Eric Bergshoeff

Supermembranes and Eleven-Dimensional Supergravity

Abstract We construct an action for a supermembrane propagating in d = 1 supergravity background. Using the constraints of d = 11 curved superspace, we show that the action is invariant under Siegel-type tranformations recently generalized by Hughes, Li and Polchinski. The transformation parameter is a world-volume scalar and d = 11 spacetime spinor. We also discuss the general problem of the coupling of n -dimensional extended objects to d -dimensional supergravity.

Super D-branes

We present a “kappa-symmetric” worldvolume action for all type II Dirichlet p-branes, 0≤p≤9, in a general type II supergravity background, including massive backgrounds in the IIA case. The p=9 case provides a supersymmetric D=10 Born-Infeld action. We emphasize the existence, in the “kappa-transformations”, of a projection operator, leading to a correct matching of Bose and Fermi degrees of freedom on the worldvolume. Some recent developments are sketched.

Duality in the type-II superstring effective action

Abstract We derive the T -duality transformations that transform a general d = 10 solution of the type-IIA string with one isometry to a solution of the type-IIB string with one isometry and vice versa. In contrast to other superstring theories, the T -duality transformations are not related to a non-compact symmetry of a d = 9 supergravity theory. We also discuss S -duality in d = 9 and d = 10 and the relationship with eleven-dimensional supergravity theory. We apply these dualities to generate new solutions of the type-11A and type-IIB superstrings and of eleven-dimensional supergravity.

Ten-dimensional Maxwell-Einstein supergravity, its currents, and the issue of its auxiliary fields

The d = 10, N = 1 Yang-Mills system is coupled to d = 10, N = 1 supergravity in a locally scale-invariant way. An analysis of the currents agrees with the Noether coupling results and reveals the existence of two ordinary axial and more low-dimension auxiliary fields. The coupling of the photon Aµ to antisymmetric tensors AµI½ is consistent because the Maxwell transformation I´Aµ = ∂µI› is extended to I´AµI½ = IoI›FµI½.

Properties of the Eleven-Dimensional Supermembrane Theory

We study in detail the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry becomes an N=8 world volume (rigid) supersymmetry in a “physicalâ€� gauge; we also present the field equations and transformation rules in a “lightconeâ€� gauge. We semiclassically quantize the closed torodial supermembrane on a spacetime (Minkowki)4 A— (flat 7-torus), and review some mathematical results that are relevant for path integral quantization.

T-duality and actions for non-BPS D-branes

We employ T-duality to restrict the tachyon dependence of effective actions for non-BPS D-branes. For the Born-Infeld part the criteria of T-duality and supersymmetry are satisfied by a simple extension of the D-brane Born-Infeld action.

κ-symmetry, supersymmetry and intersecting branes

We present a new form of κ-symmetry transformations for D-branes in which the dependence on the Born-Infeld field strength is expressed as a relative rotation on the left- and right-moving fields with opposite parameters. Then, we apply this result to investigate the supersymmetry preserved by certain intersecting brane configurations at arbitrary angles and with non-vanishing constant Born-Infeld fields. We also comment on the covariant quantization of the D-brane actions.

Extended Conformal Supergravity

Abstract We present the complete structure of extended conformal supergravity for N ⩽4. The relation with the graded algebra SU(2, 2| N ) and with the multiplet of currents is discussed. The N = 4 superconformal theory has a formulation with local SU(4)×U(1) and rigid SU(1, 1) invariance. We give the linearized invariant actions for all N . For N = 2 we exhibit the complete non-linear lagrangian.

The quartic effective action of the heterotic string and supersymmetry

We present the supersymmetric quartic effective action for the heterotic string which follows from the supersymmetrization of the Yang-Mills and Lorentz Chern-Simons forms. This includes all bosonic terms in the action, and all bosonic contributions to the supersymmetry transformation rules, thereby giving all terms to this order which are relevant for the study of compactification scenarios with unbroken supersymmetry.

N=2 supergravity in five dimensions revisited

We construct matter-coupled N = 2 supergravity in five dimensions, using the superconformal approach. For the matter sector we take an arbitrary number of vector, tensor and hypermultiplets. By allowing off-diagonal vector-tensor couplings we find more general results than currently known in the literature. Our results provide the appropriate starting point for a systematic search for BPS solutions, and for applications of M-theory compactifications on Calabi-Yau manifolds with fluxes.