Coset construction of a D-brane gauge field

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

p-brane superalgebras via integrability

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.Comment: 22 pages, typo corrected, reference adde

Self-dual supersymmetric nonlinear sigma models

In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models with four-dimensional target spaces may be realised in term of CCL (chiral and complex linear) dynamical variables which consist of a chiral scalar, a complex linear scalar and their conjugate superfields. Here we introduce CCL sigma models that are invariant under U(1) "duality rotations" exchanging the dynamical variables and their equations of motion. The Lagrangians of such sigma models prove to obey a partial differential equation that is analogous to the self-duality equation obeyed by U(1) duality invariant models for nonlinear electrodynamics. These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one. Any CCL sigma model possesses a dual formulation given in terms of two chiral multiplets. The U(1) duality invariance of the CCL sigma model proves to be equivalent, in the dual chiral formulation, to a manifest U(1) invariance rotating the two chiral scalars. Since the target space has a holomorphic Killing vector, the sigma model possesses a third formulation realised in terms of a chiral multiplet and a tensor multiplet. The family of U(1) duality invariant CCL sigma models includes a subset of N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds with a non-zero Killing vector field. In the case that the Killing vector field is triholomorphic, the sigma model admits a dual formulation in terms of a self-interacting off-shell N=2 tensor multiplet. We also identify a subset of CCL sigma models which are in a one-to-one correspondence with the U(1) duality invariant models for nonlinear electrodynamics. The target space isometry group for these sigma models contains a subgroup U(1) x U(1).Comment: 22 page

Deriving all p-brane superalgebras via integrability

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.Comment: 26 pages, table added, typos corrected, a few remarks added for clarificatio

A supersymmetric nonlinear sigma model analogue of the ModMax theory

A decade ago, it was shown that associated with any model for $\mathsf{U}(1)$ duality-invariant nonlinear electrodynamics there is a unique $\mathsf{U}(1)$ duality-invariant supersymmetric nonlinear sigma model formulated in terms of chiral and complex linear superfields. Here we study the ${\cal N}=1$ superconformal $\sigma$-model analogue of the conformal duality-invariant electrodynamics known as the ModMax theory. We derive its dual formulation in terms of chiral superfields and show that the target space is a K\"ahler cone with $\mathsf{U}(1)\times \mathsf{U}(1)$ isometry group.Comment: 8 page