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

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

Superparticle actions and gauge fixings

Recently, a covariant quantization for the superparticle has been performed. Here we show the complete gauge fixing procedure to obtain the correct BRST operator from the action proposed by one of us. This leads to a simpler form of this operator, revealing its structure. We also re-examine several previous attempts to perform a gauge fixing procedure of the Brink-Schwarz (BS) superparticle action. These all lead to a gauge-fixed action and a BRST operator which does not produce the correct physical spectrum. We clarify this issue by using the Batalin-Vilkovisky (BV) antibracket cohomology. The same gauge-fixed action with a different BRST operator is the basis for the quantization which gives the right number of physical states. From this BRST operator a classical action is reconstructed with an infinite number of classical fields and two infinite sets of symmetries which generalize the kappa symmetry of the BS action (the doubly infinite symmetric superparticle or DISP). By performing canonical transformations we bring the DISP action in a form which is close to the ES action. We comment about the differences between the two actions

Conjecture on Hidden Superconformal Symmetry of N=4 Supergravity

We argue that the observed UV finiteness of the 3-loop extended supergravities may be a manifestation of a hidden local superconformal symmetry of supergravity. We focus on the SU(2,2|4) dimensionless superconformal model. In Poincare gauge where the compensators are fixed to phi^2= 6 M_P^2 this model becomes a pure classical N=4 Einstein supergravity. We argue that in N=4 the higher-derivative superconformal invariants like phi^{-4}W^2 \bar W^2 and the consistent local anomaly delta (ln phi W^2) are not available. This conjecture on hidden local N=4 superconformal symmetry of Poincare supergravity may be supported by subsequent loop computations.Comment: 14 p A discussion of half-maximal D=6 superconformal models is adde

Brane plus Bulk Supersymmetry in Ten Dimensions

We discuss a generalized form of IIA/IIB supergravity depending on all R-R potentials C^(p) (p=0,1,...,9) as the effective field theory of Type IIA/IIB superstring theory. For the IIA case we explicitly break this R-R democracy to either p=5 which allows us to write a new bulk action that can be coupled to N=1 supersymmetric brane actions. The case of 8-branes is studied in detail using the new bulk & brane action. The supersymmetric negative tension branes without matter excitations can be viewed as orientifolds in the effective action. These D8-branes and O8-planes are fundamental in Type I' string theory. A BPS 8-brane solution is given which satisfies the jump conditions on the wall. As an application of our results we derive a quantization of the mass parameter and the cosmological constant in string units.Comment: 15 pages, proceedings of 37th Karpacz Winter School, feb 200