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Communications in Mathematical Physics

, Volume 354, Issue 1, pp 393–458 | Cite as

Conformal Nets II: Conformal Blocks

  • Arthur Bartels
  • Christopher L. Douglas
  • André Henriques
Open Access
Article

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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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Mathematisches InstitutWestfälische Wilhelms-Universität MünsterMünsterGermany
  2. 2.Mathematical InstituteRadcliffe Observatory QuarterOxfordUK
  3. 3.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands

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