Correlation Functions of the Scalar Field in Background NC U(1) Yang-Mills

TL;DR

This paper calculates correlation functions of scalar fields in a noncommutative U(1) Yang-Mills background, revealing how gauge invariance is maintained in higher correlators and connecting to noncommutative solitons.

Contribution

It introduces a method to compute gauge-invariant correlators in noncommutative gauge theories and demonstrates the emergence of noncommutative solitons in these calculations.

Findings

Gauge invariance is restored in higher correlators.

Noncommutative solitons appear naturally in the correlator calculations.

Green's functions are not gauge invariant, but composite operators' correlators are.

Abstract

We consider the complex scalar field coupled to background NC U(1) YM and calculate the correlator of two gauge invariant composite operators. We show how the noncommutative gauge invariance is restored for higher correlators (though the Green's function itself is not invariant). It is interesting that the recently discovered noncommutative solitons appear in the calculation.