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

2018

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

Kusuki, Yuya

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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.

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