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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Communicated by Y. Kawahigashi
We thank Stefan Stolz and Peter Teichner for their continuous support throughout this project. We would also like to thank Yi-Zhi Huang, Jørgen E. Andersen, and Michael Müger for their help with references. The last author thanks Roberto Longo and Sebastiano Carpi for a pleasant stay in Rome, during which he was able to present this work.
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Bartels, A., Douglas, C.L. & Henriques, A. Conformal Nets II: Conformal Blocks. Commun. Math. Phys. 354, 393–458 (2017). https://doi.org/10.1007/s00220-016-2814-5
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DOI: https://doi.org/10.1007/s00220-016-2814-5