Equivalence and/or quantum duality of the non/supersymmetric noncommutative field theories related by the theta-exact Seiberg-Witten map

TL;DR

This paper demonstrates that noncommutative U(N) quantum field theories related by the theta-exact Seiberg-Witten map are quantum equivalent at all orders, regardless of supersymmetry, establishing a fundamental duality.

Contribution

It proves the quantum equivalence of noncommutative U(N) theories connected by the Seiberg-Witten map at all perturbative orders, including supersymmetric cases.

Findings

Seiberg-Witten map commutes with quantization of NC QFT.

Quantum duality holds for supersymmetric and non-supersymmetric theories.

Proof applies at all orders in perturbation theory.

Abstract

In this article we expound a discovery of the quantum equivalence/duality of U(N) noncommutative quantum field theories (NC QFT) related by the theta-exact Seiberg-Witten (SW) maps and at all orders in the perturbation theory with respect to the coupling constant. We show that this proof holds for Super Yang-Mills (SYM) theories with N=0,1,2,4$ supersymmetry. In short, Seiberg-Witten map does commute with the quantization of the U(N) NCQFT independently, with or without supersymmetry.