q-Painleve equation from Virasoro constraints

TL;DR

This paper links the q-Painleve equation to Virasoro constraints in a 5d matrix model, providing a new perspective on integrable systems and conformal blocks at c=1.

Contribution

It interprets the q-Painleve equation as a reformulation of Virasoro constraints within the 5d Dotsenko-Fateev matrix model, connecting integrable systems with conformal field theory.

Findings

q-Painleve equation derived from Virasoro constraints

Reformulation of string equation in matrix model context

Connection between Fourier transforms of conformal blocks and integrable systems

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.