In the previous paper, the authors pointed out correspondence of a supersymmetric double-well matrix model with two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background from the viewpoint of symmetries and spectrum. In thi
s paper we further investigate the correspondence from dynamical aspects by comparing scattering amplitudes in the matrix model and those in the type IIA theory. In the latter, cocycle factors are introduced to vertex operators in order to reproduce correct transformation laws and target-space statistics. By a perturbative treatment of the Ramond-Ramond background as insertions of the corresponding vertex operators, various IIA amplitudes are explicitly computed including quantitatively precise numerical factors. We show that several kinds of amplitudes in both sides indeed have exactly the same dependence on parameters of the theory. Moreover, we have a number of relations among coefficients which connect quantities in the type IIA theory and those in the matrix model. Consistency of the relations convinces us of the validity of the correspondence.
We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size $N$ infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models is slowly
varying, and the large-$N$ limit is taken with the slowly varying limit. First, we explain our formalism, introducing an external field to detect spontaneous SUSY breaking, analogously to ordinary (bosonic) symmetry breaking. It is observed that SUSY is possibly broken even in systems in less than one-dimension, for example, discretized quantum mechanics with a finite number of discretized time steps. Then, we consider spontaneous SUSY breaking in the SUSY matrix models with slowly varying potential, where the external field is turned off after the large-$N$ and slowly varying limit, analogously to the thermodynamic limit in statistical systems. On the other hand, without taking the slowly varying limit, in the SUSY matrix model with a double-well potential whose SUSY is broken due to instantons for finite $N$, a number of supersymmetric behavior is explicitly seen at large $N$. It convinces us that the instanton effect disappears and the SUSY gets restored in the large-$N$ limit.
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 ORaifeartaigh 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 $N$.
