d=2, N=2 Superconformally Covariant Operators and Super W-Algebras

We construct and classify superconformally covariant differential operators defined on N=2 super Riemann surfaces. By contrast to the N=1 theory, these operators give rise to partial rather than ordinary differential equations which leads to novel features for their matrix representation. The latter is applied to the derivation of N=2 super W-algebras in terms of N=2 superfields.Comment: 29 pages, LaTe

Formalisme de Dirac et surprises mathematiques en mecanique quantique

Differents formalismes sont utilises en mecanique quantique pour la description des etats et des observables : la mecanique ondulatoire, la mecanique matricielle et le formalisme invariant. Nous discutons les problemes et inconvenients du formalisme invariant ainsi que ceux de la notation des bras et kets introduite par Dirac dans ce contexte. Nous indiquons comment tous les problemes peuvent etre resolus ou du moins evites. Une serie d'exemples illustre les points souleves et montre comment l'insouciance mathematique peut aisement conduire a des contradictions mathematiques surprenantes.Comment: 40 pages, French version of the preprint LYCEN 9960

Non-standard matrix formats of Lie superalgebras

The standard format of matrices belonging to Lie superalgebras consists of partitioning the matrices into even and odd blocks. In this paper, we study other possible matrix formats and in particular the so-called diagonal format which naturally occurs in various applications, e.g. in superconformal field theory, superintegrable models, for super W-algebras and quantum supergroups

Vector supersymmetry in topological field theories

We present a simple derivation of vector supersymmetry transformations for topological field theories of Schwarz- and Witten-type. Our method is similar to the derivation of BRST-transformations from the so-called horizontality conditions or Russian formulae. We show that this procedure reproduces in a concise way the known vector supersymmetry transformations of various topological models and we use it to obtain some new transformations of this type for 4d topological YM-theories in different gauges.Comment: 19 page

Non-Hermitian Hamiltonians and supersymmetric quantum mechanics

Théori

Interacting six-dimensional topological field theories

We study the gauge-fixing and symmetries (BRST-invariance and vector supersymmetry) of various six-dimensional topological models involving Abelian or non-Abelian 2-form potentials.Comment: 11 page

Contributions of M. Daoud, F. Gieres and M. Kibler to the "Concise Encyclopedia of Supersymmetry"

Théori

On the symmetries of BF models and their relation with gravity

The perturbative finiteness of various topological models (e.g. BF models) has its origin in an extra symmetry of the gauge-fixed action, the so-called vector supersymmetry. Since an invariance of this type also exists for gravity and since gravity is closely related to certain BF models, vector supersymmetry should also be useful for tackling various aspects of quantum gravity. With this motivation and goal in mind, we first extend vector supersymmetry of BF models to generic manifolds by incorporating it into the BRST symmetry within the Batalin-Vilkovisky framework. Thereafter, we address the relationship between gravity and BF models, in particular for three-dimensional space-time.Comment: 29 page

Are N=1 and N=2 supersymmetric quantum mechanics equivalent?

After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.Comment: 15 page

On the holomorphic factorization for superconformal fields

For a generic value of the central charge, we prove the holomorphic factorization of partition functions for free superconformal fields which are defined on a compact Riemann surface without boundary. The partition functions are viewed as functionals of the Beltrami coefficients and their fermionic partners which variables parametrize superconformal classes of metrics.Comment: 5 pages, LATEX, MPI-Ph/92-7