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Klein Bottles and Simple Currents
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The standard Klein bottle coefficient in the construction of open descendants is shown to equal the Frobenius-Schur indicator of a conformal field theory. Other consistent Klein bottle projections are shown to correspond to simple currents. These observations enable us to generalize the standard open string construction from C-diagonal parent theories to include non-standard Klein bottles. Using (generalizations of) the Frobenius-Schur indicator we prove positivity and integrality of the resulting open and closed string state multiplicities for standard as well as non-standard Klein bottles.
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Crosscap Defects
Crosscap defects from Z2 spacetime quotients in CFTs yield new crossing equations and O(N) model examples without displacement or tilt operators, forming defect conformal manifolds lacking exactly marginal operators.
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