Topological Extensions of Noether Charge Algebras carried by D-p-branes

TL;DR

This paper derives the extended supersymmetry algebra for D-branes in type IIA string theory, revealing topological and gauge-related charges, including monopoles, and introduces generalized gamma-matrix identities.

Contribution

It provides a general derivation of how gauge fields on branes modify Noether charge algebras, extending previous results to D-branes and including new algebraic identities.

Findings

Extended algebra includes topological and gauge field charges.

D-2-brane algebra can contain Dirac monopole charge.

Derived generalized gamma-matrix identities for IIA supersymmetry.

Abstract

We derive the fully extended supersymmetry algebra carried by D-branes in a massless type IIA superspace vacuum. We find that the extended algebra contains not only topological charges that probe the presence of compact spacetime dimensions but also pieces that measure non-trivial configurations of the gauge field on the worldvolume of the brane. Furthermore there are terms that measure the coupling of the non-triviality of the worldvolume regarded as a U(1)-bundle of the gauge field to possible compact spacetime dimensions. In particular, the extended algebra carried by the D-2-brane can contain the charge of a Dirac monopole of the gauge field. In the course of this work we derive a set of generalized Gamma-matrix identities that include the ones presently known for the IIA case. In the first part of the paper we give an introduction to the basic notions of Noether current algebras and charge algebras; furthermore we find a Theorem that describes in a general context how the presence of a gauge field on the worldvolume of an embedded object transforming under the symmetry group on the target space alters the algebra of the Noether charges, which otherwise would be the same as the algebra of the symmetry group. This is a phenomenon recently found by Sorokin and Townsend in the case of the M-5-brane, but here we show that it holds quite generally, and in particular also in the case of D-branes.