Holomorphic blocks and the 5d AGT correspondence

TL;DR

This paper reviews the holomorphic block factorization of supersymmetric partition functions and interprets 3d and 5d partition functions as correlation functions related to a deformed Virasoro algebra.

Contribution

It introduces a novel interpretation of higher-dimensional partition functions as correlation functions with a deformed Virasoro symmetry.

Findings

Holomorphic block factorization applies to supersymmetric theories on compact manifolds.

3d and 5d partition functions can be viewed as correlation functions.

Partition functions relate to a deformation of the Virasoro algebra.

Abstract

We review the holomorphic block factorisation of partition functions of supersymmetric theories on compact manifolds in various dimensions. We then show how to interpret 3d and 5d partition functions as correlation functions with underlying symmetry given by a deformation of the Virasoro algebra.