The hybrid Seiberg-Witten map, its $\theta$-exact expansion and the antifield formalism

TL;DR

This paper derives an evolution equation for the hybrid Seiberg-Witten map using the antifield formalism, enabling a $ heta$-exact expansion in ordinary gauge fields, with explicit calculations up to third order.

Contribution

It introduces a novel evolution equation for the hybrid Seiberg-Witten map and provides a method to obtain its $ heta$-exact expansion, including explicit computations.

Findings

Derived an evolution equation for the hybrid Seiberg-Witten map.

Obtained a $ heta$-exact expansion up to third order in gauge fields.

Applied the expansion to the noncommutative Standard Model Higgs.

Abstract

We deduce an evolution equation for an arbitrary hybrid Seiberg-Witten map for compact gauge groups by using the antifield formalism. We show how this evolution equation can be used to obtain the hybrid Seiberg-Witten map as an expansion, which is $\theta$-exact, in the number of ordinary fields. We compute explicitly this expansion up to order three in the number of ordinary gauge fields and then particularize it to case of the Higgs of the noncommutative Standard Model.