Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 070, 15 pages      arXiv:0910.3813      https://doi.org/10.3842/SIGMA.2011.070

Klein Topological Field Theories from Group Representations

Sergey A. Loktev a, b and Sergey M. Natanzon a, b, c
a) Department of Mathematics, Higher School of Economics, 7 Vavilova Str., Moscow 117312, Russia
b) Institute of Theoretical and Experimental Physics, 25 Bolshaya Cheremushkinskaya Str., Moscow 117218, Russia
c) A.N. Belozersky Institute, Moscow State University, Leninskie Gory 1, Bldg. 40, Moscow 119991, Russia

Received December 15, 2010, in final form July 04, 2011; Published online July 16, 2011

Abstract
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.

Key words: topological quantum field theory; group representation.

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