Gauge Invariant Matrix Model for the \^A-\^D-\^E Closed Strings

TL;DR

This paper introduces a gauge-invariant matrix model for A-D-E closed strings, linking triangulated surfaces, Dynkin diagrams, and string theory via a double scaling limit and collective field theory.

Contribution

It formulates a gauge-invariant matrix model for these string types and describes its double scaling limit through a collective field theory with nonpolynomial interactions.

Findings

Model captures triangulated surfaces embedded in Dynkin diagrams

Double scaling limit described by a collective field theory

Propagator corresponds to two-loop correlator in string theory

Abstract

The models of triangulated random surfaces embedded in (extended) Dynkin diagrams are formulated as a gauge-invariant matrix model of Weingarten type. The double scaling limit of this model is described by a collective field theory with nonpolynomial interaction. The propagator in this field theory is essentially two-loop correlator in the corresponding string theory.