Quantum duality under the theta-exact Seiberg-Witten map

TL;DR

This paper demonstrates that noncommutative U(N) Yang-Mills theories related by the theta-exact Seiberg-Witten map are quantum duals, with simplified divergence structures and gauge-fixing independence, especially in supersymmetric cases.

Contribution

It establishes quantum duality between noncommutative and ordinary gauge theories via the theta-exact Seiberg-Witten map and analyzes divergence behavior at one-loop level.

Findings

Non-local UV divergences largely disappear in the mapped theory.

Gauge-fixing independence of IR divergences is confirmed.

Supersymmetry removes quadratic IR divergences.

Abstract

We show that in the perturbative regime defined by the coupling constant, the theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with or without Supersymmetry-- gives an ordinary gauge theory which is, at the quantum level, dual to the former. We do so by using the on-shell DeWitt effective action and dimensional regularization. We explicitly compute the one-loop two-point function contribution to the on-shell DeWitt effective action of the ordinary U(1) theory furnished by the theta-exact Seiberg-Witten map. We find that the non-local UV divergences found in the propagator in the Feynman gauge all but disappear, so that they are not physically relevant. We also show that the quadratic noncommutative IR divergences are gauge-fixing independent and go away in the Supersymmetric version of the U(1) theory.