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Topological and conformal field theory as Frobenius algebras
Dept. of Mathematics, King's College, London, UK.
Cardiff School of Math., Cardiff Univ., Cardiff, UK.ORCID iD: 0000-0003-0372-5093
Institutionen för fysik, Karlstads universitet, Karlstad, Sweden.
Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany.
2007 (English)In: Categories in Algebra, Geometry and Mathematical Physics / [ed] Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack and Amnon Neeman, American Mathematical Society (AMS), 2007, p. 225-248Chapter in book (Refereed)
Abstract [en]

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a (rational) CFT can be divided into two steps, of which one is complex-analytic and one purely algebraic. We realise the algebraic part of the construction with the help of three-dimensional topological field theory and show that any symmetric special Frobenius algebra in the appropriate braided monoidal category gives rise to a solution. A special class of examples is provided by two-dimensional topological field theories, for which the relevant monoidal category is the category of vector spaces

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2007. p. 225-248
Series
Contemporary Mathematics, ISSN 0271-4132 ; 431
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:oru:diva-57727ISI: 000247366900013ISBN: 9780821839706 (print)OAI: oai:DiVA.org:oru-57727DiVA, id: diva2:1096441
Available from: 2013-01-22 Created: 2017-05-17 Last updated: 2017-10-18Bibliographically approved

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Topological and conformal field theory as Frobenius algebras

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Fjelstad, Jens

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