Strings and Discrete Fluxes of QCD

TL;DR

This paper explores the relationship between discrete magnetic fluxes and brane moduli in compactified SU(N) gauge theories, demonstrating magnetic screening, gauge theory behavior on a commutative torus, and T-duality invariance in QCD.

Contribution

It establishes a direct link between t'Hooft magnetic flux and NS two-form moduli, showing how these relate to degenerate brane vacua and gauge theory properties on a torus.

Findings

Magnetic flux m relates to NS B-field as B = 2π m/N.

Degenerate brane vacua correspond to specific B-field values.

Gauge theories on a torus are conventional at these B-field values.

Abstract

We study discrete fluxes in four dimensional SU(N) gauge theories with a mass gap by using brane compactifications which give ${\cal{N}} = 1$ or ${\cal{N}} = 0$ supersymmetry. We show that when such theories are compactified further on a torus, the t'Hooft magnetic flux $m$ is related to the NS two-form modulus $B$ by $B = 2\pi {m\over N}$. These values of $B$ label degenerate brane vacua, giving a simple demonstration of magnetic screening. Furthermore, for these values of $B$ one has a conventional gauge theory on a commutative torus, without having to perform any T-dualities. Because of the mass gap, a generic $B$ does not give a four dimensional gauge theory on a non-commutative torus. The Kaluza-Klein modes which must be integrated out to give a four dimensional theory decouple only when $B=2\pi {m\over N}$. Finally we show that $2\pi {m\over N}$ behaves like a two form modulus of the QCD string. This confirms a previous conjecture based on properties of large $N$ QCD suggesting a T-duality invariance.