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Register a new userLarge $c$ Virasoro Blocks from Monodromy Method beyond Known Limits
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Authors
Yuya Kusuki
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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. 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.
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We study large $c$ conformal blocks outside the known limits. This work seems to be hard, but it is possible numerically by using the Zamolodchikov recursion relation. As a result, we find new some properties of large $c$ conformal blocks with a pair of two different dimensions for any channel and with various internal dimensions. With light intermediate states, we find a Cardy-like asymptotic formula for large $c$ conformal blocks and also we find that the qualitative behavior of various large $c$ blocks drastically changes when the dimensions of external primary states reach the value $c/32$. And we proceed to the study of blocks with heavy intermediate states $h_p$ and we find some simple dependence on heavy $h_p$ for large $c$ blocks. The results in this paper can be applied to, for example, the calculation of OTOC or Entanglement Entropy. In the end, we comment on the application to the conformal bootstrap in large $c$ CFTs.
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