Boundary conformal field theory and fusion ring representations
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Publication:5960495
DOI10.1016/S0550-3213(01)00632-0zbMATH Open0990.81152arXivhep-th/0106105OpenAlexW3099425603MaRDI QIDQ5960495
Author name not available (Why is that?)
Publication date: 7 April 2002
Published in: (Search for Journal in Brave)
Abstract: To an RCFT corresponds two combinatorial structures: the amplitude of a torus (the 1-loop partition function of a closed string, sometimes called a modular invariant), and a representation of the fusion ring (called a NIM-rep or equivalently a fusion graph, and closely related to the 1-loop partition function of an open string). In this paper we develop some basic theory of NIM-reps, obtain several new NIM-rep classifications, and compare them with the corresponding modular invariant classifications. Among other things, we make the following fairly disturbing observation: there are infinitely many (WZW) modular invariants which do not correspond to any NIM-rep. The resolution could be that those modular invariants are physically sick. Is classifying modular invariants really the right thing to do? For current algebras, the answer seems to be: Usually but not always. For finite groups a la Dijkgraaf-Vafa-Verlinde-Verlinde, the answer seems to be: Rarely.
Full work available at URL: https://arxiv.org/abs/hep-th/0106105
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