Normalization of ZZ instanton amplitudes in type 0B minimal superstring theory

TL;DR

This paper analyzes ZZ instanton corrections in type 0B minimal superstring theory, resolving divergences in normalization constants, and demonstrates duality with matrix models, with results matching between string theory and matrix integral calculations.

Contribution

It provides a finite normalization of ZZ instanton amplitudes in type 0B minimal superstring theory and establishes their duality with matrix models, including the analysis of phase transitions.

Findings

Finite, unambiguous instanton normalization constants obtained.

Duality between superstring theories and matrix models confirmed.

Instanton corrections match between string theory and matrix integral calculations.

Abstract

We study ZZ instanton corrections in the $(2,4k)$ $N=1$ minimal superstring theory with the type 0B GSO projection, which becomes the type 0B $N=1$ super-JT gravity in the $k \to \infty$ limit. Each member of the $(2,4k)$ family of theories has two phases distinguished by the sign of the Liouville bulk cosmological constant. The worldsheet method for computing the one-loop normalization constant multiplying the instanton corrections gives an ill-defined answer in both phases. We fix these divergences using insights from string field theory and find finite, unambiguous results. Each member of the $(2,4k)$ family of theories is dual to a double-scaled one-matrix integral, where the double-scaling limit can be obtained starting either from a unitary matrix integral with a leading one-cut saddle point, or from a hermitian matrix integral with a leading two-cut saddle point. The matrix integral exhibits a gap-closing transition, which is the same as the double-scaled Gross-Witten-Wadia transition when $k=1$. We also compute instanton corrections in the double-scaled matrix integral for all $k$ and in both phases, and find perfect agreement with the string theory results.