$N=\half$ Superstring in Zero Dimension and the Spontaneous Breakdown of the Supersymmetry

TL;DR

This paper introduces zero-dimensional random matrix models with half-integer supersymmetry that spontaneously break supersymmetry, demonstrating that this breakdown persists in the continuum limit and providing exact partition functions for related string theories.

Contribution

It presents new zero-dimensional matrix models with half-integer supersymmetry and analyzes their spontaneous supersymmetry breaking and continuum limit behavior.

Findings

Supersymmetry breaks spontaneously in these models.

Double scaling limit exists and preserves supersymmetry breaking.

Exact partition functions for associated string theories are derived.

Abstract

We propose random matrix models which have $N=\half$ supersymmetry in zero dimension. The supersymmetry breaks down spontaneously. It is shown that the double scaling limit can be defined in these models and the breakdown of the supersymmetry remains in the continuum limit. The exact non-trivial partition functions of the string theories corresponding to these matrix models are also obtained.