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

TL;DR

This paper derives a Dirac equation for the supermembrane's fermionic field in a D=11 supergravity background with fluxes, using a gauge-fixed component approach to the supergravity-supermembrane system.

Contribution

It provides a simplified derivation of the supermembrane fermionic equation within a complete gauge-fixed framework, applicable to complex systems like M5-branes and D-branes.

Findings

Derived the Dirac equation for supermembrane fermions in flux backgrounds.

Analyzed the linear contributions of supermembrane fermions to the system's equations.

Proposed applicability to more complex dynamical brane systems.

Abstract

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.