q-Vertex Operator from 5D Nekrasov Function

TL;DR

This paper derives a q-deformed vertex operator from the 5D Nekrasov function, establishing a link between 2D conformal blocks and 5D gauge theory partition functions within the AGT framework.

Contribution

It introduces a q-deformation of the four-point Virasoro block using the Coulomb gas representation derived from the 5D Nekrasov function, providing a new explicit expression for the q-vertex operator.

Findings

Derived a q-deformed four-point block from 5D Nekrasov function

Obtained an explicit expression for the q-vertex operator

Identified modifications needed for vertex operator insertion points

Abstract

The five dimensional AGT correspondence implies the connection between the q-deformed Virasoro block and the 5d Nekrasov partition function. In this paper, we determine a q-deformation of the four-point block in the Coulomb gas representation from the 5d Nekrasov function, and obtain an expression of the q-deformed vertex operator. If we use only one kind of the q-vertex operators, one of the insertion points of them must be modified in order to hold the 2d/5d correspondence.