Normalization of ZZ instanton amplitudes in minimal string theory

TL;DR

This paper employs string field theory techniques to resolve divergences in minimal string theory amplitudes, achieving finite, consistent results that align with matrix model predictions and exploring extensions to more general models.

Contribution

It introduces a string field theory approach to normalize ZZ instanton amplitudes in minimal string theory, ensuring finiteness and agreement with dual matrix models.

Findings

Divergences in cylinder diagrams are cured using string field theory.

Normalized amplitudes match dual matrix model predictions.

Results extend to certain more general minimal string models.

Abstract

We use insights from string field theory to analyze and cure the divergences in the cylinder diagram in minimal string theory with both boundaries lying on a ZZ brane. We focus on theories with worldsheet matter consisting of the $(2,p)$ minimal model plus Liouville theory, with total central charge 26, together with the usual $bc$-ghosts. The string field theory procedure gives a finite, purely imaginary normalization constant for non-perturbative effects in minimal string theory, or doubly non-perturbative effects in JT gravity. We find precise agreement with the prediction from the dual double-scaled one-matrix integral. We also make a few remarks about the extension of this result to the more general $(p',p)$ minimal string.