Dirac actions for D-branes on backgrounds with fluxes

The understanding of the fermionic sector of the world-volume 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 the absence of fluxes. A non-zero 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