Conformal nets II: conformal blocks
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-dimension...
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| Format: | Journal article |
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Springer Verlag
2017
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| _version_ | 1797069298793971712 |
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| author | Bartels, A Douglas, C Henriques, A |
| author_facet | Bartels, A Douglas, C Henriques, A |
| author_sort | Bartels, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T22:22:22Z |
| format | Journal article |
| id | oxford-uuid:557c58e4-0a4f-4986-a161-95dc9e828510 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:22:22Z |
| publishDate | 2017 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:557c58e4-0a4f-4986-a161-95dc9e8285102022-03-26T16:44:20ZConformal nets II: conformal blocksJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:557c58e4-0a4f-4986-a161-95dc9e828510Symplectic Elements at OxfordSpringer Verlag2017Bartels, ADouglas, CHenriques, AConformal 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. |
| spellingShingle | Bartels, A Douglas, C Henriques, A Conformal nets II: conformal blocks |
| title | Conformal nets II: conformal blocks |
| title_full | Conformal nets II: conformal blocks |
| title_fullStr | Conformal nets II: conformal blocks |
| title_full_unstemmed | Conformal nets II: conformal blocks |
| title_short | Conformal nets II: conformal blocks |
| title_sort | conformal nets ii conformal blocks |
| work_keys_str_mv | AT bartelsa conformalnetsiiconformalblocks AT douglasc conformalnetsiiconformalblocks AT henriquesa conformalnetsiiconformalblocks |