Instanton moduli spaces and $\mathscr W$-algebras

TL;DR

This paper explores the relationship between the intersection cohomology of framed Uhlenbeck spaces and the representation theory of $\,\mathscr{W}$-algebras, revealing new algebraic structures in geometric moduli spaces.

Contribution

It establishes a novel connection between the equivariant intersection cohomology of certain moduli spaces and the representation theory of $\,\mathscr{W}$-algebras.

Findings

Description of the equivariant intersection cohomology of framed Uhlenbeck spaces.

Identification of structures such as the Poincaré pairing within this context.

Representation-theoretic interpretation of geometric structures.

Abstract

We describe the (equivariant) intersection cohomology of certain moduli spaces ("framed Uhlenbeck spaces") together with some structures on them (such as e.g.\ the Poincar\'e pairing) in terms of representation theory of some vertex operator algebras ("$\mathscr W$-algebras").