c=1 Matrix Models: Equivalences and Open-Closed String Duality

TL;DR

This paper demonstrates the explicit equivalence between the Normal Matrix Model and the Kontsevich-Penner model in c=1 string theory, exploring open-closed string duality and related transformations.

Contribution

It provides a detailed proof of the equivalence between two matrix models for c=1 string theory and discusses the implications for open-closed string duality.

Findings

Normal Matrix Model and Kontsevich-Penner model are equivalent at c=1.

Macroscopic loop expectations relate to closed string tachyon condensates.

The Kontsevich-Miwa transform encodes open-closed duality.

Abstract

We give an explicit demonstration of the equivalence between the Normal Matrix Model (NMM) of c=1 string theory at selfdual radius and the Kontsevich-Penner (KP) model for the same string theory. We relate macroscopic loop expectation values in the NMM to condensates of the closed string tachyon, and discuss the implications for open-closed duality. As in c<1, the Kontsevich-Miwa transform between the parameters of the two theories appears to encode open-closed string duality, though our results also exhibit some interesting differences with the c<1 case. We also briefly comment on two different ways in which the Kontsevich model originates.