From topological strings to minimal models

TL;DR

This paper constructs 4D and 5D instanton partition functions from topological string vertices and demonstrates how specific parameter choices yield Virasoro minimal model conformal blocks, linking topological strings to minimal models.

Contribution

It introduces a method to derive Virasoro minimal model conformal blocks from refined topological vertices through a specific parameter selection and gluing procedure.

Findings

Constructed 5D $U(2)$ quiver instanton partition functions from topological vertices.

Derived 4D instanton partition functions as limits of 5D results.

Identified parameter choices that produce Virasoro minimal model conformal blocks.

Abstract

We glue four refined topological vertices to obtain the building block of 5D $U(2)$ quiver instanton partition functions. We take the 4D limit of the result to obtain the building block of 4D instanton partition functions which, using the AGT correspondence, are identified with Virasoro conformal blocks. We show that there is a choice of the parameters of the topological vertices that we start with, as well as the parameters and the intermediate states involved in the gluing procedure, such that we obtain Virasoro minimal model conformal blocks.