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

TL;DR

This paper investigates how background fluxes influence fermionic zero modes on branes in string theory, revealing that modifications to supersymmetry variations are necessary to account for non-perturbative effects and back-reaction.

Contribution

It introduces a modified supersymmetry variation of modulino fields that incorporates non-perturbative back-reaction effects in flux backgrounds.

Findings

Identifies inconsistency in naive zero mode counting with fluxes.

Proposes a modified supersymmetry variation to resolve the inconsistency.

Highlights the importance of back-reaction effects in flux compactifications.

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.