Fermion Zero Modes in the Presence of Fluxes and a Non-perturbative Superpotential

TL;DR

The work tackles how background fluxes of general Hodge type interact with non-perturbative superpotentials in M-theory/IIB compactifications, focusing on world-volume fermion zero modes of M5/D3 branes. It shows that naive modulino variations fail when $W_{np}$ is present, since the background flux ceases to be purely $(2,2)$ (or $(2,1)$) and backreaction must be accounted for. By modifying the modulino variations to include the backreacted flux, the authors demonstrate that the count of fermion zero modes remains consistent with the generation of a non-perturbative superpotential, exemplified by the $K3 imes K3$ case. The key contribution is a consistent framework for zero-mode counting that incorporates non-perturbative effects into the bulk SUSY variations, clarifying KKLT-like stabilization scenarios and the conditions under which instanton-generated superpotentials are allowed. This work thus provides a principled resolution to apparent mismatches between flux-induced SUSY conditions and world-volume zero-mode structure.

Abstract

We study the effect of background fluxes of general Hodge type on the supersymmetry conditions and on the fermionic zero modes on the world-volume of a Euclidean M5/D3-brane in M-theory/type IIB string theory. Using the naive susy variation of the modulino fields to determine the number of zero modes in the presence of a flux of general Hodge type, an inconsistency appears. This inconsistency is resolved by a modification of the supersymmetry variation of the modulinos, which captures the back-reaction of the non-perturbative effects on the background flux and the geometry.