Klein Topological Field Theories from Group Representations

Klein Topological Field Theories from Group Representations

We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the represe...

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Bibliographic Details
Main Authors: Sergey A. Loktev, Sergey M. Natanzon
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2011-07-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
topological quantum field theory
group representation
Online Access:http://dx.doi.org/10.3842/SIGMA.2011.070
Description
Summary:We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the representation. We relate any complex simple Klein TFT to a real division ring.
ISSN:1815-0659

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