An elliptic Virasoro symmetry in 6d

TL;DR

This paper introduces an elliptic deformation of the Virasoro algebra and links it to 6d Nekrasov partition functions, revealing new algebraic structures underlying 6d supersymmetric theories.

Contribution

It defines an elliptic Virasoro algebra and demonstrates its relation to 6d Nekrasov partition functions and 4d vortex theories, establishing a novel algebraic framework.

Findings

The elliptic Virasoro algebra reproduces 6d Nekrasov partition functions.

Special moduli points reduce 6d to 4d vortex partition functions.

The algebra's correlators match free field vertex operator computations.

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.