Elliptic Virasoro Conformal Blocks

Abstract

We study certain six dimensional theories arising on $(p,q)$ brane webs living on $\mathbb{R}\times S^1$. These brane webs are dual to toric elliptically fibered Calabi-Yau threefolds. The compactification of the space on which the brane web lives leads to a deformation of the partition functions equivalent to the elliptic deformation of the Ding-Iohara algebra. We compute the elliptic version Dotsenko-Fateev integrals and show that they reproduce the instanton counting of the six dimensional theory.

35 pages, references added

References in corpus (10)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Refined Topological Vertex
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Asymptotically free N=2 theories and irregular conformal blocks
• Notes on Ding-Iohara algebra and AGT conjecture
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
• Decomposing Nekrasov Decomposition
• ADE Little String Theory on a Riemann Surface (and Triality)
• Topological String Partition Functions as Equivariant Indices

Cited by in corpus (12)

• Ding-Iohara-Miki symmetry of network matrix models
• Explicit examples of DIM constraints for network matrix models
• Triality in Little String Theories
• On elementary proof of AGT relations from six dimensions
• Refined geometric transition and $qq$-characters
• Beyond Triality: Dual Quiver Gauge Theories and Little String Theories
• Macdonald topological vertices and brane condensates
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• A Macdonald refined topological vertex
• The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture