Manin pairs and topological field theory

TL;DR

This paper explores the connection between an extended superconformal algebra, Manin pairs, and topological field theories, demonstrating their interplay and applications in topological gravity and specific model equivalences.

Contribution

It establishes a link between Kazama's extended N=2 superconformal algebra and Manin pairs, and shows how to couple these symmetries to topological gravity, with applications to specific models.

Findings

Relation between chiral algebra actions and Manin pairs

Coupling of topological conformal field theories with topological gravity

Equivalence of SL(2)/SL(2) and deformed SL(2)/SO(2) models

Abstract

Kazama has described an extension of the N=2 superconformal algebra in which the operator product of G^- with itself is singular. In this paper, we relate actions of this chiral algebra to Drinfeld's theory of Manin pairs, or equivalently, quasi-Lie bialgebras. We also show how to couple topological conformal field theories with this symmetry to topological gravity. As an application, we demonstrate the equivalence of the SL(2)/SL(2) model to a deformed SL(2)/SO(2) model tensored with a free field theory. (Revisions correct some minor errors.)