Open Descendants in Conformal Field Theory

Abstract

Open descendants extend Conformal Field Theory to unoriented surfaces with boundaries. The construction rests on two types of generalizations of the fusion algebra. The first is needed even in the relatively simple case of diagonal models. It leads to a new tensor that satisfies the fusion algebra, but whose entries are signed integers. The second is needed when dealing with non-diagonal models, where Cardy's ansatz does not apply. It leads to a new tensor with positive integer entries, that satisfies a set of polynomial equations and encodes the classification of the allowed boundary operators.

19 pages, LATEX, 4 eps figures. Contribution to the Proceedings of the CERN Meeting on STU Dualities, Dec. 95

References in corpus (6)

• Dirichlet-Branes and Ramond-Ramond Charges
• Completeness Conditions for Boundary Operators in 2D Conformal Field Theory
• Planar Duality in $SU(2)$ WZW Models
• The Open Descendants of Non-Diagonal SU(2) WZW Models
• Sewing Constraints and Non-Orientable Open Strings
• Summing Over World-Sheet Boundaries

Cited by in corpus (10)

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• Geometric Couplings and Brane Supersymmetry Breaking
• Magnetized Four-Dimensional $Z_2\times Z_2$ Orientifolds
• Boundary Conformal Field Theory and Fusion Ring Representations
• Geometry of WZW Orientifolds
• Open Descendants of Non-Diagonal Invariants
• Integers in the open string
• Finitized Conformal Spectra of the Ising Model on the Klein Bottle and Moebius Strip
• Open Descendents of U(2N) Orbifolds at Rational Radii
• Lattice Realizations of the Open Descendants of Twisted Boundary Conditions for sl(2) A-D-E Models