Modular functors with infinite dimensional Hilbert spaces
Mathematical Physics
2020-12-22 v1 math.MP
Abstract
We introduce a notion of generalized modular functors with Hilbert spaces of infinite dimension in general, and show that a generalized modular functor with data of conformal dimensions determines uniquely wave functions as its flat sections. Furthermore, we study an example of generalized modular functors derived from the Liouville conformal field theory. In this example, wave functions are seen to be gluing conformal blocks which are identified with eigenfunctions in the quantum Teichm\"uller theory.
Cite
@article{arxiv.2012.11110,
title = {Modular functors with infinite dimensional Hilbert spaces},
author = {Takashi Ichikawa},
journal= {arXiv preprint arXiv:2012.11110},
year = {2020}
}
Comments
19 pages