Gravity/Non-Commutative Yang-Mills Correspondence and Doubletons

TL;DR

This paper explores the gravity dual of non-commutative Yang-Mills theory, revealing that doubletons do not decouple unless the theory is commutative, and establishing the duality with non-commutative U(N) gauge theory.

Contribution

It demonstrates that in the non-commutative setting, doubletons remain coupled, indicating the dual gauge theory is U(N) rather than SU(N), extending the gauge/gravity correspondence.

Findings

Doubletons do not decouple in non-commutative gravity duals.

The dual gauge theory is identified as non-commutative U(N).

SU(N) gauge symmetry is not separable from U(1) in this context.

Abstract

We discuss the gravity dual description for a non-commutative Yang-Mills theory, which reduces to that on AdS_{5} x S_{5} in the commutative limit. It is found that doubletons do not decouple in this dual gravity description unless one takes the commutative limit. The decoupling of the doubletons in AdS_{5} space implies that the dual gauge theory has SU(N) gauge symmetry. Our result implies that this gravity description is dual to non-commutative U(N) gauge theory. It is compatible with the claim that U(1) and SU(N) gauge symmetries can not separate in non-commutative U(N) gauge theory.