O. Lisovyy

Conformal field theory of Painlevé VI

A bstractGeneric Painlevé VI tau function τ (t) can be interpreted as four-point correlator of primary fields of arbitrary dimensions in 2D CFT with cu2009=u20091. Using AGT combinatorial representation of conformal blocks and determining the corresponding structure constants, we obtain full and completely explicit expansion of τ (t) near the singular points. After a check of this expansion, we discuss examples of conformal blocks arising from Riccati, Picard, Chazy and algebraic solutions of Painlevé VI.

Isomonodromic tau-functions from Liouville conformal blocks

The goal of this note is to show that the Riemann–Hilbert problem to find multivalued analytic functions with

How instanton combinatorics solves Painlevé VI, V and IIIs

{{rm SL}(2,mathbb{C})}

Connection Problem for the Sine-Gordon/Painlevé III Tau Function and Irregular Conformal Blocks

SL(2,C)-valued monodromy on Riemann surfaces of genus zero with n punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at cxa0=xa01. This implies a similar representation for the isomonodromic tau-function. In the case nxa0=xa04 we thereby get a proof of the relation between tau-functions and conformal blocks discovered in Gamayun etxa0al. (J High Energy Phys, 10:038, 2012). We briefly discuss a possible application of our results to the study of relations between certain

Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions

{mathcal{N}=2}

On Painlevé/gauge theory correspondence

N=2 supersymmetric gauge theories and conformal field theory.