Comments on worldsheet theories dual to free large N gauge theories

TL;DR

This paper explores the properties of worldsheet conformal field theories proposed as duals to free large N gauge theories, focusing on modular invariance, correlation functions, and a new perturbation scheme for calculations.

Contribution

It demonstrates the inherent modular invariance of these worldsheet CFTs and introduces a novel perturbation method based on large operator dimensions for computing correlators.

Findings

Correlation functions localized on moduli space subspaces can be interpreted as delta functions.

Modular invariance is an intrinsic feature of the worldsheet CFTs.

A new perturbation scheme based on large operator dimensions improves correlator computations.

Abstract

We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in hep-th/0504229. The modular invariance of these CFTs is shown to be built into the formalism. We show that correlation functions in these CFTs which are localized on subspaces of the moduli space may be interpreted as delta-function distributions, and that this can be consistent with a local worldsheet description given some constraints on the operator product expansion coefficients. We illustrate these features by a detailed analysis of a specific four-point function diagram. To reliably compute this correlator we use a novel perturbation scheme which involves an expansion in the large dimension of some operators.