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A classifying algebra for CFT boundary conditions
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.
2009 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

Conformal field theories (CFT) constitute an interesting class of twodimensionalquantum field theories, with applications in string theoryas well as condensed matter physics. The symmetries of a CFT can beencoded in the mathematical structure of a conformal vertex algebra.The rational CFT’s are distinguished by the property that the categoryof representations of the vertex algebra is a modular tensor category.The solution of a rational CFT can be split off into two separate tasks, apurely complex analytic and a purely algebraic part.

The TFT-construction gives a solution to the second part of the problem.This construction gets its name from one of the crucial ingredients,a three-dimensional topological field theory (TFT). The correlators obtainedby the TFT-construction satisfy all consistency conditions of thetheory. Among them are the factorization constraints, whose implicationsfor boundary conditions are the main topic of this thesis.

The main result reviewed in this thesis is that the factorization constraintsgive rise to a semisimple commutative associative complex algebrawhose irreducible representations are the so-called reflection coefficients.The reflection coefficients capture essential information aboutboundary conditions, such as ground-state degeneracies and Ramond-Ramond charges of string compactifications. We also show that the annuluspartition function can be derived fromthis classifying algebra andits representation theory.

Place, publisher, year, edition, pages
Karlstad: Karlstad University , 2009. , 60 p.
Karlstad University Studies, ISSN 1403-8099 ; 2009:56
Keyword [en]
Boundary conditions, Conformal field theory, Factorization constraints, Modular tensor categories, TFT-construction
National Category
Other Physics Topics
Research subject
URN: urn:nbn:se:kau:diva-4890ISBN: 978-91-7063-279-2OAI: diva2:276168
2009-12-18, 21D 304, Karlstads universitet, Karlstad, 10:00 (English)
Available from: 2010-01-07 Created: 2009-11-11 Last updated: 2011-11-02Bibliographically approved

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