Dirac actions for D-branes on backgrounds with fluxes
  The understanding of the fermionic sector of the worldvolume D-brane dynamics on a general background with fluxes is crucial in several branches of string theory, like for example the study of nonperturbative effects or the construction of realistic models living on D-branes. In this paper we derive a new simple Dirac-like form for the bilinear fermionic action for any Dp-brane in any supergravity background, which generalizes the usual Dirac action valid in absence of fluxes. A nonzero world-volume field strength deforms the usual Dirac operator in the action to a generalized non-canonical one. We show how the canonical form can be re-established by a redefinition of the world-volume geometry. 
Luca Martucci, Jan Rosseel, Dieter Van den Bleeken and Antoine Van   Proeyen