Seiberg--Witten Maps to All Orders

TL;DR

This paper provides a comprehensive recursive formula for all-order Seiberg--Witten maps of gauge and matter fields, derived through gauge consistency conditions and differential equations, with explicit higher-order examples.

Contribution

It introduces a closed recursive formula for all-order Seiberg--Witten maps, advancing the understanding of gauge field mappings in noncommutative gauge theories.

Findings

Recursive formula for all-order Seiberg--Witten maps

Explicit third order non-abelian Seiberg--Witten maps

Explicit fourth order abelian Seiberg--Witten maps

Abstract

All order Seiberg--Witten maps of gauge parameter, gauge field and matter fields are given as a closed recursive formula. These maps are obtained by analyzing the order by order solutions of the gauge consistency and equivalence conditions as well as by directly solving Seiberg-Witten differential equations. The explicit third order non-abelian and fourth order abelian Seiberg-Witten maps of gauge parameter and gauge field are also presented.