Painlevé/CFT correspondence on a torus

Abstract

This note details the relationship between the isomonodromic tau-function and conformal blocks, on a torus with one simple pole. It is based on the author's talk at ICMP 2021.

References in corpus (17)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Application of the $\tau$-Function Theory of Painlevé Equations to Random Matrices: PIV, PII and the GUE
• On AGT conjecture
• How instanton combinatorics solves Painlevé VI, V and III's
• Conformal field theory of Painlevé VI
• On Painlevé/gauge theory correspondence
• Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions
• On some Hamiltonian properties of the isomonodromic tau functions
• Tau functions as Widom constants
• $\mathcal{N}=2^{\ast }$ gauge theory, free fermions on the torus and Painlevé VI
• Pure $SU(2)$ gauge theory partition function and generalized Bessel kernel
• Quantum spectral problems and isomonodromic deformations
• Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions
• On solutions of the Fuji-Suzuki-Tsuda system
• The $\tau$-function of the Ablowitz-Segur family of solutions to Painlevé II as a Widom constant
• Fredholm determinant representation of the Painlevé II $\tau$-function
• The Malgrange Form and Fredholm Determinants