ZZ brane amplitudes from matrix models

TL;DR

This paper investigates instanton effects in the one matrix model at multicritical points, demonstrating their universality and correspondence with ZZ branes in Liouville theory, and providing a systematic way to compute ZZ brane amplitudes.

Contribution

It establishes a universal link between matrix model instantons and ZZ branes, and shows how to systematically derive ZZ brane amplitudes from matrix model calculations.

Findings

2-instanton contributions are universal.

Connected 2-instanton parts reproduce ZZ brane annulus amplitudes.

Partition function expansion in instantons yields systematic ZZ brane amplitudes.

Abstract

We study instanton contribution to the partition function of the one matrix model in the k-th multicritical region, which corresponds to the (2,2k-1) minimal model coupled to Liouville theory. The instantons in the one matrix model are given by local extrema of the effective potential for a matrix eigenvalue and identified with the ZZ branes in Liouville theory. We show that the 2-instanton contribution in the partition function is universal as well as the 1-instanton contribution and that the connected part of the 2-instanton contribution reproduces the annulus amplitudes between the ZZ branes in Liouville theory. Our result serves as another nontrivial check on the correspondence between the instantons in the one matrix model and the ZZ branes in Liouville theory, and also suggests that the expansion of the partition function in terms of the instanton numbers are universal and gives systematically ZZ brane amplitudes in Liouville theory.