Noncommutative Gauge Theory, Divergences and Closed Strings

TL;DR

This paper investigates the renormalization of non-commutative gauge theories with matter, revealing the necessity of closed string modes in the effective action to account for infrared divergences, especially in string-theoretic contexts.

Contribution

It identifies the specific closed string modes needed in the Wilsonian effective action of non-commutative gauge theories, linking them to twisted sector fields in string theory on orbifolds.

Findings

Closed string modes are essential for correct infrared behavior.

Twisted sector fields in orbifold string theories match the required modes.

Provides a concrete string-theoretic origin for closed string modes in noncommutative field theories.

Abstract

We study the renormalization of non-commutative gauge theories with matter. As in the scalar field theory cases, there are logarithmic infrared divergences resulting from integrating out high momentum modes. In order to reproduce the correct infrared behaviour, the Wilsonian effective action has to include certain ''closed string`` modes with prescribed couplings. In the case of quiver gauge theories, realized in string theory on orbifolds, we identify the required modes with a set of twisted sector fields. These closed string modes have exactly the prescribed couplings to correct the Wilsonian effective action. This provides a concrete origin for the appearance of closed string modes in noncommutative field theories.