Virasoro blocks at large exchange dimension

TL;DR

This paper derives a simplified leading-order expression for Virasoro conformal blocks at large exchange dimensions using Zamolodchikov's recursion, revealing a quasi-modular form structure and comparing with AGT-based results.

Contribution

It introduces a new leading-order approximation for Virasoro blocks at large exchange dimensions using recursion relations and quasi-modular forms, connecting to existing AGT results.

Findings

Derived a simplified leading-order expression for Virasoro blocks.

Identified a quasi-modular form structure in the solution.

Validated the approach by comparing with AGT correspondence results.

Abstract

In this paper, we analyze Virasoro conformal blocks in the limit when the operator exchange dimension is taking to be large in comparison with the other parameters dependence of the block. We do this by using Zamolodchikov's recursion relations. We found a dramatically simplified solution at leading order in an inverse power expansion in large exchange conformal dimension in terms of a quasi-modular form in an Eisenstein series representation. We compare this solution with existing results obtained previously by using AGT correspondence.