On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions

TL;DR

This paper investigates the invariance properties of noncommutative two-dimensional Yang-Mills theory, confirming that while full invariance under area-preserving diffeomorphisms is broken, a residual invariance under linear unimodular transformations remains.

Contribution

The study provides analytical and numerical evidence that noncommutative 2D Yang-Mills theory loses invariance under area-preserving diffeomorphisms but retains invariance under linear unimodular transformations.

Findings

Invariance under area-preserving diffeomorphisms is broken.

A residual invariance under linear unimodular transformations persists.

Analytical and numerical methods confirm these invariance properties.

Abstract

We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.