AGT relation in the light asymptotic limit

Understand

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.