Conformal nets and local field theory
We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between conformal field theories. Altogether we characterize the algebraic s...
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| Format: | Journal article |
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2017
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| _version_ | 1797056105366421504 |
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| author | Douglas, C Bartels, A Henriques, A |
| author_facet | Douglas, C Bartels, A Henriques, A |
| author_sort | Douglas, C |
| collection | OXFORD |
| description | We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between conformal field theories. Altogether we characterize the algebraic structure of the collection of conformal nets as a symmetric monoidal tricategory. Dualizable objects of this tricategory correspond to conformal-net-valued 3-dimensional local topological quantum field theories. We prove that the dualizable conformal nets are the finite sums of irreducible nets with finite µ-index. This classification provides a variety of 3-dimensional local field theories, including local field theories associated to central extensions of the loop groups of the special unitary groups. |
| first_indexed | 2024-03-06T19:18:41Z |
| format | Journal article |
| id | oxford-uuid:194e005a-0763-451a-8dd9-4bb769eb92dd |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:18:41Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | oxford-uuid:194e005a-0763-451a-8dd9-4bb769eb92dd2022-03-26T10:48:12ZConformal nets and local field theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:194e005a-0763-451a-8dd9-4bb769eb92ddSymplectic Elements at Oxford2017Douglas, CBartels, AHenriques, AWe describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between conformal field theories. Altogether we characterize the algebraic structure of the collection of conformal nets as a symmetric monoidal tricategory. Dualizable objects of this tricategory correspond to conformal-net-valued 3-dimensional local topological quantum field theories. We prove that the dualizable conformal nets are the finite sums of irreducible nets with finite µ-index. This classification provides a variety of 3-dimensional local field theories, including local field theories associated to central extensions of the loop groups of the special unitary groups. |
| spellingShingle | Douglas, C Bartels, A Henriques, A Conformal nets and local field theory |
| title | Conformal nets and local field theory |
| title_full | Conformal nets and local field theory |
| title_fullStr | Conformal nets and local field theory |
| title_full_unstemmed | Conformal nets and local field theory |
| title_short | Conformal nets and local field theory |
| title_sort | conformal nets and local field theory |
| work_keys_str_mv | AT douglasc conformalnetsandlocalfieldtheory AT bartelsa conformalnetsandlocalfieldtheory AT henriquesa conformalnetsandlocalfieldtheory |