On the All Order Solutions of Seiberg-Witten Map for Noncommutative Gauge Theories

TL;DR

This paper reviews recursive solutions of the Seiberg-Witten map to all orders in the noncommutative parameter for gauge, matter, and ghost fields, highlighting the structure of homogeneous solutions and their recursive contributions.

Contribution

It provides a comprehensive review of the all-order recursive solutions of the Seiberg-Witten map, including the structure and recursive nature of homogeneous solutions.

Findings

Recursive structure of homogeneous solutions elucidated

First order homogeneous solutions contribute to second order recursively

General structure of solutions for gauge, matter, and ghost fields presented

Abstract

We review the recursive solutions of the Seiberg--Witten map to all orders in $\theta$ for gauge, matter and ghost fields. We also present the general structure of the homogeneous solutions of the defining equations. Moreover, we show that the contribution of the first order homogeneous solution to the second order can be written recursively similar to inhomogeneous solutions.