Nonabelian Gauge Theories on Noncommutative Spaces

TL;DR

This paper presents a systematic method to derive the nonabelian Seiberg-Witten map for any gauge group and order, using coboundary operators and homotopy techniques, clarifying ambiguities in the process.

Contribution

It introduces a formalism employing coboundary operators and homotopy to construct the nonabelian Seiberg-Witten map at all orders, addressing gauge and covariant ambiguities.

Findings

Explicit construction of the Seiberg-Witten map for any gauge group

Resolution of gauge and covariant ambiguities in the map

Framework applicable to all orders in theta

Abstract

In this paper, we describe a method for obtaining the nonabelian Seiberg-Witten map for any gauge group and to any order in theta. The equations defining the Seiberg-Witten map are expressed using a coboundary operator, so that they can be solved by constructing a corresponding homotopy operator. The ambiguities, of both the gauge and covariant type, which arise in this map are manifest in our formalism.