Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory

TL;DR

This paper investigates how Wilson loops in noncommutative gauge theory behave under area-preserving diffeomorphisms, revealing that quantum effects break classical twist symmetry in the usual formalism.

Contribution

It demonstrates the breakdown of twisted symmetry at the quantum level for Wilson loops in noncommutative gauge theories and explores conditions for twist invariance.

Findings

Classical gauge theory is twist covariant.

Quantum holonomy operators break twist symmetry.

Certain scalar field theories retain twisted symplectic invariance.

Abstract

We use twist deformation techniques to analyse the behaviour under area-preserving diffeomorphisms of quantum averages of Wilson loops in Yang-Mills theory on the noncommutative plane. We find that while the classical gauge theory is manifestly twist covariant, the holonomy operators break the quantum implementation of the twisted symmetry in the usual formal definition of the twisted quantum field theory. These results are deduced by analysing general criteria which guarantee twist invariance of noncommutative quantum field theories. From this a number of general results are also obtained, such as the twisted symplectic invariance of noncommutative scalar quantum field theories with polynomial interactions and the existence of a large class of holonomy operators with both twisted gauge covariance and twisted symplectic invariance.