Dirac Action on M5 and M2 Branes with Bulk Fluxes
  We derive an explicit form of the quadratic in fermions Dirac action on the M5 brane for an arbitrary on-shell background of 11D supergravity with non-vanishing fluxes and in presence of a chiral 2-form on M5. This action may be used to generalize the conditions for which the non-perturbative superpotential can be generated in M/string theory. We also derive the Dirac action with bulk fluxes on the M2 brane. 
Renata Kallosh and Dmitri Sorokin