Spontaneous Supersymmetry Breaking by Large-N Matrices

TL;DR

This paper introduces models where supersymmetry remains intact at finite matrix size but is spontaneously broken at infinite size, providing insights into supersymmetry breaking mechanisms and small parameter origins.

Contribution

The paper presents concrete models coupling supersymmetric field theories to matrix models, demonstrating supersymmetry breaking at infinite N and explaining small parameters via large N effects.

Findings

Supersymmetry is preserved at finite N but broken at infinite N.

A metastable nonsupersymmetric vacuum appears near the origin.

The lifetime of the metastable vacuum depends on N.

Abstract

Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite $N$, but gets broken at infinite $N$, where $N$ is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when $N$ is infinity. In our models, the large value of $N$ gives a natural explanation for the origin of small parameters appearing in the field theories which trigger the supersymmetry breaking. In particular, in the case of the O'Raifeartaigh model coupled to a certain supersymmetric matrix model, a nonsupersymmetric metastable vacuum appears near the origin of the field space, which is far from the position of the supersymmetric vacuum. We estimate its lifetime as a function of $N$.