$c=1$, $R=1$ and $N\gg 1$: ZZ instantons in 2D String Theory and Matrix Integrals

TL;DR

This paper investigates non-perturbative effects in the $c=1$ string theory with compactified Euclidean time, calculating instanton contributions and matching them with matrix model predictions, enhancing understanding of dualities and instanton normalizations.

Contribution

It provides detailed calculations of ZZ instanton normalizations and correlators in $c=1$ string theory, connecting worldsheet and matrix model approaches at both self-dual and generic radii.

Findings

Calculated instanton normalizations and correlators in worldsheet formalism.

Matched string theory results with matrix model predictions.

Discussed multi-instanton normalizations and general $(1,n)$ ZZ instantons.

Abstract

We explore the non-perturbative aspects of $c=1$ string with compactified Euclidean time, its $0+0$ dimensional matrix model duals (at self-dual radius), and $0+1$ dimensional Matrix Quantum Mechanics (free fermion) description. We calculate the instanton normalizations, disk two-point function, and annulus one-point function in worldsheet formalism using string field theory insights. We further match them with the corresponding predictions from the matrix model descriptions. We also have some results and remarks regarding the multi ZZ instanton normalizations and the general $(1,n)$ ZZ instanton normalization for $c=1$ string at both self-dual and generic radius.