An elliptic Virasoro symmetry in 6d

Abstract

We define an elliptic deformation of the Virasoro algebra. We argue that the $\mathbb{R}^4\times \mathbb{T}^2$ Nekrasov partition function reproduces the chiral blocks of this algebra. We support this proposal by showing that at special points in the moduli space the 6d Nekrasov partition function reduces to the partition function of a 4d vortex theory supported on $\mathbb{R}^2\times \mathbb{T}^2$, which is in turn captured by a free field correlator of vertex operators and screening charges of the elliptic Virasoro algebra.