the symplectic form arising from 2 metric and we construct a prequantum line bundle whose curvature is proportional to this symplectic form. The prequantum line bundle turns out to be Quillen’s determinant line bundle with a modified Quillen metric. Next, as in the case of abelian vortices, we construct line bundles over the moduli space whose curvatures form a family of symplectic forms which are parametrized by $\\Psi_0$, a section of a certain bundle. The equivalence of these prequantum bundles are discussed.
Magnetic structures and Z_2 vortices in a non-Abelian gauge model
Cabra, Daniel; Schaposnik, Fidel A
2015-01-01
The magnetic order of the triangular lattice with antiferromagnetic interactions is described by an SO(3) field and allows for the presence of Z2 magnetic vortices as defects. In this work we show how these Z2 vortices can be fitted into a local SU(2) gauge theory. We propose simple Ansatzes for vortex configurations and calculate their energies using well-known results of the Abelian gauge model. We comment on how Dzyaloshinskii-Moriya interactions could be derived from a non-Abelian gauge theory and speculate on their effect on non trivial configurations.
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.
2014-01-01
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z_3 Read-Rezayi quantu...
Gauge invariant Lagrangian for non-Abelian tensor fauge Fields of fourth rank
Savvidy, G
2005-01-01
Using generalized field strength tensors for non-Abelian tensor gauge fields one can explicitly construct all possible Lorentz invariant quadratic forms for rank-4 non-Abelian tensor gauge fields and demonstrate that there exist only two linear combinations of them which form a gauge invariant Lagrangian. Together with the previous construction of independent gauge invariant forms for rank-2 and rank-3 tensor gauge fields this construction proves the uniqueness of early proposed general Lagrangian up to rank-4 tensor fields. Expression for the coefficients of the general Lagrangian is presented in a compact form.
Gauge fixing and BRST formalism in non-Abelian gauge theories
Ghiotti, Marco; Williams, A G
2007-01-01
In this Thesis we present a comprehensive study of perturbative and non-perturbative non-Abelian gauge theories in the light of gauge-fixing procedures, focusing our attention on the BRST formalism in Yang-Mills theory. We propose first a model to re-write the Faddeev-Popov quantisation method in terms of group-theoretical techniques and then we give a possible way to solve the no-go theorem of Neuberger for lattice Yang-Mills theory with double BRST symmetry. In the final part we present a study of the Batalin-Vilkovisky quantisation method for non-linear gauges in non-Abelian gauge theories.
CP(N-1) model on a disk and decay of a non-Abelian string
Gorsky, A.; Milekhin, A.
2013-10-01
We consider the role of quantum effects in the nonperturbative decay of the non-Abelian string with orientational moduli in nonsupersymmetric D=4 gauge theory. To this aim the effective action in the CP(N-1) model on a disk at large N has been calculated. It exhibits a phase transition at some radius, the “wrong sign” Luscher term, and a large boundary boojumlike negative contribution. The effect of the θ term and the possibility of the spontaneous creation of the non-Abelian string are briefly discussed.
FRAME MULTIRESOLUTION ANALYSIS AND INFINITE TREES IN BANACH SPACES ON LOCALLY COMPACT ABELIAN GROUPS
S. S. Panday
2004-01-01
We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaces on locally compact abelian groups including modulation spaces.
Plasma instabilities and turbulence in non-Abelian gauge theories
Scheffler, Sebastian Herwig Juergen
2010-02-17
Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the ''colour glass condensate'' is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (
Gadda, Davide; Vannucchi, Letizia; Niccolai, Franco; Neri, Anna T.; Carmignani, Luca; Pacini, Patrizio [Ospedale del Ceppo, U.O. Radiodiagnostica, Pistoia (Italy)
2005-12-01
Maximum intensity projections reconstructions from 2.5 mm unenhanced multidetector computed tomography axial slices were obtained from 49 patients within the first 6 h of anterior-circulation cerebral strokes to identify different patterns of the dense artery sign and their prognostic implications for location and extent of the infarcted areas. The dense artery sign was found in 67.3% of cases. Increased density of the whole M1 segment with extension to M2 of the middle cerebral artery was associated with a wider extension of cerebral infarcts in comparison to M1 segment alone or distal M1 and M2. A dense sylvian branch of the middle cerebral artery pattern was associated with a more restricted extension of infarct territory. We found 62.5% of patients without a demonstrable dense artery to have a limited peripheral cortical or capsulonuclear lesion. In patients with a 7-10 points on the Alberta Stroke Early Programme Computed Tomography Score and a dense proximal MCA in the first hours of ictus the mean decrease in the score between baseline and follow-up was 5.09{+-}1.92 points. In conclusion, maximum intensity projections from thin-slice images can be quickly obtained from standard computed tomography datasets using a multidetector scanner and are useful in identifying and correctly localizing the dense artery sign, with prognostic implications for the entity of cerebral damage. (orig.)
Maximum Autocorrelation Factorial Kriging
Nielsen, Allan Aasbjerg; Conradsen, Knut; Pedersen, John L.
2000-01-01
This paper describes maximum autocorrelation factor (MAF) analysis, maximum autocorrelation factorial kriging, and its application to irregularly sampled stream sediment geochemical data from South Greenland. Kriged MAF images are compared with kriged images of varimax rotated factors from...
Minimal Binary Abelian Codes of length $p^m q^n$
Chalom, Gladys; Guerreiro, Marinês; Milies, César Polcino
2012-01-01
We consider binary abelian codes of length $p^m q^n$, where $p$ and $q$ are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases.
Generalized type IIB supergravity equations and non-Abelian classical r-matrices
Orlando, Domenico; Sakamoto, Jun-ichi; Yoshida, Kentaroh
2016-01-01
We study Yang-Baxter deformations of the $AdS_5 \\times S^5$ superstring with non-Abelian classical $r$-matrices which satisfy the homogeneous classical Yang-Baxter equation (CYBE). By performing a supercoset construction, we can get deformed $AdS_5 \\times S^5$ backgrounds. While this is a new area of research, the current understanding is that Abelian classical $r$-matrices give rise to solutions of type IIB supergravity, while non-Abelian classical $r$-matrices lead to solutions of the generalized supergravity equations. We examine here some examples of non-Abelian classical r-matrices and derive the associated backgrounds explicitly. All of the resulting backgrounds satisfy the generalized equations. For some of them, we derive "T-dualized" backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type IIB supergravity equations. Remarkably, some of the "T-dualized" backgrounds are locally identical to undeformed $AdS_5 \\times S^5$ after an appropriate coordin...
Generalized type IIB supergravity equations and non-Abelian classical r-matrices
Orlando, Domenico; Reffert, Susanne; Sakamoto, Jun-ichi; Yoshida, Kentaroh
2016-11-01
We study Yang-Baxter deformations of the {{AdS}}5× {S}5 superstring with non-Abelian classical r-matrices which satisfy the homogeneous classical Yang-Baxter equation. By performing a supercoset construction, we can get deformed {{AdS}}5× {S}5 backgrounds. While this is a new area of research, the current understanding is that Abelian classical r-matrices give rise to solutions of type IIB supergravity, while non-Abelian classical r-matrices lead to solutions of the generalized supergravity equations. We examine here some examples of non-Abelian classical r-matrices and derive the associated backgrounds explicitly. All of the resulting backgrounds satisfy the generalized equations. For some of them, we derive ‘T-dualized’ backgrounds by adding a linear coordinate dependence to the dilaton and show that these satisfy the usual type IIB supergravity equations. Remarkably, some of the ‘T-dualized’ backgrounds are locally identical to undeformed {{AdS}}5× {S}5 after an appropriate coordinate transformation, but this seems not to be generally the case.
Strong Sperner property of the subgroup lattice of an Abelian p-group
王军; 王毅
2000-01-01
Let n and k be arbitrary positive integers, p a prime number and L(kn)(p) the subgroup lattice of the Abelian p-group ( /pk )n. Then there is a positive integer N( n, k) such that when p > N( n, k), L(kn)(p) has the strong Sperner property.
Finite p-groups all of whose maximal abelian subgroups are soft
无
2010-01-01
A subgroup A of a p-group G is said to be soft in G if CG(A) = A and |NG(A)/A| = p. In this paper we determined finite p-groups all of whose maximal abelian subgroups are soft; see Theorem A and Proposition 2.4.
Strong Sperner property of the subgroup lattice of an Abelian p-group
无
2000-01-01
Let n and k be arbitrary positive integers, p a prime number and L(kn)(p) the subgroup lattice of the Abelian p-group (Z/pkZ)n. Then there is a positive integer N(n,k) such that when p>N(n,k), L(kn)(p) has the strong Sperner property.
Non-abelian quantum Hall states -- exclusion statistics, K-matrices and duality
Ardonne, E.; Bouwknegt, P.; Schoutens, K.
2001-01-01
We study excitations in edge theories for non-abelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edge-electrons and edge-quasiholes, we
The effective action for the 4-point functions in abelian open superstring theory
de Roo, M; Eenink, MGC; Eenink, Martijn G.C.
2003-01-01
We construct the derivative corrections to the four-point vertices in the abelian open string effective action to all orders in alpha'. The result is based on the structure of the string four-point function. Supersymmetry of these vertices is guaranteed by the supersymmetry of the F-4 term in the ef
Symmetry-protected non-Abelian braiding of Majorana Kramers pairs
Gao, Pin; He, Ying-Ping; Liu, Xiong-Jun
2016-12-01
We develop a complete theory for symmetry protected non-Abelian statistics of Majorana Kramers' pairs (MKPs) in time-reversal (TR) invariant topological superconductors, with fundamental results being uncovered. By introducing an effective Hamiltonian approach to describe the braiding of MKPs, we show that the non-Abelian braiding is protected when the effective Hamiltonian exhibits a new TR-like antiunitary symmetry, which is satisfied if the system is free of dynamical noise. Importantly, even the dynamical noise cannot cause error in braiding, unless the noise correlation function breaks a dynamical TR symmetry. This is a profound result and generalizes the TR symmetry protection of MKPs to the dynamical regime. Moreover, the resulted error by noise is shown to be a higher-order effect, compared with the decoherence of Majorana qubits without TR symmetry protection. This study completes the theory of symmetry-protected non-Abelian statistics of MKPs, and shows that the non-Abelian braiding of MKPs is well observable and may have versatile applications to future quantum computation technologies.
Towards a Gravitational Analog to S-duality in Non-abelian Gauge Theories
Garcia-Compean, H.; Obregon, O.; Plebanski, J. F.; Ramirez, C.
1997-01-01
For non-abelian non-supersymmetric gauge theories, generic dual theories have been constructed. In these theories the couplings appear inverted. However, they do not possess a Yang-Mills structure but rather are a kind of non-linear sigma model. It is shown that for a topological gravitational model an analog to this duality exists.
Collective States of D(D3) Non-Abelian Anyons
Finch, P. E.; Frahm, H.
2013-11-01
We study an exactly solvable model of non-Abelian anyons symmetric under the quantum double of the dihedral group D3 on a one-dimensional lattice. Bethe ansatz methods are employed to compute the ground states of this model in different regions of the parameter space. The finite size spectrum is studied and the corresponding low energy field theories are identified.
Semi-abelian Z-theory: NLSM+ ϕ 3 from the open string
Carrasco, John Joseph M.; Mafra, Carlos R.; Schlotterer, Oliver
2017-08-01
We continue our investigation of Z-theory, the second double-copy component of open-string tree-level interactions besides super-Yang-Mills (sYM). We show that the amplitudes of the extended non-linear sigma model (NLSM) recently considered by Cachazo, Cha, and Mizera are reproduced by the leading α '-order of Z-theory amplitudes in the semi-abelian case. The extension refers to a coupling of NLSM pions to bi-adjoint scalars, and the semi-abelian case involves to a partial symmetrization over one of the color orderings that characterize the Z-theory amplitudes. Alternatively, the partial symmetrization corresponds to a mixed interaction among abelian and non-abelian states in the underlying open-superstring amplitude. We simplify these permutation sums via monodromy relations which greatly increase the efficiency in extracting the α '-expansion of these amplitudes. Their α '-corrections encode higher-derivative interactions between NLSM pions and bi-colored scalars all of which obey the duality between color and kinematics. Through double-copy, these results can be used to generate the predictions of supersymmetric Dirac-Born-Infeld-Volkov-Akulov theory coupled with sYM as well as a complete tower of higher-order α '-corrections.
Electric-magnetic duality and the "loop representation" in abelian gauge theories
Leal, L C
1996-01-01
Abelian Gauge Theories are quantized in a geometric representation that generalizes the Loop Representation and treates electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of non local operators that resembles the order-disorder dual algebra of 't Hooft. These dual operators provide a complete description of the physical phase space of the theories.
Monopoles in non-Abelian Born-Infeld-Higgs theory and Born-Infeld collapse
Dyadichev, V. V.; Gal'Tsov, D. V.
2002-06-01
Regular magnetic monopoles in the non-Abelian Born-Infeld-Higgs theory are known to exist in the region of the field strength parameter β>βcr, bounded from below. Beyond this region, only pointlike (embedded Abelian) monopoles exist, and we show that the transition from the regular to singular structure is reminiscent of gravitational collapse. Near the threshold behavior is characterized by the rapidly increasing negative pressure, which typically arises in the high density non-Abelian Born-Infeld (NBI) matter. Another feature, shared by both the NBI and gravitating monopoles, is the existence of excited states, which can be thought of as bound states of monopoles and sphalerons. These are labeled by the number N of nodes of the Yang-Mills function. Their masses are greater than the mass of the ground state monopole, and they are expected to be unstable. The sequence of masses MN rapidly converges to the mass of the embedded Abelian solution with a constant Higgs boson. The ratio of the sphaleron size to that of the monopole grows with decreasing β, and, at the same time, both fall down until the solutions cease to exist, again exhibiting a collapse to the point-like monopole. The results are presented and compared both for the ordinary and the symmetrized trace NBI actions.
On subgroups of semi-abelian varieties defined by difference equations
Chatzidakis, Zoé
2011-01-01
Consider the algebraic dynamics on a torus $T=G_m^n$ given by a matrix $M$ in $GL_n(Z)$. Assume that the characteristic polynomial of $M$ is prime to all polynomials $X^m-1$. We show that any finite equivariant map from another algebraic dynamics onto $(T,M)$ arises from a finite isogeny $T \\to T$. A similar and more general statement is shown for Abelian and semi-abelian varieties. In model-theoretic terms, our result says: Working in an existentially closed difference field, we consider a definable subgroup $B$ of a semi-abelian variety $A$; assume $B$ does not have a subgroup isogenous to $A'(F)$ for some twisted fixed field $F$, and some semi-Abelian variety $A'$. Then B with the induced structure is stable and stably embedded. This implies in particular that for any $n>0$, any definable subset of $B^n$ is a Boolean combination of cosets of definable subgroups of $B^n$. This result was already known in characteristic 0 where indeed it holds for all commutative algebraic groups ([CH]). In positive characte...
The all-loop non-Abelian Thirring model and its RG flow
Itsios, G; Siampos, K
2014-01-01
We analyze the renormalization group flow in a recently constructed class of integrable sigma-models which interpolate between WZW current algebra models and the non-Abelian T-duals of PCM for a simple group G. They are characterized by the integer level k of the current algebra, a deformation parameter lambda and they exhibit a remarkable invariance involving the inversion of lambda. We compute the beta-function for lambda to leading order in 1/k. Based on agreement with previous results for the exact beta-function of the non-Abelian Thirring model and matching global symmetries, we state that our integrable models are the resummed version (capturing all counterterms in perturbation theory) of the non-Abelian Thirring model for a simple group G. Finally, we present an analogous treatment in a simple example of a closely related class of models interpolating between gauged WZW coset CFTs and the non-Abelian T-duals of PCM for the coset G/H.
Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge Theory
WU Ning
2002-01-01
In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.
Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras
Parinyawat Choosuwan
2016-01-01
Full Text Available The main focus of this paper is the complete enumeration of self-dual abelian codes in nonprincipal ideal group algebras F2k[A×Z2×Z2s] with respect to both the Euclidean and Hermitian inner products, where k and s are positive integers and A is an abelian group of odd order. Based on the well-known characterization of Euclidean and Hermitian self-dual abelian codes, we show that such enumeration can be obtained in terms of a suitable product of the number of cyclic codes, the number of Euclidean self-dual cyclic codes, and the number of Hermitian self-dual cyclic codes of length 2s over some Galois extensions of the ring F2k+uF2k, where u2=0. Subsequently, general results on the characterization and enumeration of cyclic codes and self-dual codes of length ps over Fpk+uFpk are given. Combining these results, the complete enumeration of self-dual abelian codes in F2k[A×Z2×Z2s] is therefore obtained.
Maximum Power from a Solar Panel
Michael Miller
2010-01-01
Full Text Available Solar energy has become a promising alternative to conventional fossil fuel sources. Solar panels are used to collect solar radiation and convert it into electricity. One of the techniques used to maximize the effectiveness of this energy alternative is to maximize the power output of the solar collector. In this project the maximum power is calculated by determining the voltage and the current of maximum power. These quantities are determined by finding the maximum value for the equation for power using differentiation. After the maximum values are found for each time of day, each individual quantity, voltage of maximum power, current of maximum power, and maximum power is plotted as a function of the time of day.
Wildner, Elena; Blennow, M.; Bogomilov, M.; Burgman, A.; Bouquerel, E.; Carlile, C.; Cederkäll, J.; Christiansen, P.; Cupial, P.; Danared, H.; Dracos, M.; Ekelöf, T.; Eshraqi, M.; Hall-Wilton, R.; Koutchouk, J.P.; Lindroos, M.; Martini, M.; Matev, R.; McGinnis, D.; Miyamoto, R.; Ohlsson, T.; Öhman, H.; Olvegård, M.; Ruber, R.; Schönauer, H.; Tang, J.Y.; Tsenov, R.; Vankova-Kirilova, G.; Vassilopoulos, N.
2016-01-01
Very intense neutrino beams and large neutrino detectors will be needed to enable the discovery of CP violation in the leptonic sector. The European Spallation Source (ESS), currently under construction in Lund, Sweden, is a research center that will provide, by 2023, the world's most powerful neutron source. The average power will be 5 MW. Pulsing this linac at higher frequency, at the same instantaneous power, will make it possible to raise the average beam power to 10 MW to produce, in parallel with the spallation neutron production, a high performance neutrino Super Beam of about 0.4 GeV mean neutrino energy. The ESS neutrino Super Beam, ESSnuSB, operated with a 2.0 GeV linac proton beam, together with a large underground Water Cherenkov detector located at 540 km from Lund, close to the second oscillation maximum, will make it possible to discover leptonic CP violation at 5 sigma significance level in 56 percent (65 percent for an upgrade to 2.5 GeV beam energy) of the leptonic Dirac CP-violating phase r...
Local Monte Carlo Implementation of the Non-Abelian Landau-Pomeranchuk-Migdal Effect
Zapp, Korinna; Wiedemann, Urs Achim
2009-01-01
The non-abelian Landau-Pomeranschuk-Migdal (LPM) effect arises from the quantum interference between spatially separated, inelastic radiation processes in matter. A consistent probabilistic implementation of this LPM effect is a prerequisite for extending the use of Monte Carlo (MC) event generators to the simulation of jet-like multi-particle final states in nuclear collisions. Here, we propose a local MC algorithm, which is based solely on relating the LPM effect to the probabilistic concept of formation time for virtual quanta. We demonstrate that this implementation of formation time physics alone accounts probabilistically for all analytically known features of the non-abelian LPM-effect, including the characteristic L^2-dependence of average parton energy loss and the characteristic $\\sqrt{\\omega}$-modification of the gluon energy distribution. Additional kinematic constraints are found to modify these L^2- and $\\omega$-dependencies characteristically in accordance with analytical estimates.
Relativistic longitudinal non-Abelian oscillations in quark–antiquark plasma
Vishnu M Bannur
2002-10-01
We study the relativistic version of the non-Abelian, longitudinal wave in quark–antiquark plasma reported earlier by Bhat et al [Phys. Rev. D39, 649 (1989)]. We have also relaxed various approximations they made in their analysis. Both the quark and antiquark dynamics are taken in our analysis. The non-linearity arising from non-Abelian ﬁeld as well as from plasma are included. Hence it is an exact longitudinal mode in relativistic quark–antiquark plasma, relevant to the study of quark gluon plasma. We ﬁnd that earlier results are reproduced for non-relativistic and low amplitude oscillations, but are modiﬁed for relativistic or large amplitude waves. Further more, the above results are based on just four ﬁrst-order equations for gauge invariant quantities derived from gauge covariant twelve ﬁrst-order equations.
Solving the SUSY flavour and CP problems with non-Abelian family symmetry and supergravity
Antusch, Stefan [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Foehringer Ring 6, D-80805 Muenchen (Germany)], E-mail: antusch@mppmu.mpg.de; King, Stephen F. [School of Physics and Astronomy, University of Southampton, SO16 1BJ Southampton (United Kingdom)], E-mail: sfk@hep.phys.soton.ac.uk; Malinsky, Michal [School of Physics and Astronomy, University of Southampton, SO16 1BJ Southampton (United Kingdom)], E-mail: malinsky@phys.soton.ac.uk; Ross, Graham G. [The Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX13NP (United Kingdom)], E-mail: g.ross1@physics.ox.ac.uk
2009-01-05
Can a theory of flavour capable of describing the spectrum of fermion (including neutrino) masses and mixings also contain within it the seeds for a solution of the SUSY flavour and CP problems? We argue that supergravity together with a non-Abelian family symmetry can completely resolve the SUSY flavour and CP problems in a broad class of theories in which family symmetry and CP is spontaneously broken in the flavon sector. We show that a simple superpotential structure can suppress the F-terms of the flavons and GUT scale Higgs fields and that, if this mechanism is implemented, the resulting flavour and CP violation is suppressed and comfortably within the experimental limits. For illustration, we study a specific model based on SU(3) family symmetry, but similar models based on non-Abelian (continuous or discrete) family symmetry will lead to similar results.
Dark Gauge Bosons: LHC Signatures of Non-Abelian Kinetic Mixing
Argüelles, Carlos A; Ovanesyan, Grigory; Peng, Tao; Ramsey-Musolf, Michael J
2016-01-01
We consider non-abelian kinetic mixing between the Standard Model SU(2$)_L$ and a dark sector U(1$)^\\prime$ gauge group associated with the presence of a scalar SU(2$)_L$ triplet. The magnitude of the resulting dark photon coupling $\\epsilon$ is determined by the ratio of the triplet vacuum expectation value, constrained to by $\\lsim 4$ GeV by electroweak precision tests, to the scale $\\Lambda$ of the effective theory. The corresponding effective operator Wilson coefficient can be $\\mathcal{O}(1)$ while accommodating null results for dark photon searches, allowing for a distinctive LHC dark photon phenomenology. After outlining the possible LHC signatures, we illustrate by recasting current ATLAS dark photon results into the non-abelian mixing context.
Quasinormal modes of non-Abelian hyperscaling violating Lifshitz black holes
Bécar, Ramón; González, P. A.; Vásquez, Yerko
2017-02-01
We study the quasinormal modes of scalar field perturbations in the background of non-Abelian hyperscaling violating Lifshitz black holes. We find that the quasinormal frequencies have no real part so there is no oscillatory behavior in the perturbations, only exponential decay, that is, the system is always overdamped, which guarantees the mode stability of non-Abelian hyperscaling violating Lifshitz black holes. We determine analytically the quasinormal modes for massless scalar fields for a dynamical exponent z=2 and hyperscaling violating exponent tilde{θ }>-2. Also, we obtain numerically the quasinormal frequencies for different values of the dynamical exponent and the hyperscaling violating exponent by using the improved asymptotic iteration method.
Malik, R P; Rai, S K
2009-01-01
The celebrated Curci-Ferrari (CF) type of restrictions are invoked to obtain an absolutely anticommuting and off-shell nilpotent (anti-) BRST as well as (anti-) co-BRST symmetry transformation in the context of the Lagrangian description of the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory. We show that the above conditions, which turn out to be the secondary constraints of the theory, remain invariant with respect to the time evolution of the above Abelian 2-form gauge system in the Hamiltonian formulation. This time evolution invariance (i) physically ensures the linear independence of the BRST versus anti-BRST as well as co-BRST versus anti-co-BRST symmetry transformations, and (ii) provides a logical reason behind the imposition of the CF type restrictions in the proof of the absolute anticommutativity of the off-shell nilpotent (anti-) BRST as well as (anti-) co-BRST symmetry transformations.
Proposed Aharonov-Casher interferometry of non-Abelian vortices in chiral p-wave superconductors
Grosfeld, Eytan; Seradjeh, Babak; Vishveshwara, Smitha
2011-03-01
We propose a two-path vortex interferometry experiment based on the Aharonov- Casher effect for detecting the non-Abelian nature of vortices in a chiral p-wave superconductor. The effect is based on observing vortex interference patterns upon enclosing a finite charge of externally controllable magnitude within the interference path. We predict that when the interfering vortices enclose an odd number of identical vortices in their path, the interference pattern disappears only for non-Abelian vortices. When pairing involves two distinct spin species, we derive the mutual statistics between half quantum and full quantum vortices and show that, remarkably, our predictions still hold for the situation of a full quantum vortex enclosing a half quantum vortex in its path. We discuss the experimentally relevant conditions under which these effects can be observed. Work supported by ICMT at UIUC, NSERC of Canada, CAS fellowship at UIUC, and the U.S. Department of Energy.
Three-dimensional N=4 linear quivers and non-Abelian T-duals
Lozano, Yolanda [Department of Physics, University of Oviedo,Avda. Calvo Sotelo 18, Oviedo, 33007 (Spain); Macpherson, Niall T. [Dipartimento di Fisica, Università di Milano-Bicocca and INFN, sezione di Milano-Bicocca,Milano, I-20126 (Italy); Montero, Jesús [Department of Physics, University of Oviedo,Avda. Calvo Sotelo 18, Oviedo, 33007 (Spain); Núñez, Carlos [Department of Physics, Swansea University,Swansea, SA2 8PP United Kingdom (United Kingdom)
2016-11-22
In this paper we construct a new Type IIB background with an AdS{sub 4} factor that preserves N=4 Supersymmetry. This solution is obtained using a non-Abelian T-duality transformation on the Type IIA reduction of the AdS{sub 4}×S{sup 7} background. We interpret our configuration as a patch of a more general background with localised sources, dual to the renormalisation fixed point of a T{sub ρ}{sup ρ̂}(SU(N)) quiver field theory. This relates explicitly the AdS{sub 4} geometry to a D3-D5-NS5 brane intersection, illuminating what seems to be a more general phenomenon, relating AdS{sub p+1} backgrounds generated by non-Abelian T-duality to Dp-D(p+2)-NS5 branes intersections.
Spontaneous Magnetization through Non-Abelian Vortex Formation in Rotating Dense Quark Matter
Vinci, Walter; Nitta, Muneto
2012-01-01
When a color superconductor of high density QCD is rotating, super- fluid vortices are inevitably created along the rotation axis. In the color-flavor locked phase realized at the asymptotically large chemical potential, there appear non-Abelian vortices carrying both circulations of superfluid and color magnetic fluxes. A family of solutions has a degeneracy characterized by the Nambu-Goldtone modes CP2, associ- ated with the color-flavor locked symmetry spontaneously broken in the vicinity of the vortex. In this paper, we study electromagnetic coupling of the non-Abelian vortices and find that the degeneracy is removed with the induced effective potential. We obtain one stable vortex solu- tion and a family of metastable vortex solutions, both of which carry ordinary magnetic fluxes in addition to color magnetic fluxes. We dis- cuss quantum mechanical decay of the metastable vortices by quantum tunneling, and compare the effective potential with the other known po- tentials, the quantum mechanically induced...
Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta
Aguilar, A C; Ferreira, M N; Papavassiliou, J
2016-01-01
We determine the non-Abelian version of the four longitudinal form factors of the quark-gluon vertex, using exact expressions derived from the Slavnov-Taylor identity that this vertex satisfies. In addition to the quark and ghost propagators, a key ingredient of the present approach is the quark-ghost scattering kernel, which is computed within the one-loop dressed approximation. The vertex form factors obtained from this procedure are evaluated for arbitrary Euclidean momenta, and display features not captured by the well-known Ball-Chiu vertex, deduced from the Abelian (ghost-free) Ward identity. The potential phenomenological impact of these results is evaluated through the study of special renormalization-point-independent combinations, which quantify the strength of the interaction kernels appearing in the standard quark gap and Bethe-Salpeter equations.
Three-dimensional N=4 Linear Quivers and non-Abelian T-duals
Lozano, Yolanda; Montero, Jesus; Nunez, Carlos
2016-01-01
In this paper we construct a new Type IIB background with an $AdS_4$ factor that preserves ${\\cal N}=4$ Supersymmetry. This solution is obtained using a non-Abelian T-duality transformation on the Type IIA reduction of the $AdS_4\\times S^7$ background. We interpret our configuration as a patch of a more general background with localised sources, dual to the renormalisation fixed point of a $T_{\\rho}^{\\hat{\\rho}} (SU(N))$ quiver field theory. This relates explicitly the $AdS_4$ geometry to a D3-D5-NS5 brane intersection, illuminating what seems to be a more general phenomenon, relating $AdS_{p+1}$ backgrounds generated by non-Abelian T-duality to Dp-D(p+2)-NS5 branes intersections.
Non-abelian factorisation for next-to-leading-power threshold logarithms
Bonocore, D; Magnea, L; Vernazza, L; White, C D
2016-01-01
Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a non-abelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.
Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: Superfield formalism
R P Malik; B P Mandal
2009-03-01
We demonstrate that the nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the frame-work of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D space-time variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.
Non-Abelian vortices in Chern-Simons theories and their induced effective theory
Aldrovandi, L G
2007-01-01
Non-Abelian vortices for a supersymmetric {\\cal N}=2 Chern-Simons-Higgs theory are explicitly constructed. We introduce N Higgs fields in the fundamental representation of the U(N) gauge group in order to have a color-flavor SU(N) group remaining unbroken in the asymmetric phase. Bogomol'nyi-like first order equations are found and rotationally symmetric solutions are proposed. These solutions are shown to be truly non-Abelian by parameterizing them in terms of orientational collective coordinates. The low energy effective action for the orientational moduli results to be the one-dimensional supersymmetric {\\cal N}=2 CP^{N-1} model. We analyze the quantum mechanics of this effective theory in the N=2 case.
A correspondence between maximal abelian sub-algebras and linear logic fragments
SEILLER, THOMAS
2016-01-01
We show a correspondence between a classification of maximal abelian sub-algebras (MASAs) proposed by Jacques Dixmier (Dixmier 1954. Annals of Mathematics 59 (2) 279–286) and fragments of linear logic. We expose for this purpose a modified construction of Girard's hyperfinite geometry of interact......We show a correspondence between a classification of maximal abelian sub-algebras (MASAs) proposed by Jacques Dixmier (Dixmier 1954. Annals of Mathematics 59 (2) 279–286) and fragments of linear logic. We expose for this purpose a modified construction of Girard's hyperfinite geometry...... of interaction (Girard 2011. Theoretical Computer Science 412 (20) 1860–1883). The expressivity of the logic soundly interpreted in this model is dependent on properties of a MASA which is a parameter of the interpretation. We also unveil the essential role played by MASAs in previous geometry of interaction...
Three-dimensional {N}=4 linear quivers and non-Abelian T-duals
Lozano, Yolanda; Macpherson, Niall T.; Montero, Jesús; Núñez, Carlos
2016-11-01
In this paper we construct a new Type IIB background with an AdS 4 factor that preserves {N}=4 Supersymmetry. This solution is obtained using a non-Abelian T-duality transformation on the Type IIA reduction of the AdS 4 × S 7 background. We interpret our configuration as a patch of a more general background with localised sources, dual to the renormalisation fixed point of a {T}_{ρ}^{widehat{ρ}}(SU(N)) quiver field theory. This relates explicitly the AdS 4 geometry to a D3-D5-NS5 brane intersection, illuminating what seems to be a more general phenomenon, relating AdS p+1 backgrounds generated by non-Abelian T-duality to Dp- D( p + 2)-NS5 branes intersections.
Maximum Autocorrelation Factorial Kriging
Nielsen, Allan Aasbjerg; Conradsen, Knut; Pedersen, John L.; Steenfelt, Agnete
2000-01-01
This paper describes maximum autocorrelation factor (MAF) analysis, maximum autocorrelation factorial kriging, and its application to irregularly sampled stream sediment geochemical data from South Greenland. Kriged MAF images are compared with kriged images of varimax rotated factors from an ordinary non-spatial factor analysis, and they are interpreted in a geological context. It is demonstrated that MAF analysis contrary to ordinary non-spatial factor analysis gives an objective discrimina...
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.
String Representation of the Abelian Higgs Theory and Aharonov-Bohm Effect on the Lattice
Polikarpov, M I; Zubkov, M A
1993-01-01
The partition function of the $4D$ lattice Abelian Higgs theory is represented as the sum over world sheets of Nielsen--Olesen strings. The creation and annihilation operators of the strings are constructed. The topological long--range interaction of the strings and charged particles is shown to exist; it is proportional to the linking number of the string world sheet and particle world trajectory.
A worm-inspired algorithm for the simulation of Abelian gauge theories
Korzec, Tomasz
2010-01-01
We present an algorithm in which the all-order strong coupling expansion of the Abelian U(1) gauge theory with Wilson plaquette action is sampled. In addition to the vacuum closed surface graphs of the partition function we propose to also allow for a class of defects (boundaries) related to Wilson loops in the ensemble. The efficiency of our scheme in estimating various observables is compared to a standard Metropolis algorithm.
Energy-momentum tensors for non-commutative Abelian Proca field
Darabi, F
2014-01-01
We study two different possibilities of constructing the energy-momentum tensors for non-commutative Abelian Proca field, by using (i) general Noether theorem and (ii) coupling to a weak external gravitational field. Both energy-momentum tensors are not traceless due to the violation of Lorentz invariance in non-commutative spaces. In particular, we show that the obtained energy density of the latter case coincides exactly with that of obtained by Dirac quantization method.
Non-Abelian bremsstrahlung and azimuthal asymmetries in high energy p+A reactions
Gyulassy, M.; Levai, P.; Vitev, I.; Biró, T. S.
2014-09-01
We apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute to all orders in nuclear opacity the non-Abelian gluon bremsstrahlung of event-by-event fluctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, vnM{1}, and even numbered 2ℓ gluon distribution, vnM{2ℓ}, inclusive distributions in high-energy p +A reactions as a function of harmonic n, target recoil cluster number, M, and gluon number, 2ℓ, at the RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form color scintillation antenna (CSA) arrays that lead to characteristic boost-noninvariant trapezoidal rapidity distributions in asymmetric B+A nuclear collisions. The scaling of the intrinsically azimuthally anisotropic and long range in η nature of the non-Abelian bremsstrahlung leads to vn moments that are similar to results from hydrodynamic models, but due entirely to non-Abelian wave interference phenomena sourced by the fluctuating CSA. Our analytic nonflow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd vn without invoking kT factorization. A test of the CSA mechanism is the predicted nearly linear η rapidity dependence of the vn(kT,η). Non-Abelian beam jet bremsstrahlung may, thus, provide a simple analytic solution to the beam energy scan puzzle of the near √s independence of vn(pT) moments observed down to 10 AGeV, where large-x valence-quark beam jets dominate inelastic dynamics. Recoil bremsstrahlung from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of vn in p(D)+A and noncentral A+A at the same dN/dη multiplicity as observed at the RHIC and LHC.
Algebraic cycles on the generic abelian fourfold with polarization of type (1,2,2,2)
Estrella, Russell Aarón Quiñones
2009-01-01
In this paper we construct a non-trivial element in the higher Griff{}iths group $Griff ^{3,2}$ for the generic abelian fourfold $A^4$ with polarization of type $(1,2,2,2)$. The key idea is to use that $A^4$ can be realized as a generalized Prym variety and for this reason contains in a natural way some curves i.e. dimension 1 cycles.
Product Integral Representations of Wilson Lines and Wilson Loops, and Non-Abelian Stokes Theorem
Karp, R L; Rno, J S
2000-01-01
We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as approximating them with partial sums, their convergence, and their behavior under gauge transformations. We also obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes theorem.
Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants
Mostafazadeh, A
1998-01-01
For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and the Floquet decompositions of the time-evolution operator is elucidated. In particular, a necessary condition for the occurrence of cyclic non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic states are obtained for a magnetic dipole interacting with a precessing magnetic field.
Upper bound and formula for class numbers of abelian function fields
无
2006-01-01
For any abelian function field K ( i. e. any subfield of a cyclotomic function field L = k (AP) over the rational function field k ) with conductor being an irreducible polynomial over a finite field of odd characteristic, by studying the Carlitz-module structure and the character group of K, an explicit upper bound and a calculating formula of the relative divisor class number h - (K) of K are given. Our calculated results of K develop Rosen's recent results of L.
Elementary abelian regular coverings of Platonic maps, Case I: ordinary representations
Jones, Gareth A
2012-01-01
We classify the orientably regular maps which are elementary abelian regular branched coverings of Platonic maps M, in the case where the covering group and the rotation group G of M have coprime orders. The method involves studying the representations of G on certain homology groups of the sphere, punctured at the branch-points. We give a complete classification for branching over faces (or, dually, vertices) of M, and outline how the method extends to other branching patterns.
Maximal abelian and Curci-Ferrari gauges in momentum subtraction at three loops
Bell, J M
2015-01-01
The vertex structure of QCD fixed in the maximal abelian gauge (MAG) and Curci-Ferrari gauge is analysed at two loops at the fully symmetric point for the 3-point functions corresponding to the three momentum subtraction (MOM) renormalization schemes. Consequently the three loop renormalization group functions are determined for each of these three schemes in each gauge using properties of the renormalization group equation.
Application of abelian holonomy formalism to the elementary theory of numbers
Abe, Yasuhiro
2012-05-01
We consider an abelian holonomy operator in two-dimensional conformal field theory with zero-mode contributions. The analysis is made possible by use of a geometric-quantization scheme for abelian Chern-Simons theory on S1 × S1 × R. We find that a purely zero-mode part of the holonomy operator can be expressed in terms of Riemann's zeta function. We also show that a generalization of linking numbers can be obtained in terms of the vacuum expectation values of the zero-mode holonomy operators. Inspired by mathematical analogies between linking numbers and Legendre symbols, we then apply these results to a space of Fp = Z/pZ, where p is an odd prime number. This enables us to calculate "scattering amplitudes" of identical odd primes in the holonomy formalism. In this framework, the Riemann hypothesis can be interpreted by means of a physically obvious fact, i.e., there is no notion of "scattering" for a single-particle system. Abelian gauge theories described by the zero-mode holonomy operators will be useful for studies on quantum aspects of topology and number theory.
Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
Carrasco, John Joseph M; Schlotterer, Oliver
2016-01-01
In this paper we derive the tree-level S-matrix of the effective theory of Goldstone bosons known as the non-linear sigma model (NLSM) from string theory. This novel connection relies on a recent realization of tree-level open-superstring S-matrix predictions as a double copy of super-Yang-Mills theory with Z-theory --- the collection of putative scalar effective field theories encoding all the alpha'-dependence of the open superstring. Here we identify the color-ordered amplitudes of the NLSM as the low-energy limit of abelian Z-theory. This realization also provides natural higher-derivative corrections to the NLSM amplitudes arising from higher powers of alpha' in the abelian Z-theory amplitudes, and through double copy also to Born-Infeld and Volkov-Akulov theories. The Kleiss-Kuijf and Bern-Carrasco-Johansson relations obeyed by Z-theory amplitudes thereby apply to all alpha'-corrections of the NLSM. As such we naturally obtain a cubic-graph parameterization for the abelian Z-theory predictions whose kin...
Quantum Exact Non-Abelian Vortices in Non-relativistic Theories
Nitta, Muneto; Vinci, Walter
2014-01-01
Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken in the vicinity of their cores. In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along the vortex. In relativistic theories, the Coleman-Mermin-Wagner theorem forbids the existence of a spontaneous symmetry breaking, or a long-range order, in 1+1 dimensions: quantum corrections restore the symmetry along the vortex and the NG modes acquire a mass gap. We show that in non-relativistic theories NG modes with quadratic dispersion relation confined on a vortex can remain gapless at quantum level. We provide a concrete and experimentally realizable example of a three-component Bose-Einstein condensate with U(1) x U(2) symmetry. We first show, at the classical level, the existence of S^3 = S^1 |x S^2 (S^1 fibered over S^2) NG modes associated to the breaking U(2) -> U(1) on vortices, where S^1 and S^2 correspond to type I and II NG modes, respectively. We th...
Non-Abelian Bremsstrahlung and Azimuthal Asymmetries in High Energy p+A Reactions
Gyulassy, M; Vitev, I; Biro, T
2014-01-01
We apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute the all-order in nuclear opacity non-abelian gluon bremsstrahlung of event-by-event fluctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, $v_n^M\\{1\\}$, and even number $2\\ell$ gluon, $v_n^M\\{2\\ell\\}$ inclusive distributions in high energy p+A reactions as a function of harmonic $n$, %independent target recoil cluster number, $M$, and gluon number, $2\\ell$, at RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form Color Scintillation Antenna (CSA) arrays that lead to characteristic boost non-invariant trapezoidal rapidity distributions in asymmetric $B+A$ nuclear collisions. The scaling of intrinsically azimuthally anisotropic and long range in $\\eta$ nature of the non-abelian \\br leads to $v_n$ moments that are similar to results from hydrodynamic models, but due entirely to non-abelian...
Non-Abelian vortex in four dimensions as a critical superstring
Shifman, M.; Yung, A.
2017-01-01
We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional N = 2 supersymmetric QCD with the U(2) gauge group, N f = 4 quark flavors and the Fayet-Iliopoulos term. Under certain conditions the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a twodimensional sigma model with the target space R4 × Y 6 where Y 6 is a non-compact Calabi-Yau conifold. The closed string states which emerge in four dimensions (4D) are identified with hadrons of 4D bulk N = 2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole-monopole baryon of the 4D theory (at strong coupling).
Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States
Liu, Zhao; Möller, Gunnar; Bergholtz, Emil J.
2017-09-01
We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects.
Fault-Tolerant Quantum Error Correction for non-Abelian Anyons
Dauphinais, Guillaume; Poulin, David
2017-07-01
While topological quantum computation is intrinsically fault-tolerant at zero temperature, it loses its topological protection at any finite temperature. We present a scheme to protect the information stored in a system supporting non-cyclic anyons against thermal and measurement errors. The correction procedure builds on the work of Gács (J Comput Syst Sci 32:15-78, 1986. doi: 10.1145/800061.808730) and Harrington (Analysis of quantum error-correcting codes: symplectic lattice codes and toric code, 2004) and operates as a local cellular automaton. In contrast to previously studied schemes, our scheme is valid for both abelian and non-abelian anyons and accounts for measurement errors. We analytically prove the existence of a fault-tolerant threshold for a certain class of non-Abelian anyon models, and numerically simulate the procedure for the specific example of Ising anyons. The result of our simulations are consistent with a threshold between {10^{-4}} and {10^{-3}}.
Non-Abelian Vortex in Four Dimensions as a Critical Superstring
Shifman, M
2016-01-01
We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional N=2 supersymmetric QCD with the U(2) gauge group, N_f=4 quark flavors and the Fayet-Iliopoulos term. Under certain conditions the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a two-dimensional sigma model with the target space {R}^4\\times Y_6 where Y_6 is a non-compact Calabi-Yau conifold. The closed string states which emerge in four dimensions (4D) are identified with hadrons of 4D bulk N=2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated wit...
Setting the renormalization scale in QCD: The principle of maximum conformality
Brodsky, S. J.; Di Giustino, L.
2012-01-01
the renormalization scale is set properly, all nonconformal beta not equal 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with beta...... = 0. The resulting scale-fixed predictions using the principle of maximum conformality (PMC) are independent of the choice of renormalization scheme-a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale setting in the Abelian limit...
任永泰; 李丽
2011-01-01
利用基于极大熵准则赋权和基于实数加速遗传算法的投影寻踪方法相结合的组合附权法确定了各预警指标的权重；采用层次分析法计算水资源可持续利用复合系统中各子系统所占权重；利用综合评价模型计算出哈尔滨市水资源可持续发展指数；最终得到哈尔滨市水资源可持续利用预警结果.%The weights of each warning index are determined by combination enables law which is based on the maximum entropy criterion empowerment and projection pursuit method of real accelerating genetic algorithm; Using analytic hierarchy process to calculate the weights of each subsystem in composite system of water resources sustainable utilization; Sustainable development index of Harbin water resources is calculated by using comprehensive evaluation model; Warning results of Harbin water resources sustainable utilization are got eventually.
Non Abelian structures and the geometric phase of entangled qudits
Oxman, L.E., E-mail: oxman@if.uff.br; Khoury, A.Z., E-mail: khoury@if.uff.br
2014-12-15
In this work, we address some important topological and algebraic aspects of two-qudit states evolving under local unitary operations. The projective invariant subspaces and evolutions are connected with the common elements characterizing the su(d) Lie algebra and their representations. In particular, the roots and weights turn out to be natural quantities to parametrize cyclic evolutions and fractional phases. This framework is then used to recast the coset contribution to the geometric phase in a form that generalizes the usual monopole-like formula for a single qubit.
Maximum likely scale estimation
Loog, Marco; Pedersen, Kim Steenstrup; Markussen, Bo
2005-01-01
A maximum likelihood local scale estimation principle is presented. An actual implementation of the estimation principle uses second order moments of multiple measurements at a fixed location in the image. These measurements consist of Gaussian derivatives possibly taken at several scales and/or ...
Maximum information photoelectron metrology
Hockett, P; Wollenhaupt, M; Baumert, T
2015-01-01
Photoelectron interferograms, manifested in photoelectron angular distributions (PADs), are a high-information, coherent observable. In order to obtain the maximum information from angle-resolved photoionization experiments it is desirable to record the full, 3D, photoelectron momentum distribution. Here we apply tomographic reconstruction techniques to obtain such 3D distributions from multiphoton ionization of potassium atoms, and fully analyse the energy and angular content of the 3D data. The PADs obtained as a function of energy indicate good agreement with previous 2D data and detailed analysis [Hockett et. al., Phys. Rev. Lett. 112, 223001 (2014)] over the main spectral features, but also indicate unexpected symmetry-breaking in certain regions of momentum space, thus revealing additional continuum interferences which cannot otherwise be observed. These observations reflect the presence of additional ionization pathways and, most generally, illustrate the power of maximum information measurements of th...
Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS 5 σ-model
Hoare, B.; Tseytlin, A. A.
2016-12-01
We propose that the Yang-Baxter deformation of the symmetric space σ-model parameterized by an r-matrix solving the homogeneous (classical) Yang-Baxter equation is equivalent to the non-abelian dual of the undeformed model with respect to a subgroup determined by the structure of the r-matrix. We explicitly demonstrate this on numerous examples in the case of the {{AdS}}5 σ-model. The same should also be true for the full {{AdS}}5× {S}5 supercoset model, providing an explanation for and generalizing several recent observations relating homogeneous Yang-Baxter deformations based on non-abelian r-matrices to the undeformed {{AdS}}5× {S}5 model by a combination of T-dualities and nonlinear coordinate redefinitions. This also includes the special case of deformations based on abelian r-matrices, which correspond to TsT transformations: they are equivalent to non-abelian duals of the original model with respect to a central extension of abelian subalgebras.
Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
Hoare, B
2016-01-01
We propose that the Yang-Baxter deformation of the symmetric space sigma-model parameterized by an r-matrix solving the homogeneous (classical) Yang-Baxter equation is equivalent to the non-abelian dual of the undeformed model with respect to a subgroup determined by the structure of the r-matrix. We explicitly demonstrate this on numerous examples in the case of the AdS_5 sigma-model. The same should also be true for the full AdS_5 x S^5 supercoset model, providing an explanation for and generalizing several recent observations relating homogeneous Yang-Baxter deformations based on non-abelian r-matrices to the undeformed AdS_5 x S^5 model by a combination of T-dualities and non-linear coordinate redefinitions. This also includes the special case of deformations based on abelian r-matrices, which correspond to TsT transformations: they are equivalent to non-abelian duals of the original model with respect to a central extension of abelian subalgebras.
Fuad Julardžija
2014-04-01
Full Text Available Introduction: Magnetic resonance cholangiopancreatography (MRCP is a method that allows noninvasive visualization of pancreatobiliary tree and does not require contrast application. It is a modern method based on heavily T2-weighted imaging (hydrography, which uses bile and pancreatic secretions as a natural contrast medium. Certain weaknesses in quality of demonstration of pancreatobiliary tract can be observed in addition to its good characteristics. Our aim was to compare the 3D Maximum intensity projection (MIP reconstruction and 2D T2 Half-Fourier Acquisition Single-Shot Turbo Spin-Echo (HASTE sequence in magnetic resonance cholangiopancreatography.Methods: During the period of one year 51 patients underwent MRCP on 3T „Trio“ system. Patients of different sex and age structure were included, both outpatient and hospitalized. 3D MIP reconstruction and 2D T2 haste sequence were used according to standard scanning protocols.Results: There were 45.1% (n= 23 male and 54.9% (n=28 female patients, age range from 17 to 81 years. 2D T2 haste sequence was more susceptible to respiratory artifacts presence in 64% patients, compared to 3D MIP reconstruction with standard error (0.09, result significance indication (p=0.129 and confidence interval (0.46 to 0.81. 2D T2 haste sequences is more sensitive and superior for pancreatic duct demonstration compared to 3D MIP reconstruction with standard error (0.07, result significance indication (p=0.01 and confidence interval (0.59 to 0.87Conclusion: In order to make qualitative demonstration and analysis of hepatobiliary and pancreatic system on MR, both 2D T2 haste sequence in transversal plane and 3D MIP reconstruction are required.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
Nielsen, H.B. [Niels Bohr Inst., Kobenhavn (Denmark); Rugh, H.H. [Univ. of Warwick, Coventry (United Kingdom); Rugh, S.E. [Los Alamos National Lab., NM (United States)
1996-12-31
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a {open_quote}no go{close_quotes} for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a {open_quotes}continuum limit{close_quotes} in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined.
The geometry and physics of Abelian gauge groups in F-theory
Keitel, Jan
2015-07-14
In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.
Phase diagram and non-Abelian symmetry locking for fermionic mixtures with unequal interactions
Pinto Barros, Joao C.; Lepori, Luca; Trombettoni, Andrea
2017-07-01
The realization of experiments in ultracold multicomponent mixtures, also involving more atomic species, opened the way to the study of exotic quantum phases and unconventional superfluidity, as, for instance non-Abelian superfluid phases. In this paper we study the occurrence of non-Abelian symmetry-locked superfluid states in ultracold fermionic mixtures with four components, showing that such states can be studied in current day experiments with 171Yb-173Yb isotopes. We study the phase diagram in the presence of an attractive interaction between the species of two pairs of the mixture, and general (also repulsive) interactions between the species of each pair. This system can be physically realized, e.g., in mixtures of two different earth-alkaline species, both of them with two hyperfine levels selectively populated. We find an extended region of the diagram exhibiting a two-flavors superfluid symmetry-locking (TFSL) phase. The locking corresponds to the presence of a order parameter involving—in all the possible and distinct permitted ways—two fermions, one of them belonging to the first pair and the second to the other one. This TSFL phase is present also for not too large repulsive intrapair interactions and it is characterized by a global non-Abelian symmetry group obtained by locking together two independent invariance groups of the corresponding normal state. Explicit estimates are reported for the mixture of the fermionic isotopes 171Yb-173Yb , indicating that the TFSL phase can be achieved also without tuning the interactions between Yb atoms.
Maximum Likelihood Associative Memories
Gripon, Vincent; Rabbat, Michael
2013-01-01
Associative memories are structures that store data in such a way that it can later be retrieved given only a part of its content -- a sort-of error/erasure-resilience property. They are used in applications ranging from caches and memory management in CPUs to database engines. In this work we study associative memories built on the maximum likelihood principle. We derive minimum residual error rates when the data stored comes from a uniform binary source. Second, we determine the minimum amo...
Maximum likely scale estimation
Loog, Marco; Pedersen, Kim Steenstrup; Markussen, Bo
2005-01-01
A maximum likelihood local scale estimation principle is presented. An actual implementation of the estimation principle uses second order moments of multiple measurements at a fixed location in the image. These measurements consist of Gaussian derivatives possibly taken at several scales and....../or having different derivative orders. Although the principle is applicable to a wide variety of image models, the main focus here is on the Brownian model and its use for scale selection in natural images. Furthermore, in the examples provided, the simplifying assumption is made that the behavior...... of the measurements is completely characterized by all moments up to second order....
Chern-Simons in the Seiberg-Witten map for non-commutative Abelian gauge theories in 4D
Picariello, M; Sorella, S P; Picariello, Marco; Quadri, Andrea; Sorella, Silvio P.
2002-01-01
A cohomological BRST characterization of the Seiberg-Witten (SW) map is given. We prove that the coefficients of the SW map can be identified with elements of the cohomology of the BRST operator modulo a total derivative. As an example, it will be illustrated how the first coefficients of the SW map can be written in terms of the Chern-Simons three form. This suggests a deep topological and geometrical origin of the SW map. The existence of the map for both Abelian and non-Abelian case is discussed. By using a recursive argument and the associativity of the $\\star$-product, we shall be able to prove that the Wess-Zumino consistency condition for non-commutative BRST transformations is fulfilled. The recipe of obtaining an explicit solution by use of the homotopy operator is briefly reviewed in the Abelian case.
Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
Fujiwara, T; Wu, K; Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
2000-01-01
The axial anomaly in lattice gauge theories has topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological techniques. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which validates the Leibniz rule of exterior derivatives on the lattice. The topological nature of the ``Chern character'' on the lattice becomes manifest with NCDC. Our result provides an algebraic proof of Lüscher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions.
Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the Lattice
Suzuki, H
1999-01-01
Lüscher's recent formulation of Abelian chiral gauge theories on the lattice, in the vacuum (or perturbative) sector in infinite lattice volume, is re-interpreted in terms of the lattice covariant regularization. The gauge invariance of the effective action and the integrability of the gauge current in anomaly-free cases become transparent then. The real part of the effective action is simply one-half of that of the Dirac fermion and, when the Dirac operator has proper properties in the continuum limit, the imaginary part in the continuum limit reproduces the $\\eta$-invariant.}
Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories
Eto, Minoru; Gudnason, Sven Bjarke; Konishi, Kenichi; Nagashima, Takayuki; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2009-01-01
Non-Abelian BPS vortices in SO(N) x U(1) and USp(2N) x U(1) gauge theories are constructed in maximally color-flavor locked vacua. We study in detail their moduli and transformation properties under the exact symmetry of the system. Our results generalize non-trivially those found earlier in supersymmetric U(N) gauge theories. The structure of the moduli spaces turns out in fact to be considerably richer here than what was found in the U(N) theories. We find that vortices are generally of the semi-local type, with power-like tails of profile functions.
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.
Group Approach to the Quantization of Non-Abelian Stueckelberg Models
Aldaya, V; Lopez-Ruiz, F F [Instituto de Astrofisica de AndalucIa (IAA-CSIC), Apartado Postal 3004, 18080 Granada (Spain); Calixto, M, E-mail: valdaya@iaa.es, E-mail: Manuel.Calixto@upct.es, E-mail: flopez@iaa.es [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain)
2011-03-01
The quantum field theory of Non-Linear Sigma Models on coadjoint orbits of a semi-simple group G are formulated in the framework of a Group Approach to Quantization. In this scheme, partial-trace Lagrangians are recovered from two-cocycles defined on the infinite-dimensional group of sections of the jet-gauge group J{sup 1} (G). This construction is extended to the entire physical system coupled to Yang-Mills fields, thus constituting an algebraic formulation of the Non-Abelian Stueckelgerg formalism devoid of the unitarity/renormalizability obstruction that this theory finds in the standard Lagrangian formalism under canonical quantization.
Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces
Przemysław Górka
2014-01-01
Full Text Available We continue our research on Sobolev spaces on locally compact abelian (LCA groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology. In this paper, we focus on compact embedding results and we prove an analog for LCA groups of the classical Rellich lemma and of the Rellich-Kondrachov compactness theorem. Furthermore, we introduce Sobolev spaces on subsets of LCA groups and study its main properties, including the existence of compact embeddings into Lp-spaces.
Public key cryptosystem and a key exchange protocol using tools of non-abelian group
H. K. Pathak,
2010-07-01
Full Text Available Public Key Cryptosystems assure privacy as well as integrity of the transactions between two parties. The sizes of the keys play an important role. The larger the key the harder is to crack a block ofencrypted data. We propose a new public key cryptosystem and a Key Exchange Protocol based on the generalization of discrete logarithm problem using Non-abelian group of block upper triangular matrices of higher order. The proposed cryptosystem is efficient in producing keys of large sizes without the need of large primes. The security of both the systems relies on the difficulty of discrete logarithms over finite fields.
Hints of 5d Fixed Point Theories from Non-Abelian T-duality
Lozano, Yolanda; Rodriguez-Gomez, Diego
2013-01-01
In this paper we investigate the properties of the putative 5d fixed point theory that should be dual, through the holographic correspondence, to the new supersymmetric AdS(6) solution constructed in Lozano et al. This solution is the result of a non-Abelian T-duality transformation on the known supersymmetric AdS(6) solution of massive Type IIA. The analysis of the charge quantization conditions seems to put constraints on the global properties of the background, which, combined with the information extracted from considering probe branes, suggests a 2-node quiver candidate for the dual CFT.
Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model
Sfetsos, Konstadinos
2014-01-01
We study what we call the all-loop anisotropic bosonized Thirring sigma model. This interpolates between the WZW model and the non-Abelian T-dual of the principal chiral model for a simple group. It has an invariance involving the inversion of the matrix parametrizing the coupling constants. We compute the general renormalization group flow equations which assume a remarkably simple form and derive its properties. For symmetric couplings, they consistently truncate to previous results in the literature. One of the examples we provide gives rise to a first order system of differential equations interpolating between the Lagrange and the Darboux-Halphen integrable systems.
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)
2009-05-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.
Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
Lahoche, Vincent; Rivasseau, Vincent
2015-01-01
We study a just renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
Carrozza, Sylvain; Rivasseau, Vincent
2012-01-01
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including: connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.
Gaugino mass mixing in SUSY GUTs with two Abelian gauge groups
Braam, F. [Freiburg Univ. (Germany). Physikalisches Inst.; Reuter, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2011-08-15
Supersymmetric Grand Unified Theories often involve an additional Abelian group factor apart from the standard model hypercharge. Although in many cases there is a procedure to avoid loop-induced mixing of the gauge kinetic terms by choosing a suitable basis for the two U(1) groups in group space, a residual mixing in the soft SUSY breaking gaugino mass terms remains. In this letter we generalize the renormalization group equations for the gaugino mass terms to account for this effect. In a further calculation we also present the necessary adjustments in the renormalization group equations of the trilinear soft breaking couplings and the soft breaking scalar mass squares. (orig.)
Existence of non-abelian representations of the near hexagon (5, 2) $\\otimes$ (5, 2)
Binod Kumar Sahoo
2016-05-01
In [5], a new combinatorial model with four types of points and nine types of lines of the slim dense near hexagon (5, 2) $\\otimes$ (5, 2) was provided and it was then used to construct a non-abelain representation of (5, 2) $\\otimes$ (5, 2) in the extraspecial 2-group 2$^{1+18}_{−}$ . In this paper, we give a direct proof for the existence of a non-abelian representation of (5, 2) $\\otimes$ (5, 2) in 2$^{1+18}_{−}$ .
Abelian and derived deformations in the presence of Z-generating geometric helices
De Deken, Olivier
2010-01-01
For a Grothendieck category C which, via a Z-generating sequence (O(n))_{n in Z}, is equivalent to the category of "quasi-coherent modules" over an associated Z-algebra A, we show that under suitable cohomological conditions "taking quasi-coherent modules" defines an equivalence between linear deformations of A and abelian deformations of C. If (O(n))_{n in Z} is at the same time a geometric helix in the derived category, we show that restricting a (deformed) Z-algebra to a "thread" of objects defines a further equivalence with linear deformations of the associated matrix algebra.
Weak Coupling Phase Structureof the Abelian Higgs Model at Finite Temperature
Jakovác, A
1993-01-01
Using the 1-loop reduced 3D action of the Abelian Higgs-model we discuss the order of its finite temperature phase transition. A two-variable saddle point approximation is proposed for the evaluation of the effective potential. The strength of the first order case scales like \\sim e^{3-6}. Analytic asymptotic weak coupling and numerical small coupling solutions are compared with special emphasis on the cancellation of divergences. (Figures are not included, can be sent upon request from jako@hercules.elte.hu .)
About the triviality of the higher derivative sector in the abelian Lee-Wick model
Fiorentini, D
2016-01-01
Canonical quantization is reviewed here for the Abelian Lee-Wick model by using the Dirac constraints method. New degrees of freedom associated to the (higher derivatives) Lee-Wick ghost are excluded from the (physical) space of observables by a new prescription, based on the Nielsen-type BRST-extended symmetry for the Lee-Wick mass term. We prove that this prescription is nothing but an effective form of implementing the cohomological triviality of the higher-derivative pure sector associated to the existence of a new exclusive higher-derivative BRST symmetry.
Abelian tensor hierarchy and Chern-Simons actions in 4D N=1 conformal supergravity
Yokokura, Ryo
2016-01-01
We consider Chern-Simons actions of Abelian tensor hierarchy of $p$-form gauge fields in four-dimensional ${\\cal N}=1$ supergravity. Using conformal superspace formalism, we solve the constraints on the field strengths of the $p$-form gauge superfields in the presence of the tensor hierarchy. The solutions are expressed by the prepotentials of the $p$-form gauge superfields. We show the internal and superconformal transformation laws of the prepotentials. The descent formalism for the Chern-Simons actions is exhibited.
A geometric discretisation scheme applied to the Abelian Chern-Simons theory
Sen, S; Sexton, J C; Adams, D H; Sen, Samik; Sen, Siddhartha; Sexton, James C.; Adams, David H
2000-01-01
We give a detailed general description of a recent geometrical discretisation scheme and illustrate, by explicit numerical calculation, the scheme's ability to capture topological features. The scheme is applied to the Abelian Chern-Simons theory and leads, after a necessary field doubling, to an expression for the discrete partition function in terms of untwisted Reidemeister torsion and of various triangulation dependent factors. The discrete partition function is evaluated computationally for various triangulations of $S^3$ and of lens spaces. The results confirm that the discretisation scheme is triangulation independent and coincides with the continuum partition function
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
Di Bartolo, Cayetano; Leal, Lorenzo
2012-01-01
A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.
Scale-Setting Without the Higgs Mechanism:. Non-Abelian Symmetry
Anderson, J. T.
For the non-Abelian Higgs model it is shown that the coupled equations of motion for Aμ, ϕ and ϕ* have nonanalytic singularities which must be removed if the equations are integrable. Current conservation is found to remove the singularities in the vector-field equation and give a mass scale independent of V and the Higgs mechanism. The self-consistent field solutions for Aμ and the ϕ fields give either (1) the Higgs mechanism, zero current and the pure-gauge solution, or (2) nonzero current, a gauge-covariant solution and the mass scale independent of V and the Higgs mechanism.
Non-Abelian (2,0)-super-Yang-Mills coupled to linear {sigma}-models
Goes-Negrao, M.S.; Helayel-Neto, J.A.; Negrao, M.R. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Universidade Catolica de Petropolis, RJ (Brazil). E-mail: negrao@cbpf.br; helayel@cbpf.br; guida@cbpf.br
2000-06-01
Considering a class of (2,0)-super-Yang-Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here non-Abelian coupling to ordinary matter and to non-linear {sigma}-models in (2,0)-superspace. The dynamics and the couplings of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials whenever light-cone coordinates are chosen. (author)
Self-Dual Vortices in Abelian Higgs Models with Dielectric Function on the Noncommutative Plane
Fuertes, W García
2014-01-01
We show that Abelian Higgs Models with dielectric function defined on the noncommutative plane enjoy self-dual vorticial solutions. By choosing a particular form of the dielectric function, we provide a family of solutions whose Higgs and magnetic fields interpolate between the profiles of the noncommutative Nielsen-Olesen and Chern-Simons vortices. This is done both for the usual $U(1)$ model and for the $SU(2)\\times U(1)$ semilocal model with a doublet of complex scalar fields. The variety of known noncommutative self-dual vortices which display a regular behaviour when the noncommutativity parameter tends to zero results in this way considerably enlarged.
Inflationary models with a flat potential enforced by non-abelian discrete gauge symmetries
Stewart, E D
2001-01-01
Non-abelian discrete gauge symmetries can provide the inflaton with a flatpotential even when one takes into account gravitational strength effects. Thediscreteness of the symmetries also provide special field values whereinflation can end via a hybrid type mechanism. An interesting feature of thismethod is that it can naturally lead to extremely flat potentials and so, inprinciple, to inflation at unusually low energy scales. Two examples ofeffective field theories with this mechanism are given, one with a hybrid exitand one with a mutated hybrid exit. They include an explicit example in whichthe single field consistency condition is violated.
Images of l-adic representations and automorphisms of abelian varieties
Silverberg, A
1996-01-01
Suppose F is either a global field or a finitely generated extension of {\\mathbf Q}, A is an abelian variety over F, and \\ell is a prime not equal to the characteristic of F. Let Z denote the center of the endomorphism algebra of A. Let G denote the group of {\\mathbf Q}_\\ell-points of the identity connected component of the Zariski closure of the image of the \\ell-adic representation associated to A. We prove the \\ell-independence of the intersection of G with the torsion subgroup of Z. Our results provide evidence in the direction of the Mumford-Tate Conjecture.
On Maximal Abelian Self-adjoint Subalgebras of Factors of Type Ⅱ1
Li Guang WANG
2005-01-01
In this note, we show that if (N) is a proper subfactor of a factor (M) of type Ⅱ1 with finite Jones index, then there is a maximal abelian self-adjoint subalgebra (masa) (A) of (N) that is not a masa in (M). Popa showed that there is a proper subfactor (R)O of the hyperfinite type Ⅱ1 factor (R) such that each masa in (R)O is also a masa in (R). We shall give a detailed proof of Popa's result.
A class of ${\\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra
Houdayer, Cyril
2012-01-01
We show that for every mixing orthogonal representation $\\pi : \\Z \\to \\mathcal O(H_\\R)$, the abelian subalgebra $\\LL(\\Z)$ is maximal amenable in the crossed product ${\\rm II}_1$ factor $\\Gamma(H_\\R)\\dpr \\rtimes_\\pi \\Z$ associated with the free Bogoljubov action of the representation $\\pi$. This provides uncountably many non-isomorphic $A$-$A$-bimodules which are disjoint from the coarse $A$-$A$-bimodule and of the form $\\LL^2(M \\ominus A)$ where $A \\subset M$ is a maximal amenable masa in a ${\\rm II_1}$ factor.
Non-abelian T-duality of Pilch-Warner background
Dimov, H; Rashkov, R C; Vetsov, T
2015-01-01
In this work we obtain the non-abelian T-dual geometry of the well-known Pilch-Warner supergravity solution. We derive the dual metric and the NS two-form by gauging the isometry group of the initial theory and integrating out the introduced auxiliary gauge fields. Then we use the Fourier-Mukai transform from algebraic geometry to find the transformation rules of the R-R fields. Finally, we argue that the dual theory inherit the supersymmetry of the original one by considering the general dependence of the Killing spinor on the spacetime coordinates.
Infinite-randomness fixed points for chains of non-Abelian quasiparticles.
Bonesteel, N E; Yang, Kun
2007-10-05
One-dimensional chains of non-Abelian quasiparticles described by SU(2)k Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to k-->infinity). For k=2 this phase provides a random singlet description of the infinite-randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size L in these phases scales as S(L) approximately lnd/3 log(2)L for large L, where d is the quantum dimension of the particles.
Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu
2012-11-02
We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) × U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N(2)) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter μ and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a Ø(4) theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions.
The CP(N-1) model on a Disc and Decay of a Non-Abelian String
Gorsky, A
2013-01-01
We consider the role of quantum effects in the non-perturbative decay of non-abelian string with orientational moduli in non-supersymmetric D=4 gauge theory. To this aim the effective action in the $CP(N-1)$ model on a disc at large N has been calculated. It exhibits phase transition at some radius, the "wrong sign" Luscher term and large boundary boojum-like negative contribution. The effect of $\\theta$ - term and the possibility of the spontaneous creation of the non-abelian string are briefly discussed.
F. TopsÃƒÂ¸e
2001-09-01
Full Text Available Abstract: In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over
Regularized maximum correntropy machine
Wang, Jim Jing-Yan
2015-02-12
In this paper we investigate the usage of regularized correntropy framework for learning of classifiers from noisy labels. The class label predictors learned by minimizing transitional loss functions are sensitive to the noisy and outlying labels of training samples, because the transitional loss functions are equally applied to all the samples. To solve this problem, we propose to learn the class label predictors by maximizing the correntropy between the predicted labels and the true labels of the training samples, under the regularized Maximum Correntropy Criteria (MCC) framework. Moreover, we regularize the predictor parameter to control the complexity of the predictor. The learning problem is formulated by an objective function considering the parameter regularization and MCC simultaneously. By optimizing the objective function alternately, we develop a novel predictor learning algorithm. The experiments on two challenging pattern classification tasks show that it significantly outperforms the machines with transitional loss functions.
Non-abelian T-dualizing the resolved conifold with regular and fractional D3-branes
Kooner, K.S. [Department of Physics, Swansea University,Singleton Park, Swansea SA2 8PP (United Kingdom); Zacarías, S. [Department of Nuclear and Particle Physics, Faculty of Physics, University of Athens,Athens 15784 (Greece); Departamento de Física, División de Ciencias e Ingenierías,Campus León, Universidad de Guanajuato,Loma del Bosque No. 103 Col. Lomas del Campestre, C.P. 37150, León, Guanajuato (Mexico)
2015-08-28
In this paper we obtain new solutions of Type IIA and massive Type IIA supergravity. These solutions are the result of implementing a non-abelian T-duality along the internal SU(2) isometries of several D3-brane configurations on the resolved conifold, studied by Pando Zayas and Tseytlin. We first study the pure NS resolved conifold solution, then we add fluxes by placing a stack of D3-branes at the tip of the resolved conifold and finally we consider the system of regular and fractional D3-branes at the tip. We present the non-abelian T-duals associated with these backgrounds and study their geometries and fluxes. We briefly comment on some field theory features by studying couplings and the central charge of the dual field theory. We also analyze the supersymmetry of the dual solutions and show that for the system of only D3 branes the duality defines a map between backgrounds with SU(3) and orthogonal SU(2) structures.
Quantum Computation and Non-Abelian Statistics in Chern-Simons-Higgs Theory
Brozeguini, J C
2013-01-01
We naturally obtain the NOT and CNOT logic gates, which are key pieces of quantum computing algorithms, in the framework of the non-Abelian Chern-Simons-Higgs theory in two spatial dimensions. For that, we consider the anyonic quantum vortex topological excitations occurring in this system and show that self-adjoint (Majorana-like) combinations of these vortices and anti-vortices have in general non-Abelian statistics. The associated unitary monodromy braiding matrices become the required logic gates in the special case when the vortex spin is $s=1/4$. We explicitly construct the vortex field operators, show that they carry both magnetic flux and charge and obtain their euclidean correlation functions by using the method of quantization of topological excitations, which is based on the order-disorder duality. These correlators are in general multivalued, the number of sheets being determined by the vortex spin. This, by its turn, is proportional to the vacuum expectation value of the Higgs field and therefore...
NonAbelian Vortices, Large Winding Limits and Aharonov-Bohm Effects
Bolognesi, Stefano; Konishi, Kenichi
2015-01-01
Remarkable simplification arises from considering vortex equations in the large winding limit. This was recently used in [1] to display all sorts of vortex zeromodes, the orientational, translational, fermionic as well as semi-local, and to relate them to the apparently distinct phenomena of the Nielsen-Olesen-Ambjorn magnetic instabilities. Here we extend these analyses to more general types of BPS nonAbelian vortices, taking as a prototype a system with gauged U(1) x SU(N) x SU(N) symmetry where the VEV of charged scalar fields in the bifundamental representation breaks the symmetry to SU(N)_{l+r} . The presence of the massless SU(N)_{l+r} gauge fields in 4D bulk introduces all sorts of non-local, topological phenomena such as the nonAbelian Aharonov-Bohm effects, which in the theory with global SU(N)_r group (g_r=0) are washed away by the strongly fluctuating orientational zeromodes in the worldsheet. Physics changes qualitatively at the moment the right gauge coupling constant g_r is turned on.
Internal structure of non-Abelian black holes and nature of singularity
Galtsov, D V; Zotov, M Yu
1997-01-01
Recent results concerning the internal structure of static spherically-symmetric non-Abelian black holes in the Einstein-Yang-Mills (EYM) theory and its generalizations including scalar fields are reviewed and discussed with an emphasis on the problem of a generic singularity in black holes. It is argued that in the theories admitting a violation of the naive no-hair conjecture the structure of singularity is essentially affected by the "hair roots". This invalidates an image of a non-Abelian black hole as a Schwarzschild black hole sitting inside the soliton. We give an analytic description of the generic oscillatory approach to the singularity in the pure EYM theory in terms of a divergent discrete sequence and show that the mass function is exponentially growing "in average". The second type of a generic approach to the singularity in hairy black holes is a "power-law mass inflation" which is realized in the theories including scalar fields. Both singularities are spacelike and no Cauchy horizons are met i...
Chaos-order transition in Bianchi I non-Abelian Born-Infeld cosmology
Dyadichev, V V; Moniz, P V; Dyadichev, Vladimir V.; Gal'tsov, Dmitri V.; Moniz, Paulo Vargas
2005-01-01
We investigate the Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field governed by the non-Abelian Born-Infeld action. Similar system with the standard Einstein-Yang-Mills (EYM) action is known to exhibit chaotic behavior induced by the Yang-Mills field. When the action is replaced by the Born-Infeld-type non-Abelian action (NBI), the chaos-order transition is observed in the high energy region. This is interpreted as a smothering effect due to (non-perturbative in $alpha'$) string corrections to the classical EYM action. We give a numerical evidence for the chaos-order transition, and present an analytical proof of regularity of color oscillations in the limit of strong Born-Infeld non-linearity. We also perform some general analysis of the Bianchi I NBI cosmology and derive an exact solution in the case when only the U(1) component of the Yang-Mills field is excited. Our new exact solution generalizes the Rosen solution to the Bianchi I Einstein-Maxwell cosmology to the U(1) Einstein-Born-Infeld...
Black string first order flow in N=2, d=5 abelian gauged supergravity
Klemm, Dietmar; Rabbiosi, Marco
2016-01-01
We derive both BPS and non-BPS first-order flow equations for magnetically charged black strings in five-dimensional N=2 abelian gauged supergravity, using the Hamilton-Jacobi formalism. This is first done for the coupling to vector multiplets only and U(1) Fayet-Iliopoulos (FI) gauging, and then generalized to the case where also hypermultiplets are present, and abelian symmetries of the quaternionic hyperscalar target space are gauged. We then use these results to derive the attractor equations for near-horizon geometries of extremal black strings, and solve them explicitely for the case where the constants appearing in the Chern-Simons term of the supergravity action satisfy an adjoint identity. This allows to compute in generality the central charge of the two-dimensional conformal field theory that describes the black strings in the infrared, in terms of the magnetic charges, the CY intersection numbers and the FI constants. Finally, we extend the r-map to gauged supergravity and use it to relate our flo...
Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
Zhang, Yuhe; Sreejith, G. J.; Jain, J. K.
2015-08-01
The possibility of realizing bosonic fractional quantum Hall effect in ultracold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their nontrivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor ν =1 . We show that a Hamiltonian with an appropriate three-body interaction can produce two-quasihole states in two distinct fusion channels of the topological "qubit." Characteristics of these states that are related to the non-Abelian nature can be probed and verified by a measurement of the effective relative angular momentum of the auxiliary bosons, which is directly related to their pair distribution function. Moore-Read states of more than two quasiholes can also be produced in a similar fashion. We investigate some issues related to the experimental feasibility of this approach, in particular, how large the systems should be for a realization of this physics and to what extent this physics carries over to systems with the more standard two-body contact interaction.
Non-Abelian black string solutions of N = (2,0) , d = 6 supergravity
Cano, Pablo A.; Ortín, Tomás; Santoli, Camilla
2016-12-01
We show that, when compactified on a circle, N = (2, 0), d = 6 supergravity coupled to 1 tensor multiplet and n V vector multiplets is dual to N = (2 , 0) , d = 6 supergravity coupled to just n T = n V + 1 tensor multiplets and no vector multiplets. Both theories reduce to the same models of N = 2 , d = 5 supergravity coupled to n V 5 = n V + 2 vector fields. We derive Buscher rules that relate solutions of these theories (and of the theory that one obtains by dualizing the 3-form field strength) admitting an isometry. Since the relations between the fields of N = 2 , d = 5 supergravity and those of the 6-dimensional theories are the same with or without gaugings, we construct supersymmetric non-Abelian solutions of the 6-dimensional gauged theories by uplifting the recently found 5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions describe the usual superpositions of strings and waves supplemented by a BPST instanton in the transverse directions, similar to the gauge dyonic string of Duff, Lü and Pope. One of the solutions obtained interpolates smoothly between two AdS3× S3 geometries with different radii.
张贤科
1999-01-01
Let L be an abelian extension of the rationals Q whose Galois group Gal(L) is an abelian (q-group q is any prime number). The explicit law of prime decomposition in L for any prime number p, the inertia group, residue class degree, and discriminant of L are given here; such fields L are classified into 4 or 8 classes according as q is odd or even with clear description of their structures. Then relative extension L/K is studied. L/K is proved to have a relative integral basis under certain simple conditions; relative discriminant D(L/K) is given explicitly; and necessary and sufficient conditions are obtained for D(L/K) to be generated by a rational square (and by a rational). In particular, it is proved that L/K has a relative integral basis and that D(L/K) is generated by a rational square if [L: K]≥x~* or x~*+1 (according as q is odd or even), where x~* is the exponent of Gal(L). These results contain many related results on similar fields in literature.
Critical non-Abelian vortex in four dimensions and little string theory
Shifman, M.; Yung, A.
2017-08-01
As was shown recently, non-Abelian vortex strings supported in four-dimensional N =2 supersymmetric QCD with the U(2) gauge group and Nf=4 quark multiplets (flavors) become critical superstrings. In addition to the translational moduli, non-Abelian strings under consideration carry six orientational and size moduli. Together, they form a ten-dimensional target space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space and a Calabi-Yau noncompact threefold, namely, the conifold. We study closed string states which emerge in four dimensions and identify them with hadrons of four-dimensional N =2 QCD. One massless state was found previously; it emerges as a massless hypermultiplet associated with the deformation of the complex structure of the conifold. In this paper, we find a number of massive states. To this end, we exploit the approach used in LST little string theory, namely, the equivalence between the critical string on the conifold and noncritical c =1 string with the Liouville field and a compact scalar at the self-dual radius. The states we find carry "baryonic" charge (its definition differs from standard). We interpret them as "monopole necklaces" formed (at strong coupling) by the closed string with confined monopoles attached.
Non-Abelian 1-Form Gauge Theory With Dirac Fields: Supersymmetric Unitary Operator
Bhanja, T; Malik, R P
2015-01-01
Within the framework of augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the supersymmetric (SUSY) unitary operator (and its hermitian conjugate) in the context of four (3 + 1)-dimensional (4D) interacting non-Abelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates x^\\mu (with \\mu = 0, 1, 2, 3) and a pair of Grassmannian variables (\\theta, \\bar\\theta) which satisfy the standard relationships: \\theta^2 = {\\bar\\theta}^2 = 0, \\theta\\,\\bar\\theta + \\bar\\theta\\,\\theta = 0. Various consequences of the application of the above SUSY unitary operator (and its hermitian conjugate) are discussed. In particular, we obtain the results of the application of the horizontality condition (HC) and gauge invariant restriction (GIR) in the language of the above SUSY operators. One of the no...
Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.
Li, Keren; Wan, Yidun; Hung, Ling-Yan; Lan, Tian; Long, Guilu; Lu, Dawei; Zeng, Bei; Laflamme, Raymond
2017-02-24
Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.
Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes
Critelli, R; Zaniboni, M; Noronha, J
2014-01-01
Recent estimates for the electromagnetic fields produced in the early stages of non-central ultra-relativistic heavy ion collisions indicate the presence of magnetic fields $B\\sim \\mathcal{O}(0.1-15\\,m_\\pi^2)$, where $m_\\pi$ is the pion mass. It is then of special interest to study the effects of strong (Abelian) magnetic fields on the transport coefficients of strongly coupled non-Abelian plasmas, such as the quark-gluon plasma formed in heavy ion collisions. In this work we study the anisotropy in the shear viscosity induced by an external magnetic field in a strongly coupled $\\mathcal{N} = 4$ SYM plasma. Due to the spatial anisotropy created by the magnetic field, the most general viscosity tensor has 5 shear viscosity coefficients and 2 bulk viscosities. We use the holographic correspondence to evaluate two of the shear viscosities, $\\eta_{\\perp} \\equiv \\eta_{xyxy}$ (perpendicular to the magnetic field) and $\\eta_{\\parallel} \\equiv \\eta_{xzxz}=\\eta_{yzyz}$ (parallel to the field). When $B\
General duality for Abelian-group-valued statistical-mechanics models
Caracciolo, Sergio [Dip. di Fisica and INFN, Universita degli Studi di Milano, via Celoria 16, I-20133 Milan (Italy); Sportiello, Andrea [Dip. di Fisica and INFN, Universita degli Studi di Milano, via Celoria 16, I-20133 Milan (Italy)
2004-07-30
We introduce a general class of statistical-mechanics models, taking values in an Abelian group, which includes examples of both spin and gauge models, both ordered and disordered. The model is described by a set of 'variables' and a set of 'interactions'. Each interaction is associated with a linear combination of variables; these are summarized in a matrix J. A Gibbs factor is associated with each variable (one-body term) and with each interaction. Then we introduce a duality transformation for systems in this class. The duality exchanges the Abelian group with its dual, the Gibbs factors with their Fourier transforms and the interactions with the variables. High (low) couplings in the interaction terms are mapped into low (high) couplings in the one-body terms. If the matrix J is interpreted as a vector representation of a matroid, duality exchanges the matroid with its dual. We discuss some physical examples. The main idea is to generalize the known models up to eventually include randomness into the pattern of interaction. We introduce and study a random Gaussian model, a random Potts-like model and a random variant of discrete scalar QED. Although the classical procedure as given by Kramers and Wannier does not extend in a natural way to such a wider class of systems, our weaker procedure applies to these models, too. We shortly describe the consequence of duality for each example.
On Multifield Born and Born-Infeld Theories and their non-Abelian Generalizations
Cerchiai, B L
2016-01-01
Starting from a recently proposed linear formulation in terms of auxiliary fields, we study $n$-field generalizations of Born and Born-Infeld theories. In this description the Lagrangian is quadratic in the vector field strengths and the symmetry properties (including the characteristic self-duality) of the corresponding non-linear theory are manifest as on-shell duality symmetries and depend on the choice of the (homogeneous) manifold spanned by the auxiliary scalar fields and the symplectic frame. By suitably choosing these defining properties of the quadratic Lagrangian, we are able to reproduce some known multi-field Born-Infeld theories and to derive new non-linear models, such as the $n$-field Born theory. We also discuss non-Abelian generalizations of these theories obtained by choosing the vector fields in the adjoint representation of an off-shell compact global symmetry group $K$ and replacing them by non-Abelian, $K$-covariant field strengths, thus promoting $K$ to a gauge group.
On multifield Born and Born-Infeld theories and their non-Abelian generalizations
Cerchiai, Bianca L.; Trigiante, Mario
2016-10-01
Starting from a recently proposed linear formulation in terms of auxiliary fields, we study n-field generalizations of Born and Born-Infeld theories. In this description the Lagrangian is quadratic in the vector field strengths and the symmetry properties (including the characteristic self-duality) of the corresponding non-linear theory are manifest as on-shell duality symmetries and depend on the choice of the (homogeneous) manifold spanned by the auxiliary scalar fields and the symplectic frame. By suitably choosing these defining properties of the quadratic Lagrangian, we are able to reproduce some known multi-field Born-Infeld theories and to derive new non-linear models, such as the n-field Born theory. We also discuss non-Abelian generalizations of these theories obtained by choosing the vector fields in the adjoint representation of an off-shell compact global symmetry group K and replacing them by non-Abelian, K-covariant field strengths, thus promoting K to a gauge group.
Non-Abelian black string solutions of N=(2,0),d=6 supergravity
Cano, Pablo A; Santoli, Camilla
2016-01-01
We show that, when compactified on a circle, N=(2,0),d=6 supergravity coupled to 1 tensor multiplet and nV vector multiplets is dual to N=(2,0),d=6 supergravity coupled to just nT=nV+1 tensor multiplets and no vector multiplets. Both theories reduce to the same models of N=2,d=5 supergravity coupled to nV5=nV+2 vector fields. We derive Buscher rules that relate solutions of these theories (and of the theory that one obtains by dualizing the 3-form field strength) admitting an isometry. Since the relations between the fields of N=2,d=5 supergravity and those of the 6-dimensional theories are the same with or without gaugings, we construct supersymmetric non-Abelian solutions of the 6-dimensional gauged theories by uplifting the recently found 5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions describe the usual superpositions of strings and waves supplemented by a BPST instanton in the transverse directions. One of the solutions obtained interpolates smoothly between two AdS3xS3 geome...
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms
Huo, Ming-Xia; Nie, Wei; Hutchinson, David A. W.; Kwek, Leong Chuan
2014-08-01
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a ``hairline'' solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.
Huo, Ming-Xia; Nie, Wei; Hutchinson, David A W; Kwek, Leong Chuan
2014-08-08
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.
Avalanche dynamics of the Abelian sandpile model on the expanded cactus graph
Gauthier, Gregory
2011-01-01
I investigate the avalanche dynamics of the abelian sandpile model on arbitrarily large balls of the expanded cactus graph (the Cayley graph of the free product $\\mathbb{Z}_3 * \\mathbb{Z}_2$). I follow the approach of Dhar and Majumdar (1990) to enumerate the number of recurrent configurations. I also propose the substitution method of enumerating all the recurrent configurations in which adding a grain to a designated origin vertex (far enough away from the boundary vertices) causes topplings to occur in a specific cluster (a connected subgraph that is the union of cells, or copies of the 3-cycle). This substitution method lends itself to combinatorial evaluation of the number of positions in which a certain number of cells topple in an avalanche starting at the origin, which are amenable to analysis using well-known recurrences and corresponding generating functions. Using asymptotic methods, I show that, when counting cells that topple in the avalanche, the critical exponent of the Abelian sandpile model o...
Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.
Pan, Wei; Thalakulam, Madhu; Shi, Xiaoyan; Crawford, Matthew; Nielsen, Erik; Cederberg, Jeffrey George
2013-10-01
Topological quantum computation (TQC) has emerged as one of the most promising approaches to quantum computation. Under this approach, the topological properties of a non-Abelian quantum system, which are insensitive to local perturbations, are utilized to process and transport quantum information. The encoded information can be protected and rendered immune from nearly all environmental decoherence processes without additional error-correction. It is believed that the low energy excitations of the so-called =5/2 fractional quantum Hall (FQH) state may obey non-Abelian statistics. Our goal is to explore this novel FQH state and to understand and create a scientific foundation of this quantum matter state for the emerging TQC technology. We present in this report the results from a coherent study that focused on obtaining a knowledge base of the physics that underpins TQC. We first present the results of bulk transport properties, including the nature of disorder on the 5/2 state and spin transitions in the second Landau level. We then describe the development and application of edge tunneling techniques to quantify and understand the quasiparticle physics of the 5/2 state.
Non-Abelian duality from vortex moduli: a dual model of color-confinement
Eto, M; Konishi, K; Marmorini, G; Nitta, M; Ohashi, K; Vinci, W; Yokoi, N
2006-01-01
It is argued that the dual transformation of non-Abelian monopoles occurring in a system with gauge symmetry breaking G \\longrightarrow H is to be defined by setting the low-energy H system in Higgs phase, so that the dual system is in confinement phase. The transformation law of the monopoles follows from that of monopole-vortex mixed configurations in the system (with a large hierarchy of energy scales, v_1 \\gg v_2) G {\\stackrel {v_1} {\\longrightarrow}} H {\\stackrel {v_2} {\\longrightarrow}} \\emptyset, under an unbroken, exact color-flavor diagonal symmetry H_{C+F} \\sim {\\tilde H}. The transformation property among the regular monopoles characterized by \\pi_2(G/H), follows from that among the non-Abelian vortices with flux quantized according to \\pi_1(H), via the isomorphism \\pi_1(G) \\sim {\\pi_1(H) \\over \\pi_2(G/H)}. Our idea is tested against the concrete models -- softly-broken {\\cal N}=2 supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semic...
Maximal Abelian subalgebras of pseudoeuclidean real Lie algebras and their application in physics
Thomova, Zora
1998-12-01
We construct the conjugacy classes of maximal abelian subalgebras (MASAs) of the real pseudoeuclidean Lie algebras e(p, q) under the conjugation by the corresponding pseudoeuclidean Lie groups E(p, q). The algebra e( p, q) is a semi-direct sum of the pseudoorthogonal algebra o(p, q) and the abelian ideal of translations T(p + q). We use this particular structure to construct first the splitting MASAs, which are themselves direct sums of subalgebras of o(p, q) and T(p + q). Splitting MASAs give rise to the nonsplitting MASAs of e(p, q). The results for q = 0, 1 and 2 are entirely explicit. MASAs of e(p, 0) and e( p, 1) are used to construct conformally nonequivalent coordinate systems in which the wave equation and Hamilton-Jacobi equations allow the separation of variables. As an application of subgroup classification we perform symmetry reduction for two nonlinear partial differential equations. The method of symmetry reduction is used to obtain analytical solutions of the Landau-Lifshitz and a nonlinear diffusion equations. The symmetry group is found for both equations and all two-dimensional subgroups are classified. These are used to reduce both equations to ordinary differential equations, which are solved in terms of elliptic functions.
Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality
Cvetic, Mirjam; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-01-01
We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required ...
Equalized near maximum likelihood detector
2012-01-01
This paper presents new detector that is used to mitigate intersymbol interference introduced by bandlimited channels. This detector is named equalized near maximum likelihood detector which combines nonlinear equalizer and near maximum likelihood detector. Simulation results show that the performance of equalized near maximum likelihood detector is better than the performance of nonlinear equalizer but worse than near maximum likelihood detector.
Cheeseman, Peter; Stutz, John
2005-01-01
A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].
Renormalization of the N = 1 Abelian super-Chern-Simons theory coupled to parity-preserving matter
Colatto, L.P.; Andrade, M.A. de; Franco, D.H.T.; Helayel Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Del Cima, O.M. [Technische Universitat Wien (Austria). Institut fuer Theoretische Physik; Piguet, O. [Espirito Santo Univ., Vitoria, ES (Brazil). Dept. de Fisica
1997-12-01
We analyse the renormalizability of an Abelian N=1 super-Chern-Simons model coupled to parity-preserving matter on the light of the regularization independent algebraic method. The model shows to be stable under radiative corrections and to gauge anomaly free. (author) 7 refs.
Wei Yi-Huan
2011-01-01
This paper points out that equations (18a) and (18b) in Ref. [7] [Gao Y J 2008 Chin. Phys. B 17 3574] only possess the solutions M = ±ρ(～γ)ε. So, there does not exist the so-called soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields shown in Ref. [7].
Brezinski, C, E-mail: Claude.Brezinski@univ-lille1.f [Laboratoire Paul Painleve, UMR CNRS 8524, UFR de Mathematiques Pures et Appliquees, Universite des Sciences et Technologies de Lille, 59655-Villeneuve d' Ascq cedex (France)
2010-05-21
In this paper, we give the cross rules of the discrete and confluent vector, topological and matrix {epsilon}-algorithms. Then, from the rules of these confluent algorithms, we derive non-Abelian lattice equations, in particular some extensions of the Lotka-Volterra system, in the style of the equation related to the confluent form of the scalar {epsilon}-algorithm.
Prodanov, E M; Prodanov, Emil M.; Sen, Siddhartha
2000-01-01
We show that on three-dimensional Riemannian manifolds without boundaries and with trivial first real de Rham cohomology group (and in no other dimensions) scalar field theory and Maxwell theory are equivalent: the ratio of the partition functions is given by the Ray-Singer torsion of the manifold. On the level of interaction with external currents, the equivalence persists provided there is a fixed relation between the charges and the currents.
Bae, Yun Jung; Choi, Byung Se; Yoon, Yeon Hong; Woo, Leonard Sun; Jung, Cheol Kyu; Kim, Jae Hyoung [Dept. of Radiology, Seoul National University College of Medicine, Seoul National University Bundang Hospital, Seongnam (Korea, Republic of); Lee, Kyung Mi [Dept. of Radiology, Kyung Hee University College of Medicine, Kyung Hee University Hospital, Seoul (Korea, Republic of)
2017-08-01
To evaluate the diagnostic benefits of 5-mm maximum intensity projection of improved motion-sensitized driven-equilibrium prepared contrast-enhanced 3D T1-weighted turbo-spin echo imaging (MIP iMSDE-TSE) in the detection of brain metastases. The imaging technique was compared with 1-mm images of iMSDE-TSE (non-MIP iMSDE-TSE), 1-mm contrast-enhanced 3D T1-weighted gradient-echo imaging (non-MIP 3D-GRE), and 5-mm MIP 3D-GRE. From October 2014 to July 2015, 30 patients with 460 enhancing brain metastases (size > 3 mm, n = 150; size ≤ 3 mm, n = 310) were scanned with non-MIP iMSDE-TSE and non-MIP 3D-GRE. We then performed 5-mm MIP reconstruction of these images. Two independent neuroradiologists reviewed these four sequences. Their diagnostic performance was compared using the following parameters: sensitivity, reading time, and figure of merit (FOM) derived by jackknife alternative free-response receiver operating characteristic analysis. Interobserver agreement was also tested. The mean FOM (all lesions, 0.984; lesions ≤ 3 mm, 0.980) and sensitivity ([reader 1: all lesions, 97.3%; lesions ≤ 3 mm, 96.2%], [reader 2: all lesions, 97.0%; lesions ≤ 3 mm, 95.8%]) of MIP iMSDE-TSE was comparable to the mean FOM (0.985, 0.977) and sensitivity ([reader 1: 96.7, 99.0%], [reader 2: 97, 95.3%]) of non-MIP iMSDE-TSE, but they were superior to those of non-MIP and MIP 3D-GREs (all, p < 0.001). The reading time of MIP iMSDE-TSE (reader 1: 47.7 ± 35.9 seconds; reader 2: 44.7 ± 23.6 seconds) was significantly shorter than that of non-MIP iMSDE-TSE (reader 1: 78.8 ± 43.7 seconds, p = 0.01; reader 2: 82.9 ± 39.9 seconds, p < 0.001). Interobserver agreement was excellent (κ > 0.75) for all lesions in both sequences. MIP iMSDE-TSE showed high detectability of brain metastases. Its detectability was comparable to that of non-MIP iMSDE-TSE, but it was superior to the detectability of non-MIP/MIP 3D-GREs. With a shorter reading time, the false-positive results of MIP i
Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation
Scheck, Florian
2012-01-01
The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...
Dynamics of slender monopoles and anti-monopoles in non-Abelian superconductor
Arai, Masato; Eto, Minoru; Sakai, Norisuke
2014-01-01
Low energy dynamics of magnetic monopoles and anti-monopoles in the U(2) gauge theory is studied in the Higgs (non-Abelian superconducting) phase. The monopoles in this superconducting phase are not spherical but are of slender ellipsoid which are pierced by a vortex string. We investigate scattering of the slender monopole and anti-monopole, and find that they do not always decay into radiation, contrary to our naive intuition. They can repel, make bound states (magnetic mesons) or resonances. Analytical solutions including any number of monopoles and anti-monopoles are obtained in the first non-trivial order of rigid-body approximation. We point out that some part of solutions of slender monopole system in 1+3 dimensions can be mapped exactly onto the sine-Gordon system in 1+1 dimensions. This observation allows us to visualize dynamics of monopole and anti-monopole scattering easily.
Non-abelian factorisation for next-to-leading-power threshold logarithms
Bonocore, D.; Laenen, E.; Magnea, L.; Vernazza, L.; White, C. D.
2016-12-01
Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a nonabelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.
Hints of 5d fixed point theories from non-Abelian T-duality
Lozano, Yolanda; Colgáin, Eoin Ó; Rodríguez-Gómez, Diego [Department of Physics, University of Oviedo,Avda. Calvo Sotelo 18, 33007 Oviedo (Spain)
2014-05-05
In this paper we investigate the properties of the putative 5d fixed point theory that should be dual, through the holographic correspondence, to the new supersymmetric AdS{sub 6} solution constructed in http://dx.doi.org/10.1103/PhysRevLett.110.231601. This solution is the result of a non-Abelian T-duality transformation on the known supersymmetric AdS{sub 6} solution of massive Type IIA. The analysis of the charge quantization conditions seems to put constraints on the global properties of the background, which, combined with the information extracted from considering probe branes, suggests a 2-node quiver candidate for the dual CFT.
Bounds on topological Abelian string-vortex and string-cigar from information-entropic measure
R.A.C. Correa
2016-04-01
Full Text Available In this work we obtain bounds on the topological Abelian string-vortex and on the string-cigar, by using a new measure of configurational complexity, known as configurational entropy. In this way, the information-theoretical measure of six-dimensional braneworlds scenarios is capable to probe situations where the parameters responsible for the brane thickness are arbitrary. The so-called configurational entropy (CE selects the best value of the parameter in the model. This is accomplished by minimizing the CE, namely, by selecting the most appropriate parameters in the model that correspond to the most organized system, based upon the Shannon information theory. This information-theoretical measure of complexity provides a complementary perspective to situations where strictly energy-based arguments are inconclusive. We show that the higher the energy the higher the CE, what shows an important correlation between the energy of the a localized field configuration and its associated entropic measure.
New self-dual $k$-generalized Abelian-Higgs models
Casana, R; Santos, A C
2015-01-01
We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios whose gauge field possess $k$-generalized dynamics, i.e., the kinetic part of the gauge action being highly nonlinear. We have implemented the BPS formalism providing highly nonlinear generalized self-dual equations whose solutions possess a total energy proportional to the magnetic flux. However, there is a key condition which allows to express the self-dual equations in a form mathematically similar those arising in the Maxwell-Higgs model. Under such a key condition, we have analyzed the general properties of the self-dual axially symmetric vortices. We have observed the generalization modifies the vortex core, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux. Finally, we have established a prescription which allows to obtain different $k$-generalized Abelian Higgs models providing self-dual configurations.
Propagating modes of a non-Abelian tensor gauge field of second rank
Konitopoulos, Spyros; Savvidy, George [Institute of Nuclear Physics, Demokritos National Research Center Agia Paraskevi, GR-15310 Athens (Greece)
2008-09-05
In the non-Abelian tensor gauge field theory a lower-rank field is represented by a general nonsymmetric tensor and describes the propagation of charged bosons of helicities two and zero. We clarify and prove this result from different perspectives which would include generalized Bianchi identities and the analysis of the corresponding partial differential equation. We suggest a new method for counting propagating modes in general gauge field theories. We derive also the expression for the energy-momentum tensor and confirm that its nonzero components get contribution only from helicity-two and helicity-zero states. We extended this analysis considering the interaction between two currents caused by the exchange of a tensor gauge field and proved that the residue at the pole is the sum of three terms each of which describes positive norm polarizations of helicity-two and helicity-zero bosons.
Escobar, C A
2015-01-01
After imposing current conservation together with the Gauss law as initial conditions on the Abelian Nambu model, we prove that the resulting theory is equivalent to standard QED in the non-linear gauge $\\left(A_{\\mu }A^{\\mu }-n^{2}M^{2}\\right)=0$, to all orders in perturbation theory. We show this by writing both models in terms of the same variables, which produce identical Feynman rules for the interactions and propagators. A crucial point is to verify that the Faddeev-Popov ghosts arising from the gauge fixing procedure in the QED sector decouple to all orders. We verify this decoupling by following a method like that employed in Yang-Mills theories when investigating the behavior of axial gauges. The equivalence between the two theories supports the idea that gauge particles can be envisaged as the Goldstone bosons originating from spontaneous Lorentz symmetry breaking.
Non-abelian T-duality of Pilch-Warner background
Dimov, Hristo; Mladenov, Stefan; Vetsov, Tsvetan [Department of Physics, Sofia University (Bulgaria); Rashkov, Radoslav C. [Department of Physics, Sofia University (Bulgaria); Institute for Theoretical Physics, Vienna University of Technology (Austria)
2016-08-15
In this work we obtain the non-abelian T-dual geometry of the well-known Pilch-Warner supergravity solution in its infrared point. We derive the dual metric and the NS two-form by gauging the isometry group of the initial theory and integrating out the introduced auxiliary gauge fields. Then we use the Fourier-Mukai transform from algebraic geometry to find the transformation rules of the R-R fields. The dual background preserves the N = 1 supersymmetry of the original one due to the fact that the Killing spinor does not depend on the directions on which the N-AT-D is performed. Finally, we consider two different pp-wave limits of the T-dual geometry by performing Penrose limits for two light-like geodesics. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
A dynamical programming approach for controlling the directed abelian Dhar-Ramaswamy model
Cajueiro, Daniel O
2013-01-01
A dynamical programming approach is used to deal with the problem of controlling the directed abelian Dhar-Ramaswamy model on two-dimensional square lattice. Two strategies are considered to obtain explicit results to this task. First, the optimal solution of the problem is characterized by the solution of the Bellman equation obtained by numerical algorithms. Second, the solution is used as a benchmark to value how far from the optimum other heuristics that can be applied to larger systems are. This approach is the first attempt on the direction of schemes for controlling self-organized criticality that are based on optimization principles that consider explicitly a tradeoff between the size of the avalanches and the cost of intervention.
A string realisation of Ω-deformed Abelian N=2⁎ theory
Carlo Angelantonj
2017-10-01
Full Text Available The N=2⁎ supersymmetric gauge theory is a massive deformation of N=4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-Abelian N=2⁎ theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N=2 chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Ω-background, in agreement with a recent proposal.
Non-Abelian cosmic strings in de Sitter and anti-de Sitter space
Santos, Antônio de Pádua; Bezerra de Mello, Eugênio R.
2016-09-01
In this paper we investigate the non-Abelian cosmic string in de Sitter and anti-de Sitter spacetimes. In order to do that we construct the complete set of equations of motion considering the presence of a cosmological constant. By using numerical analysis we provide the behavior of the Higgs and gauge fields and also of the metric tensor for specific values of the physical parameters of the theory. For the de Sitter case, we find the appearance of an horizon. This horizon is consequence of the presence of the cosmological constant, and its position strongly depends on the value of the gravitational coupling. In the anti-de Sitter case, we find that the system does not present horizons. In fact the new feature of this system is related with the behavior of the (00) and (z z ) components of the metric tensor. They present a strong increasing behavior for large distance from the string.
Phase space structure of non-abelian Chern-Simons particles
Kim, M H; Myung-Ho Kim; Phillial Oh
1994-01-01
We investigate the classical phase space structure of N SU(n+1) non-Abelian Chern-Simons (NACS) particles by first constructing the product space of associated SU(n+1) bundle with {\\bf CP}^n as the fiber. We calculate the Poisson bracket using the symplectic structure on the associated bundle and find that the minimal substitution in the presence of external gauge fields is equivalent to the modification of symplectic structure by the addition of field strength two form. Then, we take a direct product of the associated bundle by the space of all connections and choose a specific connection by the condition of vanishing momentum map corresponding to the gauge transformation, thus recovering the quantum mechanical model of NACS particles in Ref.\\cite{lo1}.
Topological Objects And Confinement In Non-abelian Lattice Gauge Theory
Tucker, W W
2005-01-01
We use lattice methods to study the connection between topological objects and the confining potential in SU(2) and SU(3) Yang-Mills theories. We use Monte Carlo techniques, generating and performing measurements on sample configurations of SU(2) and SU(3) gauge fields. We isolate topological objects, specifically Abelian monopoles and center vortices, in these configurations. We then measure the contribution to the string tension from these objects, and compare the results to “full” measurements made on the original configurations. In addition we investigate the effects of gauge ambiguities (Gribov effects) and cooling on these sets of measurements. For the case of SU(2) lattice gauge theory, our results from monopoles agree with full values but are somewhat lower when gauge ambiguities are taken into account. The situation is not stable under cooling. When we carry out analogous procedures on sample SU(3) lattice configurations, we find disagreement between full SU(3) values and those fr...
Exact solution of the $D_3$ non-Abelian anyon chain
Braylovskaya, Natalia; Frahm, Holger
2016-01-01
Commuting transfer matrices for linear chains of interacting non-Abelian anyons from the two-dimensional irreducible representation of the dihedral group $D_3$ (or, equivalently, the integer sector of the $su(2)_4$ spin-$1$ chain) are constructed using the spin-anyon correspondence to a $D_3$-symmetric formulation of the XXZ Heisenberg spin chain. The spectral problem is solved using discrete inversion identities satisfied by these transfer matrices and functional Bethe ansatz methods. The resulting spectrum can be related to that of the XXZ spin-$1/2$ Heisenberg chain with boundary conditions depending on the topological sector of the anyon chain. The properties of this model in the critical regime are studied by finite size analysis of the spectrum. In particular, points in the phase diagram where the anyon chain realizes some of the rational $\\mathbb{Z}_2$ orbifold theories are identified.
Exact solution of the D3 non-Abelian anyon chain
Braylovskaya, Natalia; Finch, Peter E.; Frahm, Holger
2016-08-01
Commuting transfer matrices for linear chains of interacting non-Abelian anyons from the two-dimensional irreducible representation of the dihedral group D3 [or, equivalently, the integer sector of the s u (2) 4 spin-1 chain] are constructed using the spin-anyon correspondence to a D3-symmetric formulation of the XXZ Heisenberg spin chain. The spectral problem is solved using discrete inversion identities satisfied by these transfer matrices and functional Bethe ansatz methods. The resulting spectrum can be related to that of the XXZ spin-1/2 Heisenberg chain with boundary conditions depending on the topological sector of the anyon chain. The properties of this model in the critical regime are studied by finite size analysis of the spectrum. In particular, points in the phase diagram where the anyon chain realizes some of the rational Z2 orbifold theories are identified.
Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity
Lahiri, Sayantani
2016-01-01
In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless $SU(2)$ gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by a non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.
Augmented Superfield Approach To Exact Nilpotent Symmetries For Matter Fields In Non-Abelian Theory
Malik, R P; Mandal, Bhabani Prasad
2006-01-01
We derive the nilpotent (anti-) BRST symmetry transformations for the Dirac (matter) fields of an interacting four $(3+1)$-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4, 2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates $x^\\mu$ (with $\\mu = 0,1,2,3)$ and a couple of Grassmannian variables $\\theta $ and $\\bar{\\theta}$. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five ($4, 1)$-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4, 2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed...
On the elimination of infinitesimal Gribov ambiguities in non-Abelian gauge theories
Pereira, A D
2013-01-01
An alternative method to account for the Gribov ambiguities in gauge theories is presented. It is shown that, to eliminate Gribov ambiguities, at infinitesimal level, it is required to break the BRST symmetry in a soft manner. This can be done by introducing a suitable extra constraint that eliminates the infinitesimal Gribov copies. It is shown that the present approach is consistent with the well established known cases in the literature, i.e., the Landau and maximal Abelian gauges. The method is valid for gauges depending exclusively on the gauge field and is restricted to classical level. However, occasionally, we deal with quantum aspects of the technique, which are used to improve the results.
Structure of chiral phase transitions at finite temperature in abelian gauge theories
Fukazawa, Kenji [Kure National College of Technology, Kure (Japan); Inagaki, Tomohiro [Information Media Center, Hiroshima Univ., Hiroshima (Japan); Mukaigawa, Seiji [Department of Electrical and Electronic Engineering, Faculty of Engineering, Iwate Univ., Iwate (Japan); Muta, Taizo [Department of Physics, Hiroshima Univ., Hiroshima (Japan)
2001-06-01
The mechanism of chiral symmetry breaking is investigated in strong-coupling Abelian gauge theories at finite temperature. The Schwinger-Dyson equation in the Landau gauge is employed in the real time formalism and is solved numerically within the framework of the instantaneous exchange approximation, including the effect of the thermal mass for the photon propagator. It is found that the chiral symmetry is broken below the critical temperature T for sufficiently large coupling {alpha}. The chiral phase transition is found to be of second order, and the phase diagram in the T-{alpha} plane is obtained. It is investigated how the structure of the chiral phase transition is affected by the thermal mass in the photon propagator. (author)
Structure of chiral phase transitions at finite temperature in Abelian gauge theories
Fukazawa, K; Mukaigawa, S; Muta, T; Fukazawa, Kenji; Inagaki, Tomohiro; Mukaigawa, Seiji; Muta, Taizo
1999-01-01
The mechanism of the chiral symmetry breaking is investigated in the strong-coupling Abelian gauge theories at finite temperature. The Schwinger-Dyson equation in Landau gauge is employed in the real time formalism and is solved numerically within the framework of the instantaneous exchange approximation including the effect of the hard thermal loop for the photon propagator. It is found that the chiral symmetry is broken below the critical temperature T for sufficiently large coupling. The chiral phase transition is found to be of the 2nd order and the phase diagram on the $T-\\alpha$ plane is obtained. It is investigated how the structure of the chiral phase transition is affected by the hard thermal loops in the photon propagator.
Non-Abelian chiral instabilities at high temperature on the lattice
Akamatsu, Yukinao; Rothkopf, Alexander; Yamamoto, Naoki
2016-03-01
We report on an exploratory lattice study on the phenomenon of chiral instabilities in non-Abelian gauge theories at high temperature. It is based on a recently constructed anomalous Langevin-type effective theory of classical soft gauge fields in the presence of a chiral number density n 5 = n R - n L. Evaluated in thermal equilibrium using classical lattice techniques it reveals that the fluctuating soft fields indeed exhibit a rapid energy increase at early times and we observe a clear dependence of the diffusion rate of topological charge (sphaleron rate) on the the initial n 5, relevant in both early universe baryogenesis and relativistic heavy-ion collisions. The topological charge furthermore shows a drift among distinct vacuum sectors, roughly proportional to the initial n 5 and in turn the chiral imbalance is monotonously reduced as required by helicity conservation.