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Consistent systems of correlators in non-semisimple conformal field theory
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.ORCID iD: 0000-0003-4081-6234
Hamburg University.
2017 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 307, 598-639 p.Article in journal (Refereed) Published
Abstract [en]

Based on the modular functor associated with a -- not necessarily semisimple -- finite non-degenerate ribbon category D, we present a definition of a consistent system of bulk field correlators for a conformal field theory which comprises invariance under mapping class group actions and compatibility with the sewing of surfaces. We show that when restricting to surfaces of genus zero such systems are in bijection with commutative symmetric Frobenius algebras in D, while for surfaces of any genus they are in bijection with modular Frobenius algebras in D. This provides additional insight into structures familiar from rational conformal field theories and extends them to rigid logarithmic conformal field theories.

Place, publisher, year, edition, pages
Academic Press, 2017. Vol. 307, 598-639 p.
National Category
Subatomic Physics
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-63715DOI: 10.1016/j.aim.2016.11.020ISI: 000409285300015OAI: oai:DiVA.org:kau-63715DiVA: diva2:1141472
Funder
Swedish Research Council, 621-2013-4207
Available from: 2017-09-14 Created: 2017-09-14 Last updated: 2017-10-12Bibliographically approved

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