Fivebrane instantons and Calabi-Yau fourfolds with flux

TL;DR

This work evaluates fivebrane instanton effects in M-theory compactifications on Calabi-Yau fourfolds with flux, focusing on configurations with four fermionic zeromodes. By employing a detailed theta-expansion of eleven-dimensional superfields and the PST fivebrane action, the authors derive the gravitino vertex operator and perform an explicit zeromode integral in the normal-flux regime. They prove that such instantons do not generate a nonperturbative superpotential, in line with a flux-dependent generalization of the arithmetic genus criterion encoded in the index $\chi_F$. The findings suggest that flux modifies the conventional criterion rather than simply removing it, and point to future work on relaxing normal-flux conditions and exploring higher-derivative or multi-fermion instanton couplings with potential phenomenological implications.

Abstract

Using recent results on eleven-dimensional superspace, we compute the contribution of fivebrane instantons with four fermionic zeromodes in M-theory compactifications on Calabi-Yau fourfolds with flux. We find that no superpotential is generated in this case. This result is compatible with a certain flux-dependent modification of the arithmetic genus criterion.