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arXiv · 1409.8672

Conformal nets II: conformal blocks

Arthur Bartels·Christopher L. Douglas·André Henriques
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Abstract

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.

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Arthur Bartels, Christopher L. Douglas, André Henriques. 2014-09-30. Conformal nets II: conformal blocks. https://arxiv.org/abs/1409.8672

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