Abelian and Nonabelian Lattice Chiral Gauge Theories Through Gauge Fixing

Abstract

After an introduction in which we review the fundamental difficulty in constructing lattice chiral gauge theories, we summarize the analytic and numerical evidence that abelian lattice chiral gauge theories can be nonperturbatively constructed through the gauge-fixing approach. In addition, we indicate how we believe that the method may be extended to nonabelian chiral gauge theories.

On the continuum limit of gauge-fixed compact U(1) lattice gauge theory

“…The phase diagram and behavior of the theory at g = 0.6 was investigated before [10]. We have reconfirmed the results of [10] and for reasons of clarity fig. 1 does not include the data for g = 0.6.…”

“…We expect E κ = 0 in the broken symmetric phases FM and FMD and E κ ∼ 0 in the symmetric (PM) phase. Besides, E κ is expected to be continuous at a continuous phase transition (infinite slope in the infinite volume limit) and show a discrete jump at a first order transition [10,12]. The true order parameter is V which allows us to distinguish the FMD phase (where V = 0) from the other phases where V ∼ 0.…”

“…However, in the investigation of the gauge-fixed theory as given, the dimension-two counterterm has been mostly considered, because it alone could lead to a continuous phase transition that recovers the gauge symmetry. It was argued that the marginal counterterms would not possibly create new universality classes for the continuum theory corresponding to large κ (for a discussion on other counterterms, please see [8,10]).…”

“…The parameter space of this regularization of compact U(1) theory now includes the gauge coupling, the coefficient of the gauge fixing term and the coefficients of the counterterms. In this extended parameter space it has been shown [10] that for a weak gauge coupling (g = 0.6) there exists a continuous phase transition at which the U(1) gauge symmetry is restored and the continuum theory of free photons emerge. In this study, determination of the phase diagram and the critical region as extensively as possible is very important because we are dealing with a gauge-noninvariant theory in general and it is necessary to have freedom along the critical manifold so that irrelevant parameters can be appropriately tuned to restore gauge invariance (protecting the theory from a violation of unitarity).…”

New tests of the gauge-fixing approach to lattice chiral gauge theories

“…In ref. [15] we show explicitly that factorization holds also at the next-to-leading order. In our Monte Carlo simulations, we have computed G H µν (|x − y|) and G V µν (|x − y|).…”