Conformal Anomalies in Noncommutative Gauge Theories

TL;DR

This paper computes conformal anomalies in noncommutative gauge theories using Fujikawa's path integral method, revealing differences from ordinary gauge theories due to the Moyal star product, and confirms results with perturbative analysis.

Contribution

It provides the first detailed calculation of conformal anomalies in noncommutative gauge theories and compares them with ordinary gauge theories, highlighting the effects of noncommutativity.

Findings

Conformal anomalies are deformed by the Moyal star product.

Coefficients of anomalies differ from those in ordinary gauge theories.

Beta functions from anomalies match perturbative results.

Abstract

We calculate conformal anomalies in noncommutative gauge theories by using the path integral method (Fujikawa's method). Along with the axial anomalies and chiral gauge anomalies, conformal anomalies take the form of the straightforward Moyal deformation in the corresponding conformal anomalies in ordinary gauge theories. However, the Moyal star product leads to the difference in the coefficient of the conformal anomalies between noncommutative gauge theories and ordinary gauge theories. The $\beta$ (Callan-Symanzik) functions which are evaluated from the coefficient of the conformal anomalies coincide with the result of perturbative analysis.