Equivalence of quantum field theories related by the theta-exact Seiberg-Witten map

TL;DR

This paper proves the all-order perturbative equivalence of noncommutative U(N) quantum field theories related by the theta-exact Seiberg-Witten map, including supersymmetric cases, through theoretical proof and one-loop calculations.

Contribution

It establishes the all-order perturbative equivalence of noncommutative gauge theories connected by the theta-exact Seiberg-Witten map, extending to supersymmetric theories.

Findings

Equivalence holds for all orders in perturbation theory.

One-loop quantum corrections confirm the duality.

The proof applies to various supersymmetry levels.

Abstract

The equivalence of the noncommutative U(N) quantum field theories related by the theta-exact Seiberg-Witten maps is in this letter proven to all orders in the perturbation theory with respect to the coupling constant. We show that this duality holds for Super Yang-Mills theories with N=0,1,2,4 supersymmetry. A direct check of this equivalence relation is performed by computing the one-loop quantum corrections to the quadratic part of the effective action in the noncommutative U(1) gauge theory with N=0,1,2,4 supersymmetry.