The role of the Seiberg-Witten field redefinition in renormalization of noncommutative chiral electrodynamics

TL;DR

This paper investigates whether the Seiberg-Witten field redefinition improves the renormalizability of noncommutative chiral electrodynamics, concluding that it does not when fermions are included, as the SW expansion is not preserved after quantization.

Contribution

The study provides a detailed analysis of the renormalization of $ heta$-expanded noncommutative chiral electrodynamics, showing that the SW map does not ensure renormalizability with fermions.

Findings

The relation between coupling constants changes after renormalization.

$ heta$-expanded chiral electrodynamics is not renormalizable with fermions.

The SW expansion is not preserved in the quantized theory.

Abstract

It has been conjectured in the literature that renormalizability of the $\theta$-expanded noncommutative gauge theories improves when one takes into account full nonuniqueness of the Seiberg-Witten expansion, which relates noncommutative (`high-energy') with commutative (`low-energy') fields. In order to check this conjecture we analyze renormalizability of the noncommutative chiral electrodynamics: we quantize the action which contains all possible terms implied by the SW map. After renormalization we arrive at a different theory in which the relation between the coupling constants is changed. This means that the $\theta$-expanded chiral electrodynamics is not renormalizable: when fermions are included, the SW expansion is not preserved in quantization.