Sergey A. Loktev, Sergey M. Natanzon, “Klein Topological Field Theories from Group Representations”, SIGMA, 2011, Volume 7,070, 15 pp.

This article is cited in 5 papers

Klein Topological Field Theories from Group Representations

Sergey A. Loktev^ab, Sergey M. Natanzon^cab

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

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.

Keywords: topological quantum field theory; group representation.

MSC: 57R56; 20C05

Received: December 15, 2010; in final form July 4, 2011; Published online July 16, 2011

Language: English

DOI: 10.3842/SIGMA.2011.070