AGT relation in the light asymptotic limit

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.