Lattice gauge theory

The average action per plaquette is calculated for the pure SU(N)/ZN, N = 2, 3, 4, 5 and 6 gauge groups using strong coupling expansions up to 13th order for euclidean lattice gauge theory in four space-time dimensions. These expansions are compared with Monte Carlo generated data and agreement is found to be excellent for 0 ~< fl ~ fie, where tic is the critical inverse temperature for the appropriate gauge group considered.

The functional integral for QCD is reformulated by introducing explicitly an integration over the fluctuations of composite quarkantiquark bound states. Chiral symmetry breaking by the color singlet scalar field induces masses for the fermions. Our formulation with scalar fluctuations may be useful for lattice gauge theories by modifying the spectrum of the Dirac operator in the vacuum and permitting a simple connection to chiral perturbation theory. We propose that a "condensate" of quark-antiquark bound states in the color octet channel generates masses of the gluons by the Higgs mechanism. A simple effective action for quarks, gluons and (composite) scalars yields a surprisingly good description of the charges, masses and interactions of all low mass physical excitations -baryons, pseudoscalars and vector mesons. Dressed quarks appear as baryons and dressed gluons as vector mesons. 1

This report was prepared as an account of work sponsored by an agency of the United States _: "_ Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service,by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-".... mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

The effects of gauge interactions in graphene have been analyzed up to now in terms of effective models of Dirac fermions. However, in several cases lattice effects play an important role and need to be taken consistently into account. In this paper we introduce and analyze a lattice gauge theory model for graphene, which describes tight binding electrons hopping on the honeycomb lattice and interacting with a three-dimensional quantum U (1) gauge field. We perform an exact Renormalization Group analysis, which leads to a renormalized expansion that is finite at all orders. The flow of the effective parameters is controlled thanks to Ward Identities and a careful analysis of the discrete lattice symmetry properties of the model. We show that the Fermi velocity increases up to the speed of light and Lorentz invariance spontaneously emerges in the infrared. The interaction produces critical exponents in the response functions; this removes the degeneracy present in the non interacting case and allow us to identify the dominant excitations. Finally we add mass terms to the Hamiltonian and derive by a variational argument the correspondent gap equations, which have an anomalous non-BCS form, due to the non trivial effects of the interaction.

The interplay of symmetry, topology, and many-body effects in the classification of phases of matter poses a formidable challenge in condensed-matter physics. Such many-body effects are typically induced by inter-particle interactions involving an action at a distance, such as the Coulomb interaction between electrons in a symmetry-protected topological (SPT) phase. In this work we show that similar phenomena also occur in certain relativistic theories with interactions mediated by gauge bosons, and constrained by gauge symmetry. In particular, we introduce a variant of the Schwinger model or quantum electrodynamics (QED) in 1+1 dimensions on an interval, which displays dynamical edge states localized on the boundary. We show that the system hosts SPT phases with a dynamical contribution to the vacuum θ-angle from edge states, leading to a new type of topological QED in 1+1 dimensions. The resulting system displays an SPT phase which can be viewed as a correlated version of the Su-Schrieffer-Heeger topological insulator for polyacetylene due to non-zero gauge couplings. We use bosonization and density-matrix renormalization group techniques to reveal the detailed phase diagram, which can further be explored in experiments of ultra-cold atoms in optical lattices. Global and local symmetries play a crucial role in our understanding of Nature at very different energy scales [1, 2]. At high energies, they govern the behavior of fundamental particles [3], their spectrum and interactions [4, 5]. At low energies [6], spontaneous symmetry breaking and local order parameters characterize a wide range of phases of matter [7] and a rich variety of collective phenomena [8]. There are, however, fundamental physical phenomena that can only be characterized by non-local order parameters, such as the Wil-son loops distinguishing confined and deconfined phases in gauge theories [9], or hidden order parameters distinguishing topological phases in solids [10]. The former, requiring a non-perturbative approach to quantum field theory (e.g. lattice gauge theories (LGTs)), and the latter, demanding the introduction of mathematical tools of topology in condensed matter (e.g. topological invariants), lie at the forefront of research in both high-energy and condensed-matter physics. The interplay of symmetry and topology can lead to a very rich, and yet partially-uncharted, territory. For instance, different phases of matter can arise without any symmetry breaking: symmetry-protected topological (SPT) phases. Beyond the celebrated integer quantum Hall effect [11-14], a variety of SPT phases have already been identified [15-17] and realized [18]. Let us note that some representative models of these SPT phases [19] can be understood as lower-dimensional versions of the so-called domain-wall fermions [20], introduced in the context of chiral symmetry in lattice field theories [21]. A current problem of considerable interest is to understand strong-correlation effects in SPT phases as interactions are included [22], which may, for instance, lead to exotic fractional excitations [23, 24]. So far, the typical interactions considered involve an action at a distance (e.g. screened Coulomb or Hubbard-like nearest or next-to-nearest neighbor interactions). To the best of our knowledge, and with the recent exception [25], the study of correlated SPT phases with mediated interactions remains a largely-unexplored subject. In this work, we initiate a systematic study of SPT phases with interactions dictated by gauge symmetries focusing on a 2a x c 2n+1 c † 2n (1 − )U 2n U 2n−1 c † 2n−1 c 2n a b U n c n+1 +m s −m s c † n c n n+ + +1 +m m s −m m m m s fermion fields gauge fields FIG. 1. Discretizations for standard and topological QED 2 : (a) Staggered-fermion approach to the massive Schwinger model. The relativistic Dirac field is discretized into spinless lattice fermions subjected to a staggered on-site energy ±m s , represented by filled/empty circles in a 1D chain with alternating heights. The gauge field is discretized into rotor-angle operators that reside on the links, depicted as shaded ellipses with various levels representing the electric flux eigenbasis. The gauge-invariant term c † n U n c n+1 involves the tunneling of neighboring fermions, dressed by a local excitation of the gauge field in the electric-flux basis U n | = | + 1, represented by the zigzag grey arrow joining two neighboring fermion sites, via an excitation of the link electric-flux level. (b) Dimerized-tunneling approach to the topological Schwinger model. The previous staggered mass is substituted by a gauge-invariant tunneling with alternating strengths (1 − δ n)c † n U n c n+1 , where δ n = 0, ∆ for even/odd sites. This dimerization of the tunneling matrix elements is represented by alternating big/small ellipses at the odd/even links. the lattice Schwinger model, an Abelian LGT that regularizes quantum electrodynamics in 1+1 dimensions (QED 2) [26]. We show that a discretization alternative to the standard lattice approach [27] leads to a topological Schwinger model, and derive its continuum limit referred to as topological QED 2. This continuum quantum field theory is used to predict a phase diagram that includes SPT, confined, and fermion-condensate phases, which are then discussed in the context of the afore-mentioned domain-wall fermions in LGTs.

We represent QCD at the hadronic scale by means of an effective Hamiltonian, H, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon applications for the u, d, s and c quark flavors and compute the mass spectrum for the pseudoscalar, scalar and vector mesons. We also perform a comparative study of alternative many-body techniques for approximately diagonalizing H: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. The Dirac structure of the field theoretical Hamiltonian naturally generates spin-dependent interactions, including tensor, spin-orbit and hyperfine, and we clarify the degree of level splitting due to both spin and chiral symmetry effects. Significantly, we find that roughly two-thirds of the π-ρ mass difference is due to chiral symmetry and that only the RPA preserves chiral symmetry. We also document how hadronic mass scales are generated by chiral symmetry breaking in the model vacuum. In addition to the vacuum condensates, we compute meson decay constants and detail the Nambu-Goldstone realization of chiral symmetry by numerically verifying the Gell-Mann-Oaks-Renner relation. Finally, by including D waves in our charmonium calculation we have resolved the anomalous overpopulation of J/Ψ states relative to observation. PAC number(s): 12.39.Pn, 12.40.Yx Jona-Lasinio model. In Sec. III we detail our numerical, supercomputer solution of the gap equation along with the quark condensate and constituent mass values. Sections IV A and IV B describe the TDA and RPA, respectively, while Sec. IV C addresses weak decays and Sec IV D presents a derivation of the Gell-Mann-Oakes-Renner relation. The TDA and RPA meson spectra are compared and discussed in Sec. V. This section also includes results from a simple SU f (3) flavor mixing analysis for the η-η ′ system and our predictions for the charmed mesons. Conclusions and future work are summarized in Sec. VI. Finally, Appendix A provides further details regarding the BCS transformation and vacuum state while Appendix B presents the most general TDA equation for arbitrary angular momentum.

Dirac-Weyl fermions are massless relativistic particles with a well-defined helicity which arise in the context of high-energy physics. Here we propose a quantum simulation of these paradigmatic fermions using multicomponent ultracold atoms in a two-dimensional square optical lattice. We find that laser-assisted spin-dependent hopping, specifically tuned to the (2s+1)-dimensional representations of the su(2) Lie algebra, directly leads to a regime where the emerging massless excitations correspond to Dirac-Weyl fermions with arbitrary pseudospin s. We show that this platform hosts two different phases: a semimetallic phase that occurs for half-integer s, and a metallic phase that contains a flat zero-energy band at integer s. These phases host a variety of interesting effects, such as a very rich anomalous quantum Hall effect and a remarkable multirefringent Klein tunneling. In addition, we show that these effects are directly related to the number of underlying Dirac-Weyl species and zero modes.

The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac gauge invariant states is used to derive a necessary modification of the Hamiltonian path integral in gauge theories of the Yang-Mills type with fermions that takes into account the non-Euclidean geometry of the physical phase space. The new path integral is applied to resolve the Gribov obstruction. Applications to the Kogut-Susskind lattice gauge theory are given. The basic ideas are illustrated with examples accessible for non-specialists.

Description/Abstract The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by ...

We investigate the Taylor expansion of the baryon number susceptibility, and hence, pressure, in a series in the baryon chemical potential (µB) through a lattice simulation with light dynamical staggered quarks at a finer lattice cutoff a = 1/6T. We determine the QCD cross over coupling at µB = 0. We find the radius of convergence of the series at various temeperatures, and bound the location of the QCD critical point to be T E /Tc ≈ 0.94 and µ E B /T < 1.8. We also investigate the extrapolation of various susceptibilities and linkages to finite chemical potential.

We describe the current search for confinement mechanisms in lattice QCD. We report on a recent derivation of a lattice Ehrenfest-Maxwell relation for the Abelian projection of SU(2) lattice gauge theory. This gives a precise lattice definition of field strength and electric current due to static sources, charged dynamical fields, gauge fixing and ghosts. In the maximal Abelian gauge the electric charge is anti-screened analogously to the non-Abelian charge.

We propose a new algorithm to compute the order-order interface tension in SU(N) lattice gauge theories. The algorithm is trivially generalizable to a variety of models, e.g., spin models. In the case N = 3, via the perfect wetting hypothesis, we can estimate the order-disorder interface tension. In the case N = 4, we study the ratio of dual k−tensions and find that it satisfies Casimir scaling down to T = 1.2 Tc.

Vertices are of central importance for constructing QCD bound states out of the individual constituents of the theory, i.e. quarks and gluons. In particular, the determination of three-point vertices is crucial in non-perturbative investigations of QCD. We use numerical simulations of lattice gauge theory to obtain results for the 3-point vertices in Landau-gauge SU(2) Yang-Mills theory in three and four space-time dimensions for various kinematic configurations. In all cases considered, the ghost-gluon vertex is found to be essentially tree-level-like, while the three-gluon vertex is suppressed at intermediate momenta. For the smallest physical momenta, reachable only in three dimensions, we find that some of the three-gluon-vertex tensor structures change sign.

We investigate numerically on the lattice the interplay of universality classes of the threedimensional Yukawa model with U(1) chiral symmetry, using the Binder method of finite size scaling. At zero Yukawa coupling the scaling related to the magnetic Wilson-Fisher fixed point is confirmed. At sufficiently strong Yukawa coupling the dominance of the chiral fixed point associated with the 3D Gross-Neveu model is observed for various values of the coupling parameters, including infinite scalar selfcoupling. In both cases the Binder method works consistently in a broad range of lattice sizes. However, when the Yukawa coupling is decreased the finite size behavior gets complicated and the Binder method gives inconsistent results for different lattice sizes. This signals a cross-over between the universality classes of the two fixed points. * Supported by BMBF and DFG.

We represent QCD at the hadronic scale by means of an effective Hamiltonian, H, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is dynamically broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. We perform a comparative study of alternative many-body techniques for approximately diagonalizing H: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. We adequately describe the experimental meson and lattice glueball spectra and perform the first relativistic, three quasiparticle calculation for hybrid mesons. In general agreement with alternative theoretical approaches, we predict the lightest hybrid states near but above 2 GeV , indicating the two recently observed J P C = 1 −+ exotics at 1.4 and 1.6 GeV are of a different, perhaps four quark, structure. We also detail a new isospin dependent interaction from qq color octet annihilation (analogous to ortho positronium) which splits I = 0 and I = 1 states.

We present results for the heavy quark potential computed in SU(3) from magnetic monopoles and from center vortices. The monopoles are identified after fixing SU(3) lattice configurations to the maximal abelian gauge. The center vortices are identified after using an indirect center gauge fixing scheme which we describe for SU(3). Z(3) center vortices are extracted and used to compute the potential. The values of the string tensions from monopoles and vortices are compared to the full SU(3) string tension.

We study planar random holonomy fields which are processes indexed by paths on the plane which behave well under the concatenation and orientation-reversing operations on paths. We define the Planar Markovian Holonomy Fields as planar random holonomy fields which satisfy some independence and invariance by area-preserving homeomorphisms properties. We use the theory of braids in the framework of classical probabilities: for finite and infinite random sequences the notion of invariance by braids is defined and we prove a new version of the de-Finetti's Theorem. This allows us to construct a family of Planar Markovian Holonomy Fields, the Yang-Mills fields, and we prove that any regular Planar Markovian Holonomy Field is a planar Yang-Mills field. This family of planar Yang-Mills fields can be partitioned into three categories according to the degree of symmetry: we study some equivalent conditions in order to classify them. Finally, we recall the notion of Markovian Holonomy Fields and construct a bridge between the planar and non-planar theories. Using the results previously proved in the article, we compute, for any Markovian Holonomy Field, the "law" of any family of contractible loops drawn on a surface.

The low-lying eigenmodes of the Dirac operator associated with typical gauge field configurations in QCD encode, among other low-energy properties, the physics behind the solution to the U_A(1) problem (i.e. the origin of the η&#39; mass), the nature of spontaneous chiral symmetry breaking, and the physics of string-breaking, quark-antiquark pair production, and the OZI rule. Moreover, the space-time chiral structure of these eigenmodes reflects the space-time topological structure of the underlying gauge field. We present evidence from lattice QCD on the local chiral structure of low Dirac eigenmodes leading to the conclusion that topological charge fluctuations of the QCD vacuum are not instanton-dominated. The result supports Witten&#39;s arguments that topological charge is produced by confinement-related gauge fluctuations rather than instantons.

Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored. In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition. Numerical results are obtained from calculations on D-Wave Advantage hardware for eigenvalues, eigenvectors, vacuum expectation values, and time evolution. The success of this initial exploration indicates that the quantum annealer might become a useful hardware platform for some aspects of lattice gauge theories.

Some features of the high temperature gluonic matter, such as the breakdown of the fundamental group symmetry by the kinetic energy, the screening of test quarks by some unusual gluon states and the explanation of the absence of isolated quarks in the vacuum without the help of infinities are presented in this talk. Special attention is paid to separate the dynamical input inferred from the numerical results of lattice gauge theory from the kinematics.

budgets. An alternative approach uses compute nodes based on a commercial processor tightly coupled to a custom-designed network processor. Preliminary analysis shows that this solution offers good performance, but it also entails several challenges, including those arising from the processor's multicore structure and from implementing the network processor on a fieldprogrammable gate array.

We have simulated QCD using 2+1 flavors of domain wall quarks on a (2.74 fm) 3 volume with an inverse lattice scale of a −1 = 1.729(28) GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617 and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter B K and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulae from both approaches fit our data for light quarks, we find the higher order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory

The hadron mass spectrum is calculated in lattice QCD using a novel fatlink clover fermion action in which only the irrelevant operators in the fermion action are constructed using smeared links. The simulations are performed on a 16 3 × 32 lattice with a lattice spacing of a = 0.125 fm. We compare actions with n = 4 and 12 smearing sweeps with a smearing fraction of 0.7. The n = 4 Fat-Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative O(a) improvement, including a reduced exceptional configuration problem.

A scaling analysis is made of the order parameter describing monopole condensation at the deconfining transition of N_f=2 QCD around the chiral point. In accordance with scaling properties of the specific heat, studied in a previous paper, scaling is consistent with a first order transition. The status of dual superconductivity of the vacuum as a mechanism of color confinement is reviewed.

SU(3) lattice gauge theory is studied by means of an improved action where a 2 × 2 Wilson loop is supplemented to the standard plaquette term. By contrast to earlier studies using a tree level improvement, the prefactor of the 2 × 2 Wilson term is determined by minimizing the breaking of rotational symmetry detected from the static quark-antiquark potential. On coarse lattices, the novel action is superior to the Iwasaki action and comparable with DBW2 action. The scaling behavior of the novel action is studied by using the static quark potential and the ratio of the deconfinement temperature and the string tension.

We study quantum electrodynamics in a (2+1)-dimensional space-time with two flavors of dynamical fermions by numerical simulations on the lattice. We discretize the theory using both the compact and the noncompact formulations and analyze the behavior of the chiral condensate and of the monopole density in the finite lattice regime as well as in the continuum limit. By comparing the results obtained with the two approaches, we draw some conclusions about the possible equivalence of the two lattice formulations in the continuum limit.

The slowly evolving gauge coupling of gauge-fermion systems near the conformal window makes numerical investigations of these models challenging. We consider finite size scaling and show that this often used technique leads to inconsistent results if the leading order scaling corrections are neglected. When the corrections are included the results become consistent not only between different operators but even when data obtained at different gauge couplings or with different lattice actions are combined. Our results indicate that the SU(3) 12-fermion system is conformal with mass anomalous dimension γm = 0.235(15).

Discretization of supersymmetric Yang-Mills (SYM) theories is an old problem in lattice field theory. It has resisted solution until recently when new ideas drawn from orbifold constructions and topological field theories have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theories in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local, free of doublers and also possess exact gauge-invariance. In principle they form the basis for a truly non-perturbative definition of the continuum SYM theories. In the continuum limit they lead to a version of the Yang-Mills theory formulated in terms of twisted fields. In this paper, we briefly review these ideas and then go on to describe the details of a C++ code, which can be used to simulate these theories. We sketch the design of the code, with particular emphasis being placed on SYM theories with N = 2 in two dimensions and N = 4 in three and four dimensions, making one-to-one comparisons between the essential components of the SYM theories and their corresponding counterparts appearing in the simulation code.

The starting point of any lattice QCD computation is the generation of a Markov chain of gauge field configurations. Due to the large number of lattice links and due to the matrix multiplications, generating SU(N c ) lattice QCD configurations is a highly demanding computational task, requiring advanced computer parallel architectures such as clusters of several Central Processing Units (CPUs) or Graphics Processing Units (GPUs). In this paper we present and explore the performance of CUDA codes for NVIDIA GPUs to generate SU(N c ) lattice QCD pure gauge configurations. Our implementation in one GPU uses CUDA and in multiple GPUs uses OpenMP and CUDA. We present optimized CUDA codes for SU(2), SU(3) and SU(4). We also show a generic SU(N c ) code for N c ≥ 4 and compare it with the optimized version of SU(4). Our codes are publicly available for free use by the lattice QCD community.

We investigate topological charge and the index theorem on finite lattices numerically. Using mean field improved gauge field configurations we calculate the topological charge Q using the gluon field definition with O(a 4 )-improved cooling and an O(a 4 )-improved field strength tensor F µν . We also calculate the index of the massless overlap fermion operator by directly measuring the differences of the numbers of zero modes with left-and right-handed chiralities. For sufficiently smooth field configurations we find that the gluon field definition of the topological charge is integer to better than 1% and furthermore that this agrees with the index of the overlap Dirac operator, i.e., the Atiyah-Singer index theorem is satisfied. This establishes a benchmark for reliability when calculating lattice quantities which are very sensitive to topology.

Dramatic progress has been made over the last decade in the numerical study of quantum chromodynamics (QCD) through the use of improved formulations of QCD on the lattice (improved actions), the development of new algorithms and the rapid increase in computing power available to lattice gauge theorists. In this article we describe simulations of full QCD using the improved staggered quark formalism, ``asqtad'' fermions. These simulations were carried out with two degenerate flavors of light quarks (up and down) and with one heavier flavor, the strange quark. Several light quark masses, down to about 3 times the physical light quark mass, and six lattice spacings have been used. These enable controlled continuum and chiral extrapolations of many low energy QCD observables. We review the improved staggered formalism, emphasizing both advantages and drawbacks. In particular, we review the procedure for removing unwanted staggered species in the continuum limit. We then describe the asqtad lattice ensembles created by the MILC Collaboration. All MILC lattice ensembles are publicly available, and they have been used extensively by a number of lattice gauge theory groups. We review physics results obtained with them, and discuss the impact of these results on phenomenology. Topics include the heavy quark potential, spectrum of light hadrons, quark masses, decay constant of light and heavy-light pseudoscalar mesons, semileptonic form factors, nucleon structure, scattering lengths and more. We conclude with a brief look at highly promising future prospects.

The gluon propagator is investigated in Landau and in maximal center gauge for the gauge group SU(2) by means of lattice gauge simulations. We find that Gribov ambiguities arising from the implementation of Landau gauge have a small influence on the propagator. In agreement with previous findings, we obtain that the small momentum behavior is dominated by a mass, which is of order (1.48 ± 0.05) √ σ, where σ is the string tension. By removing the confining vortices from the full Yang-Mills ensemble, we convert full YM-theory into a theory which does not confine quarks. We find that in the latter case the strength of the gluon propagator in the intermediate momentum range is strongly reduced. The spectral functions which reproduce the numerical data for the propagators are analyzed using a generalized Maximum Entropy Method.

We present lattice simulation results corresponding to an SU(2) pure gauge theory defined on the orbifold space E 4 × I 1 , where E 4 is the four-dimensional Euclidean space and I 1 is an interval, with the gauge symmetry broken to a U(1) subgroup at the two ends of the interval by appropriate boundary conditions. We demonstrate that the U(1) gauge boson acquires a mass from a Higgs mechanism. The mechanism is driven by two of the extra-dimensional components of the five-dimensional gauge field which play respectively the role of the longitudinal component of the gauge boson and a massive real physical scalar, the Higgs particle. Despite the non-renormalizable nature of the theory, we observe only a mild cut-off dependence of the physical observables. We also show evidence that there is a region in the parameter space where the system behaves in a way consistent with dimensional reduction.

This paper is concerned with integrals which integrands are the monomials of matrix elements of irreducible representations of classical groups. Based on analysis on Young tableaux, we discuss some related duality theorems and compute the asymptotics of the group integrals when the signatures of the irreducible representations are fixed, as the rank of the classical groups go to infinity. These group integrals have physical origins in quantum mechanics, quantum information theory, and lattice Gauge theory.

Renormalization of composite fields is employed to suppress the statistical noise in lattice gauge calculations. We propose a new action which differs from the standard Wilson action by "irrelevant" operators, but suppresses the fluctuations of the plaquette. We numerically study the Creutz ratios and find a scaling window. The SU(2) mass gap is estimated. We prove that the contributions of the "irrelevant" operators to the screening mass decrease towards the continuum limit. The results obtained from the action with noise suppression are compared with those of the standard Wilson action.

We explore simulations on periodic lattices in the Tomboulis $SO(3) \times Z(2)$ formulation. We measure gauge invariant vortex counters for &quot;thin&quot;, &quot;thick&quot; and &quot;hybrid&quot; vortex sheets in order to tag Wilson loops by the occurance of gauge invariant vortices linking them. We also measure projection vortex counters defined in the maximal center gauge for comparison.

The case is made in this paper for encouraging the scientist to become familiar with architectural features of the supercomputer in use. This is essential for a proper choice of an efficient computational procedure for a given problem, as demonstrated by matching two vectorized algorithms to the CDC CYBER 205 and its special features. The two problems reported here are the Monte Carlo method for lattice gauge theory calculations and the multigrid method for partial differential equation solvers, combined with the description of the relevant aspects of the CDC CYBER 205 architecture.

This paper is concerned with integrals which integrands are the monomials of matrix elements of irreducible representations of classical groups. Based on analysis on Young tableaux, we discuss some related duality theorems and compute the asymptotics of the group integrals when the signatures of the irreducible representations are fixed, as the rank of the classical groups go to infinity. These group integrals have physical origins in quantum mechanics, quantum information theory, and lattice Gauge theory.

Suppressing monopoles and vortices by introducing large chemical potentials for them in the Wilson action for the SU(2) lattice gauge theory, we study the nature of the deconfinement phase transition on N 3 σ × N τ lattices for N τ = 4, 5, 6 and 8 and N σ = 8-16. Using finite size scaling theory, we obtain ω ≡ γ/ν = 1.93 ± 0.03 for N τ = 4, in excellent agreement with universality. Corresponding determinations for the N τ = 5 and 6 lattices are also found to be in very good agreement with this estimate. The critical couplings for N τ = 4, 5, 6 and 8 lattices exhibit large shifts towards the strong coupling region when compared with the usual Wilson action, and suggest a lot smoother approach to scaling.

We analyze the distribution of the chromoelectric field generated by a static quark-antiquark pair in the SU(3) vacuum and revisit previous results for SU(2). We find that the transverse profile of the flux tube resembles the dual version of the Abrikosov vortex field distribution. We give an estimate of the London penetration length of the chromoelectric field in the confined vacuum. We also speculate on the value of the ratio between the penetration lengths for SU(2) and SU(3) gauge theories.