AGT relation in the light asymptotic limit

TL;DR

This paper explores how four-point correlators in Liouville theory simplify in the light asymptotic limit, revealing a potential 2D gauge theory description through path integral analysis on squashed ellipsoids.

Contribution

It demonstrates the emergence of a simplified integral form for correlators and proposes a 2D gauge theory framework in the light asymptotic limit.

Findings

Finite-dimensional integral for correlators in the limit

Connection to 2D gauge theory description

Path integral reduction on squashed ellipsoids

Abstract

It is known that the path integral of correlators in Liouville theory reduces to a finite dimensional integral in the limit of vanishing coupling b. We take the example of four-point functions on sphere and investigate how the simple integral expression is reproduced from the path integral of gauge theory on extremely squashed ellipsoids. The simplified form for correlators suggests there is a 2D gauge theory describing the limit.