Proving AGT relations in the large-c limit

TL;DR

This paper demonstrates that in the large central charge limit, the 4-point Virasoro conformal block simplifies to a hypergeometric function, extending the AGT relation proof to a broader class of states.

Contribution

It extends the proof of the AGT relation to generic external states in the large-c limit by explicitly evaluating the conformal blocks as hypergeometric functions.

Findings

Conformal blocks reduce to hypergeometric functions at large c.

The AGT relation is validated for a broader set of states in this limit.

Explicit evaluation of Nekrasov functions supports the proof.

Abstract

In the limit of large central charge $c$ the 4-point Virasoro conformal block becomes a hypergeometric function. It is represented by a sum of chiral Nekrasov functions, which can also be explicitly evaluated. In this way the known proof of the AGT relation is extended from special to generic set of external states, but in the special limit of c=\infty.