TFT construction of RCFT correlators II: unoriented world sheets
By Jürgen Fuchs, Ingo Runkel, Christoph Schweigert. 2003
144 citations recorded by the source corpus.
A full rational CFT, consistent on all orientable world sheets, can be constructed from the underlying chiral CFT, i.e., a vertex algebra, its representation category C, and the system of chiral blocks, once we select a symmetric special Frobenius algebra A in the category C [Nucl. Phys. B 646 (2002) 353]. Here we show that the construction of [Nucl. Phys. B 646 (2002) 353] can be extended to unoriented world sheets by specifying one additional datum: a reversion σ on A—an isomorphism from the opposed algebra of A to A that squares to the twist. A given full CFT on oriented surfaces can admit inequivalent reversions, which give rise to different amplitudes on unoriented surfaces, in particular to different Klein bottle amplitudes. We study the classification of reversions, work out the construction of the annulus, Mobius strip and Klein bottle partition functions, and discuss properties of defect lines on non-orientable world sheets. As an illustration, the Ising model is treated in detail.
Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Spectroscopy
View Paper: https://www.semanticscholar.org/paper/ac81a42a5bf91005bbf51d35d95e4e65e7c8b18f
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In Atomic and Molecular Physics, and Optics
In Geometry and Topology
- A. Gainutdinov
- I. Tipunin
- A. M. Semikhatov
- B. Feigin
- Stephen Hwang
- Jürgen Fuchs
- T. Creutzig
- David Ridout
In Spectroscopy
Citations in the corpus
- Nonsemisimple Fusion Algebras and the Verlinde Formula (2003, methodology): “benius algebra in the category C, and the correlation functions of the full CFT can be determined by combining methods from three-dimensionalTFT and from noncommutative algebra in monoidal categories [27, 28]. In the nonrational case, Cis no longer modular, in particular not semisimple, but in any c”
- Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center (2005, background): “accidental,” we hope that a more systemat ic derivation can be given. In fact, the task to place the structures encountered in the study of nonsemisimpleVerlinde algebras into the categorical context [32, 33, 34, 35] was already formulated in [15]. With the quantum-group counterpart of nonsemisimple”