A PBW commutator lemma for U_q[gl(m|n)]

We present and prove in detail a Poincare--Birkhoff--Witt commutator lemma for the quantum superalgebra U_q[gl(m|n)].Comment: 16 pages, no figure

Tensor supermultiplets and toric quaternion-Kahler geometry

We review the relation between 4n-dimensional quaternion-Kahler metrics with n+1 abelian isometries and superconformal theories of n+1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kahler metrics with three abelian isometries in terms of a single function obeying a set of linear second-order partial differential equations.Comment: 8 pages, Contribution to the proceedings of the RTN ForcesUniverse Network Workshop, Napoli, October 9th - 13th, 200

Open and Closed Supermembranes with Winding

Motivated by manifest Lorentz symmetry and a well-defined large-N limit prescription, we study the supersymmetric quantum mechanics proposed as a model for the collective dynamics of D0-branes from the point of view of the 11-dimensional supermembrane. We argue that the continuity of the spectrum persists irrespective of the presence of winding around compact target-space directions and discuss the central charges in the superalgebra arising from winding membrane configurations. Along the way we comment on the structure of open supermembranes.Comment: Contribution to the proc. Strings '97, 10 pages, LaTeX, uses espcrc

When do finite sample effects significantly affect entropy estimates ?

An expression is proposed for determining the error caused on entropy estimates by finite sample effects. This expression is based on the Ansatz that the ranked distribution of probabilities tends to follow an empirical Zipf law.Comment: 10 pages, 2 figure

Maximal Supergravity from IIB Flux Compactifications

Using a recently proposed group-theoretical approach, we explore novel gaugings of maximal supergravity in four dimensions with gauge group embeddings that can be generated by fluxes of IIB string theory. The corresponding potentials are positive without stationary points. Some allow domain wall solutions which can be elevated to ten dimensions. Appropriate truncations describe type-IIB flux compactifications on T^6 orientifolds leading to non-maximal, four-dimensional, supergravities.Comment: 13 pages, LaTeX2e, references added, version to appear in PL

Special geometry and symplectic transformations

Special Kahler manifolds are defined by coupling of vector multiplets to $N=2$ supergravity. The coupling in rigid supersymmetry exhibits similar features. These models contain $n$ vectors in rigid supersymmetry and $n+1$ in supergravity, and $n$ complex scalars. Apart from exceptional cases they are defined by a holomorphic function of the scalars. For supergravity this function is homogeneous of second degree in an $(n+1)$-dimensional projective space. Another formulation exists which does not start from this function, but from a symplectic $(2n)$- or $(2n+2)$-dimensional complex space. Symplectic transformations lead either to isometries on the manifold or to symplectic reparametrizations. Finally we touch on the connection with special quaternionic and very special real manifolds, and the classification of homogeneous special manifolds.Comment: 11 pages, latex using espcrc2, no figures. Some factors and minor corrections. Version to be published in the proceedings of the Spring workshop on String theory, Trieste, April 199

The maximal D=7 supergravities

The general seven-dimensional maximal supergravity is presented. Its universal Lagrangian is described in terms of an embedding tensor which can be characterized group-theoretically. The theory generically combines vector, two-form and three-form tensor fields that transform into each other under an intricate set of nonabelian gauge transformations. The embedding tensor encodes the proper distribution of the degrees of freedom among these fields. In addition to the kinetic terms the vector and tensor fields contribute to the Lagrangian with a unique gauge invariant Chern-Simons term. This new formulation encompasses all possible gaugings. Examples include the sphere reductions of M theory and of the type IIA/IIB theories with gauge groups SO(5), CSO(4,1), and SO(4), respectively.Comment: 42 page

Generalized gaugings and the field-antifield formalism

We discuss the algebra of general gauge theories that are described by the embedding tensor formalism. We compare the gauge transformations dependent and independent of an invariant action, and argue that the generic transformations lead to an infinitely reducible algebra. We connect the embedding tensor formalism to the field-antifield (or Batalin-Vilkovisky) formalism, which is the most general formulation known for general gauge theories and their quantization. The structure equations of the embedding tensor formalism are included in the master equation of the field-antifield formalism.Comment: 42 pages; v2: some clarifications and 1 reference added; version to be published in JHE