Klein Topological Field Theories from Group Representations

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.

References in corpus (4)

• D-branes and K-theory in 2D topological field theory
• Cardy algebras and sewing constraints, I
• Cardy algebras and sewing constraints, II
• Brane Topological Field Theories and Hurwitz numbers for CW-complexes

Cited by in corpus (5)

• Orientation twisted homotopy field theories and twisted unoriented Dijkgraaf-Witten theory
• Hurwitz numbers from Feynman diagrams
• Universal Algebras of Hurwitz Numbers
• Cardy-Frobenius extension of algebra of cut-and-join operators
• A Klein TQFT: the local Real Gromov-Witten theory of curves