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

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.