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.

v1: 20 pages + appendix; v2: one appendix added, references added, typos corrected, notation improved, published version

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• Universal Features of BPS Strings in Six-dimensional SCFTs
• Quiver elliptic W-algebras
• A slow review of the AGT correspondence
• Triality in Little String Theories
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Refined geometric transition and $qq$-characters
• Beyond Triality: Dual Quiver Gauge Theories and Little String Theories
• Intersecting Defects and Supergroup Gauge Theory
• 3d Expansions of 5d Instanton Partition Functions
• Macdonald topological vertices and brane condensates
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• An Elliptic Vertex of Awata-Feigin-Shiraishi type for M-strings
• On complete solution of the quantum Dell system
• An elliptic topological vertex
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Deconstructing Defects
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• MacMahon KZ equation for Ding-Iohara-Miki algebra
• Quasi-Hopf twist and elliptic Nekrasov factor
• Elliptic deformation of ${\mathcal{W}}_N$-algebras
• Symmetry structure of the interactions in near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• On refined Chern-Simons and refined ABJ matrix models
• Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations