On Open String Sigma-Model and Noncommutative Gauge Fields

TL;DR

This paper explores the connection between open string sigma-models and noncommutative gauge theories, introducing a new regularization scheme and deriving the noncommutative Yang-Mills action.

Contribution

It proposes a hybrid point splitting regularization scheme that directly yields the Seiberg-Witten description and introduces a Wilson factor ensuring classical noncommutative gauge invariance.

Findings

Derivation of the noncommutative Yang-Mills action from sigma-model partition function

Demonstration of a regularization scheme that reproduces Seiberg-Witten map

Establishment of gauge invariance at the classical level for noncommutative fields

Abstract

We consider the ordinary and noncommutative Dirac-Born-Infeld theories within the open string sigma-model. First, we propose a renormalization scheme, hybrid point splitting regularization, that leads directly to the Seiberg-Witten description including their two-form. We also show how such a form appears within the standard renormalization scheme just by some freedom in changing variables. Second, we propose a Wilson factor which has the noncommutative gauge invariance on the classical level and then compute the sigma-model partition function within one of the known renormalization scheme that preserves the noncommutative gauge invariance. As a result, we find the noncommutative Yang-Mills action.