Quantum aspects of Seiberg-Witten map in noncommutative Chern-Simons theory

TL;DR

This paper investigates whether the classical equivalence between noncommutative and commutative Chern-Simons theories, established via the Seiberg-Witten map, remains valid at the quantum level by computing specific correlation functions.

Contribution

It provides evidence supporting the quantum-level persistence of the Seiberg-Witten map's equivalence in noncommutative Chern-Simons theory through explicit perturbative calculations.

Findings

Two-point functions match under the Seiberg-Witten map at first order.

Three-point functions also exhibit consistency at the same order.

Supports quantum-level equivalence of the theories.

Abstract

Noncommutative Chern-Simons theory can be classically mapped to commutative Chern-Simons theory by the Seiberg-Witten map. We provide evidence that the equivalence persists at the quantum level by computing two and three-point functions of field strengths on the commutative side and their Seiberg-Witten transforms on the noncommutative side to the first nontrivial order in perturbation theory.