SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings

TL;DR

This paper investigates nonperturbative effects in a supersymmetric matrix model for 2D type IIA superstrings, revealing spontaneous supersymmetry breaking due to instantons and suggesting a possible S-dual weakly coupled theory.

Contribution

It provides an explicit analytical and numerical analysis of nonperturbative effects, including instanton contributions, in a matrix model for 2D type IIA superstrings, demonstrating supersymmetry breaking.

Findings

Supersymmetry is spontaneously broken by instantons.

The free energy remains finite in the strongly coupled limit.

Evidence suggests a weakly coupled S-dual theory may exist.

Abstract

We explicitly compute nonperturbative effects in a supersymmetric double-well matrix model corresponding to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background. We analytically determine the full one-instanton contribution to the free energy and one-point function, including all perturbative fluctuations around the one-instanton background. The leading order two-instanton contribution is determined as well. We see that supersymmetry is spontaneously broken by instantons, and that the breaking persists after taking a double scaling limit which realizes the type IIA theory from the matrix model. The result implies that spontaneous supersymmetry breaking occurs by nonperturbative dynamics in the target space of the IIA theory. Furthermore, we numerically determine the full nonperturbative effects by recursive evaluation of orthogonal polynomials. The free energy of the matrix model appears well-defined and finite even in the strongly coupled limit of the corresponding type IIA theory. The result might suggest a weakly coupled theory appearing as an S-dual to the two-dimensional type IIA superstring theory.