Area preserving diffeomorphisms and Yang-Mills theory in two noncommutative dimensions

TL;DR

This paper investigates the symmetry properties of noncommutative two-dimensional Yang-Mills theory, showing it lacks invariance under area-preserving diffeomorphisms but retains invariance under linear unimodular transformations.

Contribution

It provides evidence that noncommutative Yang-Mills theory in two dimensions differs from the commutative case in its symmetry invariances, specifically under area-preserving diffeomorphisms.

Findings

Noncommutative Yang-Mills theory is not invariant under area-preserving diffeomorphisms.

Invariance under linear unimodular maps is preserved.

The results are supported by a general theoretical argument.

Abstract

We present some evidence that noncommutative Yang-Mills theory in two dimensions is not invariant under area preserving diffeomorphisms, at variance with the commutative case. Still, invariance under linear unimodular maps survives, as is proven by means of a fairly general argument.