Phase diagram and spectrum of gauge-fixed Abelian lattice gauge theory

Abstract

We consider a lattice discretization of a covariantly gauge-fixed Abelian gauge theory. The gauge fixing is part of the action defining the theory, and we study the phase diagram in detail. As there is no BRST symmetry on the lattice, counterterms are needed, and we construct those explicitly. We show that the proper adjustment of these counterterms drives the theory to a new type of phase transition, at which we recover a continuum theory of ͑free͒ photons. We present both numerical and ͑one-loop͒ perturbative results, and show that they are in good agreement near this phase transition. Since perturbation theory plays an important role, it is important to choose a discretization of the gauge-fixing action such that lattice perturbation theory is valid. Indeed, we find numerical evidence that lattice actions not satisfying this requirement do not lead to the desired continuum limit. While we do not consider fermions here, we argue that our results, in combination with previous work, provide very strong evidence that this new phase transition can be used to define Abelian lattice chiral gauge theories.

Tricritical points in a compactU(1)lattice gauge theory at strong coupling

“…WCPT analysis and numerical investigations performed earlier [13], only in the weak gauge coupling region of the above compact Abelian pure gauge theory, confirmed the existence of a new continuous phase transition between a regular ordered phase and a spatially modulated ordered phase, for sufficiently large value of the coefficient of the HD term. At this phase transition, gauge symmetry is restored and the scalar fields (lgdofs) decouple, leading to the desired emergence of massless free photons only, in the continuum limit taken from the regular broken phase.…”

“…The two extra terms (with coefficients κ andκ) ensure that in the neighborhood of the perturbative point (i.e., for small g and largeκ) the lgdofs are weakly coupled, and indeed numerical simulations confirm that the lgdofs decouple at a new phase transition separating the regular ordered phase (to be called FM in the following) from a so-called spatially modulated ordered phase (FMD) [13].…”

Lattice Chiral Gauge Theories Through Gauge Fixing

“…[21]. A complete description of the phase diagram in the four-parameter space spanned by the couplings g,κ,r and κ can be found there, as well as a discussion of the other counter terms and a study of gauge-field propagators.…”

“…In fact, we showed, through a combination of numerical and mean-field techniques, that the naive choice of gauge-fixing action of eq. (5) does not lead to a phase diagram with the desired properties [21]. The vacuum degeneracy of S g.f.,naive can be lifted by adding irrelevant terms to it [22,24], so that…”

“…These counter terms include one dimension 2 operator (the gauge-field mass counter term), no dimension 3 operators (because of the shift symmetry), and a host of dimension-4 counter terms (see refs. [18,21] for a detailed discussion). Tuning these counter terms to the appropriate values (by requiring the Ward-Takahashi identities of the continuum target theory to be satisfied) should then bring us to the critical point(s) in the phase diagram at which a ChGT can be defined.…”