Topological and conformal field theory as Frobenius algebras

Details Topological and conformal field theory as Frobenius algebras Topological and conformal field theory as Frobenius algebras

2005-12-03

arxiv.org/abs/math/0512076v2

Contemp.Math.431:225-248,2007

Mathematics

Category Theory

23 pages, several figures, proceedings to the Streetfest (Canberra 07/2005); v2: section 2.4 expanded, version accepted for pu

Scientific paper

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.

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