221 research outputs found
Maurer-Cartan forms and equations for two-dimensional superdiffeomorphisms
We present explicit expressions for the Maurer-Cartan forms of the
superdiffeomorphism group associated to a super Riemann surface. As an
application to superconformal field theory, we use these forms to evaluate the
effective action for the factorized superdiffeomorphism anomaly.Comment: (LATEX, 8 pages), MPI-Ph/92-4
About Symmetries in Physics
The goal of this introduction to symmetries is to present some general ideas,
to outline the fundamental concepts and results of the subject and to situate a
bit the following lectures of this school. [These notes represent the write-up
of a lecture presented at the fifth ``Seminaire Rhodanien de Physique: Sur les
Symetries en Physique" held at Dolomieu (France), 17-21 March 1997. Up to the
appendix and the graphics, it is to be published in "Symmetries in Physics",
F.Gieres, M.Kibler,C.Lucchesi and O.Piguet, eds. (Editions Frontieres, 1998).]Comment: Latex, 42 pages, 4 figure
Conformal covariance in 2d conformal and integrable models, in W-algebras and in their supersymmetric extensions
Conformal symmetry underlies the mathematical description of various
two-dimensional integrable models (e.g. for their Lax representation, Poisson
algebra, zero curvature representation,...) or of conformal models (for the
anomalous Ward identities, operator product expansion, Krichever-Novikov
algebra,...) and of W-algebras. Here, we review the construction of conformally
covariant differential operators which allow to render the conformal covariance
manifest. The N=1 and N=2 supersymmetric generalizations of these results are
also indicated and it is shown that they involve nonstandard matrix formats of
Lie superalgebras.Comment: Proceedings of the workshop "Supersymmetries and Quantum Symmetries"
(SQS'99, Dubna, July 1999
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
Superconformally covariant operators and super W algebras
We study superdifferential operators of order which are covariant with
respect to superconformal changes of coordinates on a compact super Riemann
surface. We show that all such operators arise from super M\"obius covariant
ones. A canonical matrix representation is presented and applications to
classical super W algebras are discussed.Comment: 23 pages, LATEX, MPI-Ph/92-66 and KA-THEP-7/9
Classical and super W-algebras from a zero-curvature condition
Starting from superdifferential operators in an superfield formulation,
we present a systematic prescription for the derivation of classical and
super W-algebras by imposing a zero-curvature condition on the connection
of the corresponding first order system. We illustrate the procedure on the
first non-trivial example (beyond the superconformal algebra) and also
comment on the relation with the Gelfand-Dickey construction of -algebras.Comment: 18 pages, tex, LMU-TPW 93-0
Relating Weyl and diffeomorphism anomalies on super Riemann surfaces
Starting from the Wess-Zumino action associated to the super Weyl anomaly, we
determine the local counterterm which allows to pass from this anomaly to the
chirally split superdiffeomorphism anomaly (as defined on a compact super
Riemann surface without boundary). The counterterm involves the graded
extension of the Verlinde functional and the results can be applied to the
study of holomorphic factorization of partition functions in superconformal
field theory.Comment: (LATEX, 18 pages), MPI-Ph/92-38, LPTB 92-
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
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
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