Conformal covariance in 2d conformal and integrable models, in W-algebras and in their supersymmetric extensions

Abstract

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.

Proceedings of the workshop "Supersymmetries and Quantum Symmetries" (SQS'99, Dubna, July 1999)