Wilson loops in strongly coupled noncommutative gauge theories

TL;DR

This paper studies Wilson loops in 4D non-commutative super Yang-Mills theory using supergravity, revealing a crossover from Coulomb to area law behavior influenced by non-commutativity and supporting string theory connections.

Contribution

It introduces a supergravity-based approach to analyze Wilson loops in non-commutative gauge theories, highlighting a crossover in behavior linked to non-commutativity scale.

Findings

Wilson loops show Coulomb behavior at large scales

Small loops exhibit an area law influenced by non-commutativity

Crossover length scale is much larger than the non-commutativity scale

Abstract

We discuss Wilson loop averages in 4-dimensional non-commutative superYang-Mills theory using the dual supergravity description. We postulate that the Wilson loops are located at the mimimum length scale $R$ in the fifth radial coordinate. We find that they exhibit a crossover from Coulomb type of behaviour for large loops, for which non-commutativity is unimportant, to area law for small loops, for which non-commutativity effects are large. The string tension, which can be read off from the area law, is controlled by the non-commutativity scale. The crossover itself, however, appears to involve loops of size of order $R$ which is much larger than the non-commutativity scale. The existence of the area law in non-commutative super Yang-Mills theory which persists up to a large crossover length scale provides further evidence for connection to an underlying string theory.