J. M. Izquierdo

Superconformal mechanics, black holes, and nonlinear realizations

The OSp(2|2)-invariant planar dynamics of a D = 4 superparticle near the horizon of a large mass extreme black hole is described by an N = 2 superconformal mechanics, with the SO(2) charge being the superparticle’s angular momentum. The non-manifest superconformal invariance of the superpotential term is shown to lead to a shift in the SO(2) charge by the value of its coefficient, which we identify asthe orbital angular momentum. The full SU(1,1|2)-invariant dynamics is found from an extension to N = 4 superconformal mechanics.

The geometry of branes and extended superspaces

Abstract We argue that a description of supersymmetric extended objects from a unified geometric point of view requires an enlargement of superspace. To this aim we study in a systematic way how superspace groups and algebras arise from Grassmann spinors when these are assumed to be the only primary entities. In the process, we recover generalized space-time superalgebras and extensions of supersymmetry found earlier. The enlargement of ordinary superspace with new parameters gives rise to extended superspace groups, on which manifestly supersymmetric actions may be constructed for various types of p -branes, including D-branes (given by Chevalley-Eilenberg cocycles) with their Born-Infeld fields. This results in a field/extended superspace democracy for superbranes: all brane fields appear as pull-backs from a suitable target superspace. Our approach also clarifies some facts concerning the origin of the central charges for the different p -branes.

Extensions, expansions, Lie algebra cohomology and enlarged superspaces

After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.

On the higher-order generalizations of Poisson structures

The characterization of the Nambu - Poisson n-tensors as a subfamily of the generalized Poisson ones recently introduced (and here extended to the odd-order case) is discussed. The homology and cohomology complexes of both structures are compared, and some physical considerations are made.

Expansions of Algebras and Superalgebras and Some Applications

Abstract After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the İnönü–Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).

Cohomology of Filippov algebras and an analogue of Whitehead's lemma

We show that two cohomological properties of semisimple Lie algebras also hold for Filippov (n-Lie) algebras, namely, that semisimple n-Lie algebras do not admit non-trivial central extensions and that they are rigid i.e., cannot be deformed in Gerstenhaber sense. This result is the analogue of Whiteheads Lemma for Filippov algebras. A few comments about the n-Leibniz algebras case are made at the end.

Free differential algebras and generic 2D dilatonic (super)gravities

The field equations for both generic bosonic and generic locally supersymmetric 2D dilatonic gravity theories in the absence of matter are written as free differential algebras. This constitutes a generalization of the gauge theoretic formulation. Moreover, it is shown that the condition of free differential algebra can be used to obtain the equations in the locally supersymmetric case. Using this formulation, the general solution of the field equations is found in the language of differential forms. The relation with the ordinary formulation and the coupling to supersymmetric conformal matter are also studied.

Gravity, p -branes, and a spacetime counterpart of the Higgs effect

We point out that the worldvolume coordinate functions

Superalgebra cohomology, the geometry of extended superspaces and superbranes

{x}^{\ensuremath{\mu}}(\ensuremath{\xi})

Minimal D=4 supergravity from the superMaxwell algebra

of a p-brane, treated as an independent object interacting with dynamical gravity, are Goldstone fields for spacetime diffeomorphisms gauge symmetry. The presence of this gauge invariance is exhibited by its associated Noether identity, which expresses that the source equations follow from the gravitational equations. We discuss the spacetime counterpart of the Higgs effect and show that a p-brane does not carry any local degrees of freedom, extending early known general relativity features. Our considerations are also relevant for brane world scenarios.