Chiral equivariant cohomology of a point: a first look

TL;DR

This paper explores the structure of chiral equivariant cohomology for a point under G=SU(2), revealing its potential to distinguish manifolds beyond classical invariants.

Contribution

It provides initial insights into the structure of chiral equivariant cohomology for a point, a largely unexplored conformal vertex algebra.

Findings

Chiral equivariant cohomology generalizes classical equivariant cohomology.

For G=SU(2), the cohomology forms a complex conformal vertex algebra.

The paper offers a first look into the structure of this algebra.

Abstract

The chiral equivariant cohomology contains and generalizes the classical equivariant cohomology of a manifold M with an action of a compact Lie group G. For any simple G, there exist compact manifolds with the same classical equivariant cohomology, which can be distinguished by this invariant. When M is a point, this cohomology is an interesting conformal vertex algebra whose structure is still mysterious. In this paper, we scratch the surface of this object in the case G=SU(2).