Non-Commutative Yang-Mills and the AdS/CFT Correspondence

TL;DR

This paper investigates the effects of non-commutativity in supersymmetric Yang-Mills theory at strong coupling using the AdS/CFT correspondence, revealing how non-commutativity influences UV behavior and establishing a minimal scale in the dual supergravity description.

Contribution

It provides a supergravity dual for non-commutative N=4 SYM, analyzes the UV/IR relation, and determines how the non-commutativity scale depends on the 't Hooft coupling at strong coupling.

Findings

Non-commutativity affects the ultra-violet but not the infra-red of the Yang-Mills dynamics.

The supergravity solution has no boundary and defines a minimal scale.

The relation between the B field and the non-commutativity scale is corrected at large coupling.

Abstract

We study the non-commutative supersymmetric Yang-Mills theory at strong coupling using the AdS/CFT correspondence. The supergravity description and the UV/IR relation confirms the expectation that the non-commutativity affects the ultra-violet but not the infra-red of the Yang-Mills dynamics. We show that the supergravity solution dual to the non-commutative N=4 SYM in four dimensions has no boundary and defines a minimal scale. We also show that the relation between the B field and the scale of non-commutativity is corrected at large coupling and determine its dependence on the 't Hooft coupling \lambda.