Representations of p -brane topological charge algebras

D-branes have a world-volume U(1) gauge field A whose field strength F = dA gives rise to a Born-Infeld term in the D-brane action. Supersymmetry and kappa symmetry transformations of A are traditionally inferred by the requirement that the Born-Infeld term is consistent with both supersymmetry and kappa symmetry of the D-brane action. In this paper, we show that integrability of the assigned supersymmetry transformations leads to a extension of the standard supersymmetry algebra that includes a fermionic central charge. We construct a superspace one-form on an enlarged superspace related by a coset construction to this centrally extended algebra whose supersymmetry and kappa symmetry transformations are derived, rather than inferred. It is shown that under pullback, these transformations are of the form expected for the D-brane U(1) gauge field. We relate these results to manifestly supersymmetric approaches to construction of D-brane actions.Comment: 15 pages; new section and references adde

Section: Introductionmentioning

confidence: 99%

Coset construction of a D-brane gauge field

McArthur

2016

“…The difference is that we have systematically derived the algebra; in [12], the algebra is stated without derivation. The right hand sides of (5.11)-(5.14) also reproduce the Noether charges constructed in [28] (up to a different choice of normalization).…”

Section: The Case P =mentioning

confidence: 64%

p-Brane superalgebras via integrability

Grasso¹,

McArthur²

2018

It has long been appreciated that superalgebras with bosonic and fermionic generators additional to those in the super-Poincare algebra underlie p-brane and D-brane actions in superstring theory. These algebras have been revealed via "bottom up" approaches, involving consideration of Noether charges, and by "top down" approaches, involving the construction of manifestly supersymmetry invariant Wess-Zumino actions. In this paper, we give an alternative derivation of these algebras based on integrability of supersymmetry transformations assigned to fields in order to solve a cohomology problem related to the construction of Wess-Zumino terms for p-brane and D-brane actions. 1

“…With appropriate rescaling of generators, the general algebra given above incorporates, as special cases, all of the known algebras from p = 1 to p = 5, which are all separately displayed in [20] (which come from [13] and [17] for p = 1, [13] for p = 2 and p = 3, and have been derived for the cases p = 4 and p = 5 from an ansatz for Maurer-Cartan equations appearing in [17]). Additionally, taking into account notational differences, the right hand sides of our expressions (6.3) and (6.23) -where the constants are given by (5.11)-(5.13), (6.27), (6.28) and (6.41) -reproduces the p = 1 to p = 5 Noether charges constructed in [20] (up to a different choice of normalization). Previously, all of these results were determined on a case by case basis -here we have given a general expression applicable to any valid value of p.…”

Section: Computing δ ǫ a (P)mentioning

confidence: 99%

Deriving all p -brane superalgebras via integrability

Grasso

McArthur

2018

In previous work we demonstrated that the enlarged super-Poincare algebras which underlie p-brane and D-brane actions in superstring theory can be directly determined based on the integrability of supersymmetry transformations assigned to fields appearing in Wess-Zumino terms. In that work we derived p-brane superalgebras for p = 2 and 3. Here we extend our previous results and give a compact expression for superalgebras for all valid p.