q-Painleve equation from Virasoro constraints

Abstract

The q-Painleve equation, satisfied by the Fourier transform of the q-Virasoro conformal blocks at c=1, is interpreted as a reformulation of the string equation and two other Virasoro constraints in the $5d$ Dotsenko-Fateev matrix model.

6 pages

References in corpus (10)

• 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
• Instantons and Merons in Matrix Models
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Symplectic invariants, Virasoro constraints and Givental decomposition
• Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state
• On determinant representation and integrability of Nekrasov functions
• CFT approach to the $q$-Painlevé VI equation
• Conformal blocks and Painlevé functions

Cited by in corpus (10)

• Cluster integrable systems, q-Painleve equations and their quantization
• A slow review of the AGT correspondence
• Argyres-Douglas theories, Painlevé II and quantum mechanics
• $\mathcal{N}=2^{\ast }$ gauge theory, free fermions on the torus and Painlevé VI
• BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations
• Orthogonal Polynomials in Mathematical Physics
• Elliptic $q,t$ matrix models
• Discrete Painleve equation, Miwa variables, and string equation in 5d matrix models
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• AGT correspondence, (q-)Painlevè equations and matrix models