Seiberg-Witten maps and commutator anomalies in noncommutative electrodynamics

TL;DR

This paper investigates the structure of commutator anomalies in noncommutative electrodynamics using Seiberg-Witten maps, revealing their relation to covariant anomalies and current algebra at first order in the noncommutativity parameter.

Contribution

It provides the first-order  structure of commutator anomalies in noncommutative U(1) gauge theory using Seiberg-Witten maps, ensuring consistency with covariant anomalies.

Findings

Derived the O( heta) structure of commutator anomalies.

Established compatibility with covariant anomalies.

Analyzed current-current and current-field algebra anomalies.

Abstract

We exploit the Seiberg-Witten maps for fields and currents in a U(1) gauge theory relating the noncommutative and commutative (usual) descriptions to obtain the O(\theta) structure of the commutator anomalies in noncommutative electrodynamics. These commutators involve the (covariant) current-current algebra and the (covariant) current-field algebra. We also establish the compatibility of the anomalous commutators with the noncommutative covariant anomaly through the use of certain consistency conditions derived here.