Topological extensions of Noether charge algebras carried by Dp-branes

Abstract

We derive the fully extended supersymmetry algebra carried by Dbranes 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 nontriviality 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.

Expansions of Algebras and Superalgebras and Some Applications

“…The worldvolume BI fields, as the spacetime A 3 field of CJS supergravity above, become composite fields. Moreover, a Chevalley-Eilenberg Lie algebra cohomology analysis [57,12,58] of the Wess-Zumino terms of many different superbrane actions determines the possible ones and how the ordinary supersymme-try algebra has to be extended (see also [56,59]). This again suggests an enlarged superspace variables/worldvolume fields correspondence.…”

Superalgebras from D-brane actions

“…The equation (49) has no solution if A is defined as a superspace form (the nontriviality of H prevents such a solution); therefore A must be a new degree of freedom defined on the worldvolume. The algebra of conserved charges of the D-brane action contains an anomalous term due to the transformation properties of the BI gauge field [6,7]. Let (P M , P i ) denote the momenta conjugate to (Z M , A i ).…”

“…This leads to constraints on the conjugate momenta P i [7]. Firstly, since ∂L ∂(∂ 0 A 0 ) = 0, there is the primary constraint:…”

“…As a result, when the topology of the background superspace is nontrivial, the Noether charge algebra can be extended by a topological "anomalous term" [5]. For branes with worldvolume gauge fields, there is a second modification to the algebra that results from the transformation properties of the gauge field [6,7]. For D-branes, this modification is due to the presence of the BI (Born-Infeld) worldvolume gauge field.…”

“…For D-branes, this modification is due to the presence of the BI (Born-Infeld) worldvolume gauge field. Terms of the D-brane Noether charge algebra associated with bosonic topology were explicitly found for the type IIA cases [7]. One must necessarily solve a series of descent equations to find the anomalous terms.…”