Manin triples and $N=2$ superconformal field theory

TL;DR

This paper explores the connection between Manin triples and $N=2$ superconformal field theories, constructing a deformation with a continuously variable central charge, extending previous models like Kazama-Suzuki.

Contribution

It introduces a novel deformation of $N=2$ superconformal field theories associated with Manin triples, allowing for a continuous variation of the central charge.

Findings

Constructed a deformation with variable central charge.

Extended the class of $N=2$ superconformal theories.

Linked Manin triples to a broader family of models.

Abstract

This work was inspired by the article of Parkhomenko, who drew attention to the central role played in the work of Spindel, Sevrin, Troust and van Proyen, by Manin triples. These authors have shown how to associate to a Manin triple an $N=2$ superconformal field theory (the work of Kazama-Suzuki is a special case of their results). In this paper, we construct a deformation of their theory, with continuously varying central charge, analogous to the Fock representations of the Virasoro algebra with stress-energy tensor $-(\phi')^2/2+\alpha\phi''$.