Fermion Zero Modes in the Presence of Fluxes and a Non-perturbative   Superpotential
  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. 
Dieter Lust, Susanne Reffert, Waldemar Schulgin, Prasanta Tripathy