On determinant representation and integrability of Nekrasov functions

Abstract

Conformal blocks and their AGT relations to LMNS integrals and Nekrasov functions are best described by "conformal" (or Dotsenko-Fateev) matrix models, but in non-Gaussian Dijkgraaf-Vafa phases, where different eigenvalues are integrated along different contours. In such matrix models, the determinant representations and integrability are restored only after a peculiar Fourier transform in the numbers of integrations. From the point of view of conformal blocks, this is Fourier transform w.r.t. the intermediate dimensions and this explains why such quantities are expressed through tau-functions in Miwa parametrization, with external dimensions playing the role of multiplicities. In particular, these determinant representations provide solutions to the Painlevé VI equation. We also explain how this pattern looks in the pure gauge limit, which is described by the Brezin-Gross-Witten matrix model.

15 pages

References in corpus (22)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Asymptotically free N=2 theories and irregular conformal blocks
• Generation of Matrix Models by W-operators
• On KP-integrable Hurwitz functions
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• On the complete perturbative solution of one-matrix models
• Correlators in tensor models from character calculus
• Matrix Models for Random Partitions
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state
• Random Matrix Theory and the Sixth Painlevé Equation
• CFT approach to the $q$-Painlevé VI equation
• Character Expansions in Physics
• An Elliptic Garnier System from Interpolation
• Conformal blocks and Painlevé functions
• New results in $\mathcal{N}=2$ theories from non-perturbative string

Cited by in corpus (4)

• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• Elliptic $q,t$ matrix models
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• AGT correspondence, (q-)Painlevè equations and matrix models