A noncommutative anomaly through Seiberg-Witten map and non-locally regularized BV quantization

TL;DR

This paper investigates anomalies in noncommutative gauge theories by employing the Seiberg-Witten map and non-locally regularized BV quantization to compute the NC anomaly of the chiral Schwinger model.

Contribution

It introduces a method to calculate noncommutative anomalies using the Seiberg-Witten map combined with non-local BV regularization.

Findings

Computed the NC anomaly of the BV quantized chiral Schwinger model.

Demonstrated the application of the SW map in noncommutative anomaly calculations.

Provided insights into the structure of anomalies in NC gauge theories.

Abstract

Anomalies are one essential concept for the renormalization of noncommutative (NC) gauge theories. A NC space can be visualized as a deformation of the usual spacetime with the $\star$-product and can be constructed after the quantization of a given space with its symplectic structure. The Seiberg-Witten (SW) map connects NC fields, transformations parameters and gauge potential to their commutative analogs. In this work we used the SW map to calculate the NC version of the anomaly of the BV quantized chiral Schwinger model with nonlocal regularization.