Wess-Zumino sigma models with non-Kahlerian geometry

Supersymmetry of the Wess-Zumino (N=1, D=4) multiplet allows field equations that determine a larger class of geometries than the familiar Kahler manifolds, in which covariantly holomorphic vectors rather than a scalar superpotential determine the forces. Indeed, relaxing the requirement that the field equations be derivable from an action leads to complex flat geometry. The Batalin-Vilkovisky formalism is used to show that if one requires that the field equations be derivable from an action, we once again recover the restriction to Kahler geometry, with forces derived from a scalar superpotential.Comment: 13 pages, Late

Hypermultiplets and hypercomplex geometry from 6 to 3 dimensions

The formulation of hypermultiplets that has been developed for 5-dimensional matter multiplets is by dimensional reductions translated into the appropriate spinor language for 6 and 4 dimensions. We also treat the theories without actions that have the geometrical structure of hypercomplex geometry. The latter is the generalization of hyper-Kaehler geometry that does not require a Hermitian metric and hence corresponds to field equations without action. The translation tables of this paper allow the direct application of superconformal tensor calculus for the hypermultiplets using the available Weyl multiplets in 6 and 4 dimensions. Furthermore, the hypermultiplets in 3 dimensions that result from reduction of vector multiplets in 4 dimensions are considered, leading to a superconformal formulation of the c-map and an expression for the main geometric quantities of the hyper-Kaehler manifolds in the image of this map.Comment: 18 pages; v2: several clarifications in text and formulae, version to appear in Class.Quantum Gravit

The identification of conformal hypercomplex and quaternionic manifolds

We review the map between hypercomplex manifolds that admit a closed homothetic Killing vector (i.e. `conformal hypercomplex' manifolds) and quaternionic manifolds of 1 dimension less. This map is related to a method for constructing supergravity theories using superconformal techniques. An explicit relation between the structure of these manifolds is presented, including curvatures and symmetries. An important role is played by `\xi transformations', relating connections on quaternionic manifolds, and a new type `\hat\xi transformations' relating complex structures on conformal hypercomplex manifolds. In this map, the subclass of conformal hyper-Kaehler manifolds is mapped to quaternionic-Kaehler manifolds.Comment: 22 pages, 2 figures, Contribution to the proceedings volume for the Conference "Symmetry in Geometry and Physics" in honour of Dmitri Alekseevsky, September 200

Pure de Sitter Supergravity

Using superconformal methods we derive an explicit de Sitter supergravity action invariant under spontaneously broken local ${\cal N}=1$ supersymmetry. The supergravity multiplet interacts with a nilpotent goldstino multiplet. We present a complete locally supersymmetric action including the graviton and the fermionic fields, gravitino and goldstino, no scalars. In the global limit when supergravity multiplet decouples, our action reproduces the Volkov-Akulov theory. In the unitary gauge where goldstino vanishes we recover pure supergravity with the positive cosmological constant. The classical equations of motion, with all fermions vanishing, have a maximally symmetric solution: de Sitter space.Comment: 22 pages, version to appear in PRD; v4: minor typos corrected; v5: correction of torsion lagrangian (2.2); v6: Minor error in Sec.4.3 corrected. This simplifies previous proof that any zero mode vanishes identicall

Effective supergravity descriptions of superstring cosmology

This text is a review of aspects of supergravity theories that are relevant in superstring cosmology. In particular, it considers the possibilities and restrictions for `uplifting terms', i.e. methods to produce de Sitter vacua. We concentrate on N=1 and N=2 supergravities, and the tools of superconformal methods, which clarify the structure of these theories. Cosmic strings and embeddings of target manifolds of supergravity theories in others are discussed in short at the end.Comment: 12 pages, contribution to the proceedings of the 2nd international conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelona, July 11-15, 2006, Journal of Physics

Conformal Theory of M2, D3, M5 and `D1+D5' Branes

The bosonic actions for M2, D3 and M5 branes in their own d-dimensional near-horizon background are given in a manifestly SO(p+1,2) x SO(d-p-1) invariant form (p=2,3,5). These symmetries result from a breakdown of ISO(d,2) (with d=10 for D3 and d=11 for M2 and M5) symmetry by the Wess-Zumino term and constraints. The new brane actions, reduce after gauge-fixing and solving constraints to (p+1) dimensional interacting field theories with a non-linearly realized SO(p+1,2) conformal invariance. We also present an interacting two-dimensional conformal field theory on a D-string in the near-horizon geometry of a D1+D5 configuration.Comment: 32 pages, two figures, Latex. A version to appear in JHEP. A comment is added on infinite dimensional Kac-Moody type symmetry of D1+D5 system observed by Brandt, Gomis, Sim'o