Dirac equation for the supermembrane in a background with fluxes from a component description of the D=11 supergravity-supermembrane interacting system

We present a simple derivation of the 'Dirac' equation for the supermembrane fermionic field in a D=11 supergravity background with fluxes by using a complete but gauge-fixed description of the supergravity-supermembrane interacting system previously developed. We also discuss the contributions linear in the supermembrane fermions -the Goldstone fields for the local supersymmetry spontaneously broken by the superbrane- to the field equations of the supergravity-supermembrane interacting system. The approach could also be applied to more complicated dynamical systems such as those involving the M5-brane and the D=10 Dirichlet branes.