The c-Functions of Noncommutative Yang-Mills Theory from Holography

TL;DR

This paper explores the holographic dual of noncommutative Yang-Mills theory, deriving its gravity description and analyzing its renormalization group flows to confirm the validity of the C-theorem.

Contribution

It demonstrates that the gravity dual of NCYM with self-dual theta parameters can be described by five-dimensional dilatonic gravity and applies holographic RG techniques to study its anomalies.

Findings

The gravity dual is a five-dimensional dilatonic gravity theory.

The C-theorem holds for the NCYM in the holographic framework.

Holographic RG flow functions are explicitly calculated.

Abstract

In this paper we study non-commutative Yang-Mills theory (NCYM) through its gravity dual. First it is shown that the gravity dual of an NCYM with self-dual $\theta$-parameters has a Lagrangian in the form of five-dimensional dilatonic gravity. Then we use the de-Boer-Verlinde-Verlinde formalism for holographic renormalization group flows to calculate the coefficient functions in the Weyl anomaly of the NCYM at low energies under the assumption of potential dominance, and show that the $C$-theorem holds true in the present case.