A non-perturbative study of non-commutative U(1) gauge theory

TL;DR

This paper investigates the phase structure and continuum limits of non-commutative U(1) gauge theory on a 4D torus using Monte Carlo simulations, revealing a phase with broken translational symmetry and scaling behaviors.

Contribution

It provides a non-perturbative analysis of non-commutative U(1) gauge theory, identifying phases and continuum behaviors through lattice simulations.

Findings

Existence of a phase with non-zero open Wilson line vevs

Scaling behaviors in the continuum limit at intermediate coupling

Negative IR-singular term in dispersion relation causes phase transition

Abstract

We study U(1) gauge theory on a 4d non-commutative torus, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter theta, which provides evidence for a possible continuum theory. In the weak coupling symmetric phase, the dispersion relation involves a negative IR-singular term, which is responsible for the observed phase transition.