4,316 research outputs found
TFT construction of RCFT correlators II: Unoriented world sheets
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.Comment: 112 pages, table of contents, several figures. v2: typos corrected,
version to be published in Nucl.Phys.
Two Results in Drawing Graphs on Surfaces
In this work we present results on crossing-critical graphs drawn on non-planar surfaces and results on edge-hamiltonicity of graphs on the Klein bottle. We first give an infinite family of graphs that are 2-crossing-critical on the projective plane. Using this result, we construct 2-crossing-critical graphs for each non-orientable surface. Next, we use 2-amalgamations to construct 2-crossing-critical graphs for each orientable surface other than the sphere. Finally, we contribute to the pursuit of characterizing 4-connected graphs that embed on the Klein bottle and fail to be edge-hamiltonian. We show that known 4-connected counterexamples to edge-hamiltonicity on the Klein bottle are hamiltonian and their structure allows restoration of edge-hamiltonicity with only a small change
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