Antti Kupiainen

Virasoro Conformal Blocks and modular functor from Liouville CFT

In this article, we give a global construction of the Virasoro conformal blocks on Teichm\"uller space of Riemann surfaces of genus $g$ with $m$ marked points, when the central charge is $c>25$. We prove that they are global holomorphic sections of a holomorphic line bundle and they satisfy the Ward identity, which enc...