Seiberg-Witten-type Maps for Currents and Energy-Momentum Tensors in Noncommutative Gauge Theories

TL;DR

This paper derives Seiberg-Witten-type maps connecting currents and energy-momentum tensors in noncommutative gauge theories to their commutative counterparts, enabling generalized force laws and anomaly relations.

Contribution

It introduces explicit maps for currents and energy-momentum tensors in noncommutative gauge theories, extending their applications to anomalies and energy-momentum constructions.

Findings

Generalized Lorentz force law in NC electrodynamics

Relation between NC and commutative anomalies

Implications for Sugawara energy-momentum tensor in 2D

Abstract

We derive maps relating the currents and energy-momentum tensors in noncommutative (NC) gauge theories with their commutative equivalents. Some uses of these maps are discussed. Especially, in NC electrodynamics, we obtain a generalization of the Lorentz force law. Also, the same map for anomalous currents relates the Adler-Bell-Jackiw type NC covariant anomaly with the standard commutative-theory anomaly. For the particular case of two dimensions, we discuss the implications of these maps for the Sugawara-type energy-momentum tensor.