Large c Virasoro blocks from monodromy method beyond known limits

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 conjecture [1, 2], 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 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 work [1, 2]. 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.