Superconformal structures on generalized Calabi-Yau metric manifolds

TL;DR

This paper constructs superconformal structures on generalized Calabi-Yau metric manifolds, embedding N=2 superconformal vertex algebras into their chiral de Rham complexes, and explores related algebraic and geometric properties.

Contribution

It introduces a novel embedding of N=2 superconformal vertex algebras into the chiral de Rham complex of generalized Calabi-Yau manifolds, including flux and dilaton effects.

Findings

Embedded two commuting N=2 superconformal algebras in the chiral de Rham complex.

Defined BRST charges on generalized Kähler manifolds.

Connected classical identities to an infinite-dimensional Lie superalgebra.

Abstract

We construct an embedding of two commuting copies of the N=2 superconformal vertex algebra in the space of global sections of the twisted chiral-anti-chiral de Rham complex of a generalized Calabi-Yau metric manifold, including the case when there is a non-trivial H-flux and non-vanishing dilaton. The 4 corresponding BRST charges are well defined on any generalized Kahler manifold. This allows one to consider the half-twisted model defining thus the chiral de Rham complex of a generalized Kahler manifold. The classical limit of this result allows one to recover the celebrated generalized Kahler identities as the degree zero part of an infinite dimensional Lie superalgebra attached to any generalized Kahler manifold. As a byproduct of our study we investigate the properties of generalized Calabi-Yau metric manifolds in the Lie algebroid setting.