The supersymmetric tensor hierarchy of N=1,d=4 supergravity

In this paper we construct the supersymmetric tensor hierarchy of N=1, d=4 supergravity. We find some differences with the general bosonic construction of 4-dimensional gauged supergravities. The global symmetry group of N=1,d=4 supergravity consists of three factors: the scalar manifold isometry group, the invariance group of the complex vector kinetic matrix and the U(1) R-symmetry group. In contrast to (half)-maximal supergravities, the latter two symmetries are not embedded into the isometry group of the scalar manifold. We identify some components of the embedding tensor with Fayet-Iliopoulos terms and we find that supersymmetry implies that the inclusion of R-symmetry as a factor of the global symmetry group requires a non-trivial extension of the standard p-form hierarchy. This extension involves additional 3- and 4-forms. One additional 3-form is dual to the superpotential (seen as a deformation of the simplest theory). We study the closure of the supersymmetry algebra on all the bosonic p-form fields of the hierarchy up to duality relations. In order to close the supersymmetry algebra without the use of duality relations one must construct the hierarchy in terms of supermultiplets. Such a construction requires fermionic duality relations among the hierarchy's fermions and these turn out to be local.Comment: Latex2e, 42 pages, no figures Improved version to be published in JEH

Lectures on Gauged Supergravity and Flux Compactifications

The low-energy effective theories describing string compactifications in the presence of fluxes are so-called gauged supergravities: deformations of the standard abelian supergravity theories. The deformation parameters can be identified with the various possible (geometric and non-geometric) flux components. In these lecture notes we review the construction of gauged supergravities in a manifestly duality covariant way and illustrate the construction in several examples.Comment: 48 pages, lectures given at the RTN Winter School on Strings, Supergravity and Gauge Theories, CERN, January 200

Lectures on Nongeometric Flux Compactifications

These notes present a pedagogical review of nongeometric flux compactifications. We begin by reviewing well-known geometric flux compactifications in Type II string theory, and argue that one must include nongeometric "fluxes" in order to have a superpotential which is invariant under T-duality. Additionally, we discuss some elementary aspects of the worldsheet description of nongeometric backgrounds. This review is based on lectures given at the 2007 RTN Winter School at CERN.Comment: 31 pages, JHEP

The maximal D=5 supergravities

The general Lagrangian for maximal supergravity in five spacetime dimensions is presented with vector potentials in the 27 and tensor fields in the 27 representation of E_6_(_6_). This novel tensor-vector system is subject to an intricate set of gauge transformations, describing 3(27-t) massless helicity degrees of freedom for the vector fields and 3t massive spin degrees of freedom for the tensor fields, where the (even) value of t depends on the gauging. The kinetic term of the tensor fields is accompanied by a unique Chern-Simons coupling which involves both vector and tensor fields. The Lagrangians are completely encoded in terms of the embedding tensor which defines the E_6_(_6_) subgroup that is gauged by the vectors. The embedding tensor is subject to two constraints which ensure the consistency of the combined vector-tensor gauge transformations and the supersymmetry of the full Lagrangian. This new formulation encompasses all possible gaugings. (orig.)Available from TIB Hannover: RA 2999(04-245) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman