A Note on Supergravity Duals of Noncommutative Yang-Mills Theory

TL;DR

This paper discusses supergravity duals of noncommutative Yang-Mills theories, addressing ambiguities in correlation function calculations and proposing a method to recover expected results in the low energy limit.

Contribution

It proposes a resolution to the ambiguity in supergravity correlation function calculations by using an operator-based holographic approach applicable to noncommutative Yang-Mills theories.

Findings

Correlation functions match ordinary Yang-Mills results at low energy

Ambiguity in classical action evaluations is addressed

Holographic operators create states with definite energy and momentum

Abstract

A class of supergravity backgrounds have been proposed as dual descriptions of strong coupling large-N noncommutative Yang-Mills (NCYM) theories in 3+1 dimensions. However calculations of correlation functions in supergravity from an evaluation of relevant classical actions appear ambiguous. We propose a resolution of this ambiguity. Assuming that {\it some} holographic description exists - regardless of whether it is the NCYM theory - we argue that there should be operators in the holographic boundary theory which create normalized states of definite energy and momenta. An operator version of the dual correspondence then provides a calculation of correlators of these operators in terms of bulk Green's functions. We show that in the low energy limit the correlators reproduce expected answers of the ordinary Yang-Mills theory.