Modular functors with infinite dimensional Hilbert spaces
arXiv:2012.11110
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 Teichmüller theory.
arXiv comment19 pages
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