Nonperturbative Effect in c=1 Noncritical String Theory and Penner Model

TL;DR

This paper investigates the nonperturbative effects caused by instantons in the Penner matrix model and their correspondence to similar effects in c=1 noncritical string theory at the self-dual radius, revealing a deep connection between the two.

Contribution

It establishes a detailed link between instantons in the Penner model and nonperturbative effects in c=1 noncritical string theory, expanding understanding of their equivalence in the double scaling limit.

Findings

Instantons in the Penner model correspond to nonperturbative effects in c=1 string theory.

The free energies of the Penner model and c=1 string theory agree in the double scaling limit.

Nonperturbative effects are characterized by instantons in the matrix model.

Abstract

We derive the effect of instantons in the Penner model. It is known that the free energies of the Penner model and the c=1 noncritical string at self-dual radius agree in a suitable double scaling limit. On the other hand, the instanton in the matrix model describes a nonperturbative effect in the noncritical string theory. We study the correspondence between the instantons in the Penner model and the nonperturbative effect in c=1 noncritical string at self-dual radius.