On the worldsheet theories of strings dual to free large N gauge theories

TL;DR

This paper investigates the properties of worldsheet theories dual to free large N gauge theories, analyzing correlation functions, operator product expansions, and symmetry properties through explicit computations of Strebel differentials.

Contribution

It provides a detailed analysis of the worldsheet structure and correlation functions in string duals of free large N gauge theories, highlighting unique symmetry and moduli space features.

Findings

Worldsheet correlation functions are non-zero only on specific subspaces of moduli space.

The worldsheet OPE is consistent with conformal field theory expectations.

Full conformal symmetry is not preserved in the worldsheet mapping for conformal field theories.

Abstract

We analyze in detail some properties of the worldsheet of the closed string theories suggested by Gopakumar to be dual to free large N SU(N) gauge theories (with adjoint matter fields). We use Gopakumar's prescription to translate the computation of space-time correlation functions to worldsheet correlation functions for several classes of Feynman diagrams, by explicit computations of Strebel differentials. We compute the worldsheet operator product expansion in several cases and find that it is consistent with general worldsheet conformal field theory expectations. A peculiar property of the construction is that in several cases the resulting worldsheet correlation functions are non-vanishing only on a sub-space of the moduli space (say, for specific relations between vertex positions). Another strange property we find is that for a conformally invariant space-time theory, the mapping to the worldsheet does not preserve the special conformal symmetries, so that the full conformal group is not realized as a global symmetry on the worldsheet (even though it is, by construction, a symmetry of all integrated correlation functions).