Fermions and nonperturbative supersymmetry breaking in the one-dimensional superstring

Abstract

The one-dimensional superstring of Marinari and Parisi is analyzed taking into account the fermionic sector. The original matrix model is reduced to a manifestly supersymmetric quantum mechanics of eigenvalues with an effective superpotential. Unlike the bosonic sector, the fermionic sector has long-range interactions between the eigenvalues. It is shown that in the double-scaling limit the dynamics of the top eigenvalue can be described in terms of scaled supercharges. The one-eigenvalue instanton and the corresponding fermionic zero mode responsible for supersymmetry breaking are identified. The supersymmetry breaking parameter is calculated and is shown to be nonzero. The nonperturbative breaking of supersymmetry in this string model goes as exp(-C/χ ), where χ ² is the loop counting parameter. This is much stronger than the exp(-C/χ ²) nonperturbative effects characteristic of low-energy field theory. Possible implications of this result for critical string theory are discussed.