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arXiv · hep-th/9708141

A classifying algebra for boundary conditions

J. Fuchs·C. Schweigert
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Abstract

We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer spin simple current, modular invariant), this classifying algebra contains the fusion algebra of the untwisted sector as a subalgebra. Proper treatment of fields in the twisted sector, so-called fixed points, leads to structures that are intriguingly close to the ones implied by modular invariance for conformal field theories on closed orientable surfaces.

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J. Fuchs, C. Schweigert. 1997-08-27. A classifying algebra for boundary conditions. https://doi.org/10.1016/s0370-2693(97)01180-5

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