Seiberg-Witten equations from Fedosov deformation quantization of endomorphism bundle

TL;DR

This paper demonstrates how Seiberg-Witten equations can be derived using Fedosov deformation quantization of endomorphism bundles, providing a recursive method to compute the Seiberg-Witten map for arbitrary gauge groups.

Contribution

It introduces a novel approach linking Seiberg-Witten equations with Fedosov deformation quantization, generalizing to Fedosov-type noncommutativity.

Findings

Recursive computation of Seiberg-Witten map for any gauge group

Generalization of Seiberg-Witten equations to Fedosov noncommutativity

Connection between deformation quantization and gauge theory

Abstract

It is shown how Seiberg-Witten equations can be obtained by means of Fedosov deformation quantization of endomorphism bundle and the corresponding theory of equivalences of star products. In such setting, Seiberg-Witten map can be iteratively computed for arbitrary gauge group up to any given degree with recursive methods of Fedosov construction. Presented approach can be also considered as a generalization of Seiberg-Witten equations to Fedosov type of noncommutativity.