Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups

TL;DR

This paper reformulates Seiberg-Witten maps and noncommutative Yang-Mills theories for any gauge group, making their all-order existence clear and analyzing ambiguities that could lead to inequivalent models.

Contribution

It provides a manifest formulation of Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups, clarifying their all-order existence and ambiguity implications.

Findings

Existence of Seiberg-Witten maps is established to all orders.

Ambiguities in the construction are analyzed for potential inequivalent models.

Framework applicable to arbitrary gauge groups.

Abstract

Seiberg-Witten maps and a recently proposed construction of noncommutative Yang-Mills theories (with matter fields) for arbitrary gauge groups are reformulated so that their existence to all orders is manifest. The ambiguities of the construction which originate from the freedom in the Seiberg-Witten map are discussed with regard to the question whether they can lead to inequivalent models, i.e., models not related by field redefinitions.