Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-06-17
Nucl.Phys. B678 (2004) 511-637
Physics
High Energy Physics
High Energy Physics - Theory
112 pages, table of contents, several figures. v2: typos corrected, version to be published in Nucl.Phys.B
Scientific paper
10.1016/j.nuclphysb.2003.11.026
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.
Fuchs J"urgen
Runkel Ingo
Schweigert Christoph
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