Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study

TL;DR

This study uses lattice simulations to investigate how area-preserving diffeomorphism symmetry in non-commutative U(1) gauge theory breaks down from perturbative to non-perturbative regimes, revealing a loss of symmetry.

Contribution

It provides the first explicit non-perturbative evidence of APD symmetry breaking in non-commutative gauge theory using lattice methods.

Findings

APD symmetry breaks at finite coupling and non-commutativity.

Wilson loop measurements show invariance loss under shape variations.

Non-perturbative results suggest SL(2,R) symmetry does not hold.

Abstract

We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results are consistent with the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either.