A Cohomological Approach to the Non-Abelian Seiberg-Witten Map

TL;DR

This paper introduces a cohomological framework using ghost fields and coboundary operators to systematically derive the non-Abelian Seiberg-Witten map for arbitrary gauge groups and orders in theta.

Contribution

It provides a novel cohomological method that generalizes the construction of the Seiberg-Witten map to any gauge group and order, using homotopy operators.

Findings

Cohomological approach successfully derives the Seiberg-Witten map.

Method applicable to any gauge group and order in theta.

Framework simplifies the computation of non-Abelian Seiberg-Witten maps.

Abstract

We present a cohomological method for obtaining the non-Abelian Seiberg-Witten map for any gauge group and to any order in theta. By introducing a ghost field, we are able to express the equations defining the Seiberg-Witten map through a coboundary operator, so that they can be solved by constructing a corresponding homotopy operator.