On new exact conformal blocks and Nekrasov functions

Abstract

Recently, an intriguing family of the one-point toric conformal blocks AGT related to the $\mathcal{N}=2^{\ast }SU(2)$ Nekrasov functions was discovered by M. Beccaria and G. Macorini. Members of the family are distinguished by having only finite amount of poles as functions of the intermediate dimension/v.e.v. in gauge theory. Another remarkable property is that these conformal blocks/Nekrasov functions can be found in closed form to all orders in the coupling expansion. In the present paper we use Zamolodchikov's recurrence equation to systematically account for these exceptional conformal blocks. We conjecture that the family is infinite-dimensional and describe the corresponding parameter set. We further apply the developed technique to demonstrate that the four-point spheric conformal blocks feature analogous exact expressions. We also study the modular transformations of the finite-pole blocks.

Version 2: significantly revised and extended to include spheric blocks and modular transformations, 27 pages

References in corpus (8)

• Seiberg-Witten Theory and Random Partitions
• Liouville theory with a central charge less than one
• Seiberg-Witten prepotential from instanton counting
• S-duality as a beta-deformed Fourier transform
• Modular anomaly equations in N=2* theories and their large-N limit
• On modular transformations of non-degenerate toric conformal blocks
• From Liouville Theory to the Quantum Geometry of Riemann Surfaces
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory

Cited by in corpus (4)

• Modular crossings, OPE coefficients and black holes
• A slow review of the AGT correspondence
• Virasoro blocks and quasimodular forms
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours