[Abstract unavailable

No abstract

We construct a new class of (p, q)-extended Poincaré supergravity theories in 2+1 dimensions as Chern-Simons theories of supersymmetry algebras with both central and automorphism charges. The new theories have the advantage that they are limits of corresponding (p, q) adS supergravity theories and, for not too large a value of N = p + q, that they have a natural formulation in terms of offshell superfields, in which context the distinction between theories having the same value of N but different (p, q) arises because of inequivalent conformal compensator superfields. We also show that, unlike previously constructed N-extended Poincaré supergravity theories, the new (2,0) theory admits conical spacetimes with Killing spinors. Many of our results on (2,0) Poincaré supergravity continue to apply in the presence of coupling to N=2 supersymmetric sigma-model matter.

Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fibre bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.

We study how to generate new Lie algebras G(N 0 , . . . , N p , . . . , N n ) from a given one G. The (order by order) method consists in expanding its Maurer-Cartan oneforms in powers of a real parameter λ which rescales the coordinates of the Lie (super)group G, g ip → λ p g ip , in a way subordinated to the splitting of G as a sum V 0 ⊕ · · · ⊕ V p ⊕ · · · ⊕ V n of vector subspaces. We also show that, under certain conditions, one of the obtained algebras may correspond to a generalizedİnönü-Wigner contraction in the sense of Weimar-Woods, but not in general. The method is used to derive the M-theory superalgebra, including its Lorentz part, from osp(1|32). It is also extended to include gauge free differential (super)algebras and Chern-Simons theories, and then applied to D = 3 CS supergravity.

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 spacetime 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.Comment: Latex file, 31 pgs. Version to appear in NP

We present dyonic multi-membrane solutions of the N=2 D=8 supergravity theory that serves as the effective field theory of the T 2 -compactified type II superstring theory. The 'electric' charge is fractional for generic asymptotic values of an axion field, as for D=4 dyons. These membrane solutions are supersymmetric, saturate a Bogomolnyi bound, fill out orbits of an Sl(2; Z) subgroup of the type II D=8 T-duality group, and are non-singular when considered as solutions of T 3 -compactified D=11 supergravity. On K 3 compactification to D=4, the conjectured type II/heterotic equivalence allows the Sl(2; Z) group to be reinterpreted as the S-duality group of the toroidally compactified heterotic string and the dyonic membranes wrapped around homology two-cycles of K 3 as S-duals of perturbative heterotic string states.

Abstract. This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two entries Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the rôle of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. Three-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-LambertGustavsson model. Because of this, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations (it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras.The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A 4 model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization.