On the supersymmetries of branes with fluxes

TL;DR

This paper explores the supersymmetry properties of D branes with fluxes, demonstrating the equivalence of Lagrangian and Hamiltonian approaches to the kappa-symmetry projector, which encodes preserved supersymmetries.

Contribution

It establishes the equivalence between the Lagrangian and Hamiltonian methods for constructing the kappa-symmetry projector in branes with fluxes.

Findings

The Lagrangian and Hamiltonian approaches to the kappa-symmetry projector are equivalent.

The projector depends on velocity and electric fields but not on conserved charges.

The paper clarifies the relation between different formalisms for supersymmetry analysis in branes.

Abstract

The Dirac-Born-Infled action that describes the dynamics of D branes also allows one to compute the supersymmetries they preserve using the Kappa-symmetry projector. The ''Lagrangian'' expression of this projector depends on the velocity and electric fields of the branes, but not on the corresponding conserved charges. One can also construct the projector in a ''Hamiltonian'' approach, by multiplying the conserved string, brane and momentum charges with the corresponding gamma matrix involutions, adding them to the mass of the brane multiplied by the unit matrix, and normalizing the resulting expression. We show that these two procedures are equivalent.