Non-perturbative Aspect of Zero Dimensional Supersring

Abstract

We discuss the non-perturbative aspect of zero dimensional superstring. The perturbative expansions of correlation functions diverge as $\sum_l(3l)!κ^{2l}$, where $κ$ is a string coupling constant. This implies there are non-perturbative contributions of order $\e^{Cκ^{-{2 \over 3}}}$. (Here $C$ is a constant.) This situation contrasts with those of critical or non-critical bosonic strings, where the perturbative expansions diverge as $\sum_ll!κ^{2l}$ and non-perturbative behaviors go as $\e^{Cκ^{-1}}$. It is explained how such nonperturbative effects of order $\e^{Cκ^{-{2 \over 3}}}$ appear in zero dimensional superstring theory. Due to these non-perturbative effects, the supersymmetry in target space breaks down spontaneously.