Strong coupling expansion for the mass gap in SU(2) lattice gauge theory with mixed action

We perform a strong coupling expansion up to O(β⁷) for the mass-gap in SU(2) lattice gauge theory with mixed action. A novel feature of the strong coupling expansion is discussed. The strong coupling series appears to approach the scaling region more smoothly and Padé approximants become more stable than in the case with simple Wilson action. The region of validity of a recently proposed resummation of perturbation theory as applied to the determination of the asymptotic scaling behavior is investigated. Results of a strong coupling calculation for the heat kernel action, which is related to the mixed action for a special choice of parameters, are also reported.     

Strong coupling expansion of meson propagator in finite temperature lattice gauge theories

We consider Susskind fermions on a (d+1)-dimensional lattice interacting with aU(n) gauge field at finite temperature. We calculate the meson propagator in an expansion in 1/g ² and 1/d and determine the meson masses. To the order considered the results are identical to those obtained at zero temperature.     

Higher order mean field expansions for lattice gauge theories

The leading contribution to the free energy of lattice gauge theories is evaluated in the mean field expansion to the two-loop level. The methods are general but we only deal with theU(1) case in this paper. The corrections improve the agreement with Monte Carlo calculations. We show that in order to obtain a satisfactory formalism it is necessary to include a new redundant parameter, γ, in the mean field expansion. For γ→0 we recover the usual mean field expansion whereas for γ→∞ we obtain the weak coupling expansion. Thus γ measures the amount of resummation that is done by the mean field formalism.     

Glueball mass estimate by strong coupling expansion in lattice gauge theories

In the formalism presented in the previous paper, the plaquette-plaquette correlation functions in arbitrary directions are calculated for Z(2), SU(2) and SU(3) up to order g^?8. Approximate restoration of rotational symmetry is observed in the continuum limit for SU(2), but much higher order corrections seem to be required in order to restore the symmetry for SU(3). The scalar glueball mass deduced from the plaquette-plaquette correlation function in the diagonal direction is 0.80 GeV, while the on-axis computation up to order g^?16 predicts it to be 0.64 GeV.     

High-temperature expansions for the free energy of vortices and the string tension in lattice gauge theories

We derive high-temperature cluster expansions for the free energy of vortices in SU(2) and Z₂ lattice gauge theories in 3 and 4 dimensions. The expected behaviour of the vortex free energy is verified. It obeys an area law behaviour. The coefficient of the area is shown to be equal to the string tension between static quarks. We calculate its expansion up to 12th order. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement at strong and intermediate coupling.     

Computation of the action for on-shell improved lattice gauge theories at weak coupling

The coefficient in Symanzik's improved lattice action for (pure) SU(2) and SU(3) gauge theories are determined to one-loop order by requiring the absence of leading scaling violations in a set of on-shell quantities, which arise in a world where two dimensions are compactified in a twisted manner.     

Averaging operations for lattice gauge theories

Usually renormalization group transformations are defined by some averaging operations. In this paper we study such operations for lattice gauge fields and for gauge transformations. We are interested especially in characterizing some classes of field configurations on which the averaging operations are regular (e.g., analytic). These results will be used in subsequent papers on the renormalization group method in lattice gauge theories.Research supported in part by the National Science Foundation under Grant PHY-82-03669     

Stochastic models for lattice gauge theories

Stochastic equations are derived which describe the (Euclidean) time evolution of lattice field configurations, with and without fermions, on a three-dimensional space lattice. It is indicated how the drifts and transition functions may be obtained as asymptotic solutions of a differential equation or from a ground state ansatz. For non-Abelian gauge fields (without fermions) a ground state is constructed which is an exact eigenstate of a Hamiltonian with the same (naive) continuum limit as the Kogut-Susskind Hamiltonian. It is described how Euclidean correlations (like the Wilson loop) are obtained from the stochastic equations and how mass gaps may be obtained from the technique of exit times.     

Uniformly valid amplitude expansions for non-Abelian gauge theories

The imposition of a particular gauge condition in a non-Abelian gauge theory may lead to large-r nonuniformities in an amplitude expansion when used in the construction of an approximate solution of the field equations of the theory. We show that for both the Yang-Mills theory and general relativity it is always possible to find a class of gauge conditions that do not suffer from this defect and at the same time lead to solvable equations in each order of the approximation employed. We further show how one can construct such gauge conditions by a method similar to Lighthill's method of strained coordinates. An example of such a construction is given for the Yang-Mills theory.     

Chiral gauge theories on the lattice

We propose a method for constructing lattice gauge theories in which fermions transform as a complex representation of the gauge group.     

On-shell improved lattice gauge theories

By means of a spectrum conserving transformation, we show that one of the 3 coefficients in Symanzik's improved action can be chosen freely, if only spectral quantities (masses of stable particles, heavy quark potential etc.) are to be improved. In perturbation theory, the other 2 coefficients are however completely determined and their values are obtained to lowest order.Heisenberg foundation fellow     

Optical Abelian lattice gauge theories

We discuss a general framework for the realization of a family of Abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable for quantum simulations. Within this class, we study in detail the phases of a U(1)$U\left(1\right)$-invariant lattice gauge theory in 2+1$2+1$ dimensions, originally proposed by P. Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4×4$4\times 4$. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices, where we discuss in detail a protocol for the preparation of the ground-state. We propose two key experimental tests that can be used as smoking gun of the proper implementation of a gauge theory in optical lattices. These tests consist in verifying the absence of spontaneous (gauge) symmetry breaking of the ground-state and the presence of charge confinement. We also comment on the relation between standard compact U(1)$U\left(1\right)$ lattice gauge theory and the model considered in this paper.     

The Bethe approximation for lattice gauge theories

The Bethe approximation is defined for general lattice gauge theories. It amounts to solving the model on an infinite Cayley lattice of cubes. The approximation is tested on the 4-d Z₄ model, where it is shown to reproduce accurately most of the phase diagram. It also suggests which mass vanishes in the Coulomb phase.     

Internal space decimation for lattice gauge theories

By a systematic decimation of internal space lattice gauge theories with continuous symmetry groups are mapped into effective lattice gauge theories with finite symmetry groups. The decimation of internal space makes a larger lattice tractable with the same computational resources. In this sense the method is an alternative to Wilson's and Symanzik's programs of improved actions. As an illustrative test of the method U(1) is decimated to Z(N) and the results compared with Monte Carlo data for Z(4)- and Z(5)-invariant lattice gauge theories. The result of decimating SU(3) to its 1080-element crystal-group-like subgroup is given and discussed.     

A quenching scenario for lattice gauge theories

We study lattice gauge theories with complex, random and quenched couplings. Such theories are argued to have the same continuum limits as the annealed case. The first-order phase transitions are shown to be absent and the smoother cross-over behavior of the quenched theory leads to the universal scaling law.