Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits

TL;DR

This paper analytically extends the understanding of large central charge Virasoro blocks beyond known limits, revealing a drastic change in asymptotic behavior at a critical dimension and connecting it to bulk particle collision phenomena.

Contribution

It provides an analytic proof of the asymptotic forms of large $c$ Virasoro blocks beyond classical limits and uncovers a transition at the critical dimension $c/32$.

Findings

Asymptotic behavior of large $c$ conformal blocks changes at dimension $c/32$

Large $c$ solutions follow a Cardy-like formula

Bulk heavy particle collisions exhibit a transition related to their masses

Abstract

In this paper, we study large $c$ Virasoro blocks by using the Zamolodchikov monodromy method beyond its known limits. We give an analytic proof of our recent conjectur, which implied that the asymptotics of the large $c$ conformal blocks can be expressed in very simple forms, even if outside its known limits, namely the semiclassical limit or the heavy-light limit. In particular, we analytically discuss the fact that the asymptotic behavior of large $c$ conformal blocks drastically changes when the dimensions of external primary states reach the value $\frac{c}{32}$, which is conjectured by our numerical studies. The results presented in this work imply that the general solutions to the Zamolodchikov recursion relation are given by Cardy-like formula, which is an important conclusion that can be numerically drawn from our recent works. Mathematical derivations and analytical results imply that, in the bulk, the collision behavior between two heavy particles may undergo a remarkable transition associated with their masses.