TFT construction of RCFT correlators. 2. Unoriented world sheets

Fuchs, Jurgen; Runkel, Ingo; Schweigert, Christoph

doi:10.1016/j.nuclphysb.2003.11.026

TFT construction of RCFT correlators. 2. Unoriented world sheets

Jurgen Fuchs
(
- Karlstad U.
)
,
Ingo Runkel
(
- Humboldt U., Berlin
)
,
Christoph Schweigert
(
- Aachen, Tech. Hochsch. and
- Hamburg U.
)

Jun, 2003

112 pages

Published in:

Nucl.Phys.B 678 (2004) 511-637

e-Print:

hep-th/0306164 [hep-th]

DOI:

10.1016/j.nuclphysb.2003.11.026

Report number:

HU-EP-03-23

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Abstract:

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 [I]. Here we show that the construction of [I] can be extended to unoriented world sheets by specifying one additional datum: a reversion 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, Moebius 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.

Note:

112 pages, table of contents, several figures. v2: typos corrected, version to be published in Nucl.Phys.B Subj-class: High Energy Physics - Theory: Category Theory: Quantum Algebra

11.25.Hf
11.25.-w
02.10.Tq
02.10.Ws
field theory: conformal
field theory: rational
dimension: 2
field theory: topological
algebra: vertex
operator: algebra

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