Noncritical String Correlators, Finite-N Matrix Models and the Vortex Condensate

TL;DR

This paper systematically computes correlation functions in the Euclidean c=1 string theory using the Normal Matrix Model, providing explicit formulas and insights into vortex condensates and T-duality.

Contribution

It introduces the Normal Matrix Model as a tool for calculating finite-N c=1 string correlators and derives a combinatoric formula for vortex condensates.

Findings

Explicit expressions for correlators in terms of special functions

A combinatoric formula for 2n-point functions of unit momentum modes

Insights into vortex condensates and T-duality at c=1

Abstract

We carry out a systematic study of correlation functions of momentum modes in the Euclidean c=1 string, as a function of the radius and to all orders in perturbation theory. We obtain simple explicit expressions for several classes of correlators in terms of special functions. The Normal Matrix Model is found to be a powerful calculational tool that computes c=1 string correlators even at finite N. This enables us to obtain a simple combinatoric formula for the 2n-point function of unit momentum modes, which after T-duality determines the vortex condensate. We comment on possible applications of our results to T-duality at c=1 and to the 2d black hole/vortex condensate problem.