Perturbative Analysis of the Seiberg-Witten Map

TL;DR

This paper analyzes the quantization of theta-expanded noncommutative U(1) Yang-Mills theory via the Seiberg-Witten map, revealing non-renormalizable terms and proposing a deformation of the trace to address quantum corrections.

Contribution

It provides a perturbative analysis of the Seiberg-Witten map's quantization, highlighting gauge independence and proposing a trace deformation for consistency.

Findings

Identified non-renormalizable terms in the quantized theory.

One-loop propagator corrections are gauge independent.

Proposed deformation of the trace in noncommutative field theory.

Abstract

We investigate the quantization of the theta-expanded noncommutative U(1) Yang-Mills action, obtained via the Seiberg-Witten map. As expected we find non-renormalizable terms. The one-loop propagator corrections are gauge independent, and lead us to a unique extention of the noncommutative classical action. We interpret our results as a requirement that also the trace in noncommutative field theory should be deformed.