Year: 2026
Type: preprint
Abstract: In this article, we give a global construction of the Virasoro conformal blocks on Teichmüller 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 encodes their conformal invariance. For the sphere with $3$ points, the space of conformal blocks is one-dimensional. For a given marked Riemann surface and a marked pair of pants decomposition, it is in general an infinite dimensional Hilbert space, isomorphic to $L^2(\R_+^{3g-3+m})$ with respect to some measure involving the DOZZ structure constants. We show that it carries a projective unitary representation of the mapping class group. More generally, there are unitary isomorphisms for each Moore-Seiberg move, changing a marked pair of pants decomposition into another one.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220473435