Maps for currents and anomalies in noncommutative gauge theories

TL;DR

This paper develops explicit maps connecting currents and anomalies in noncommutative U(N) gauge theories with their commutative counterparts, including derivative corrections up to second order in the noncommutativity parameter.

Contribution

It provides explicit formulas for relating noncommutative and commutative gauge theory currents and anomalies, including derivative corrections up to second order in .

Findings

Derived maps relating noncommutative and commutative currents and divergences.

Connected noncommutative star-gauge anomalies with standard anomalies.

Computed derivative corrections to the maps up to ^2.

Abstract

We derive maps relating currents and their divergences in non-abelian U(N) noncommutative gauge theory with the corresponding expressions in the ordinary (commutative) description. For the U(1) theory, in the slowly-varying-field approximation, these maps are also seen to connect the star-gauge-covariant anomaly in the noncommutative theory with the standard Adler--Bell--Jackiw anomaly in the commutative version. For arbitrary fields, derivative corrections to the maps are explicitly computed up to O(\theta^2).