Non-perturbative Aspect of Zero Dimensional Supersring

TL;DR

This paper investigates the non-perturbative effects in zero dimensional superstring theory, revealing divergence in perturbative expansions and spontaneous supersymmetry breaking due to non-perturbative contributions.

Contribution

It provides a detailed analysis of non-perturbative effects in zero dimensional superstring, highlighting differences from bosonic strings and explaining supersymmetry breaking.

Findings

Perturbative expansions diverge as _l(3l)! ppa^{2l}

Non-perturbative contributions are of order ^{Cppa^{-rac{2}{3}}}

Supersymmetry breaks spontaneously due to non-perturbative effects

Abstract

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