Cardy algebras and sewing constraints,II |
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| Authors: | Liang Kong Qin Li Ingo Runkel |
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| Affiliation: | 1. Institute for Advanced Study, Tsinghua University, Beijing, 100084, China;2. Department of Mathematics and Statistics, University of New Hampshire, 33 Academic Way, Durham, 03824, USA;3. School of Mathematical Sciences, Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China;4. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, China;5. Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, D-20146 Hamburg, Germany |
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| Abstract: | This is the part II of a two-part work started in [18]. In part I, Cardy algebras were studied, a notion which arises from the classification of genus-0, 1 open–closed rational conformal field theories. In this part, we prove that a Cardy algebra also satisfies the higher genus factorisation and modular-invariance properties formulated in [7] in terms of the notion of a solution to the sewing constraints. We present the proof by showing that the latter notion, which is defined as a monoidal natural transformation, can be expressed in terms of generators and relations, which correspond exactly to the defining data and axioms of a Cardy algebra. |
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| Keywords: | Open&ndash closed conformal field theory Modular tensor category Relative quantum field theory Cardy algebra Mapping class group |
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