Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping

Abstract

We consider supersymmetric matrix models of the type of the Wess-Zumino model, whose supersymmetry (SUSY) may be spontaneously broken. When SUSY is broken, the partition function vanishes since it is equivalent to the Witten index. We need some regularization to give a small value to the partition function in computing expectation values of observables in a well-defined way. Here, we employ twisted boundary condition to fermionic variables with a small angle α, and use this as the above regularization. Interestingly, the twist can be interpreted as an external field to detect spontaneous SUSY breaking, which is analogous to the magnetic field in Ising model whose Z2 symmetry is spontaneously broken. Also, we discuss the SUSY breaking from the viewpoints of localization and Nicolai mapping, and find interesting localization phenomena specific to matrix models.