Elliptic Virasoro Conformal Blocks
Amer Iqbal, Can Kozcaz, Shing-Tung Yau

TL;DR
This paper explores elliptic Virasoro conformal blocks by connecting six-dimensional brane web theories with elliptic deformations of algebraic structures, providing new computational tools for instanton counting.
Contribution
It introduces elliptic deformations of Ding-Iohara algebra and computes elliptic Dotsenko-Fateev integrals matching six-dimensional instanton partition functions.
Findings
Elliptic deformation of Ding-Iohara algebra derived.
Elliptic Dotsenko-Fateev integrals reproduce 6D instanton counting.
Established duality between brane webs and elliptic algebra structures.
Abstract
We study certain six dimensional theories arising on brane webs living on . 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.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory
