One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings

TL;DR

This paper computes all-genus correlation functions in a matrix model linked to type IIA superstring theory, revealing non-Borel summable series for unprotected operators and instanton effects, thus strengthening the matrix-string correspondence.

Contribution

It extends previous work by calculating all-order genus correlation functions and analyzing non-perturbative effects in the matrix model for type IIA superstrings.

Findings

Protected operators' one-point functions terminate at finite genus.

Unprotected operators exhibit non-Borel summable series.

Universal logarithmic scaling behavior observed for non-supersymmetric operators.

Abstract

In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background from the viewpoint of symmetry and spectrum. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. In order to investigate the correspondence further, in this paper we compute correlation functions to all order of genus expansion in the double scaling limit of the matrix model. One-point functions of operators protected by supersymmetry terminate at some finite order, whereas those of unprotected operators yield non-Borel summable series. The behavior of the latter is characteristic in string perturbation series, providing further evidence that the matrix model describes a string theory. Moreover, instanton corrections to the planar one-point functions are also computed, and universal logarithmic scaling behavior is found for non-supersymmetric operators.