On the identification of finite operator algebras in two-dimensional conformally invariant field theories |
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| Affiliation: | 1. Departamento de Ciências Naturais, Universidade Federal de São João del Rei, C.P. 110, CEP 36301-160 São João del Rei, MG, Brazil;2. Departamento de Matemática, Universidade Federal de São João del Rei, C.P. 110, CEP 36301-160 São João del Rei, MG, Brazil;3. Emeritus Professor, Departamento de Física, Universidade Federal de Minas Gerais, C.P. 110, CEP 31270-901 Belo Horizonte, MG, Brazil;4. Instituto de Física Teórica, Universidade Estadual Paulista, C.P. 110, CEP 01140-070 São Paulo, SP, Brazil;1. Stanford Institute for Materials and Energy Science, SLAC and Stanford University, Menlo Park, CA 94025, USA;2. Department of Physics, University of California, Berkeley, CA 94720, USA;3. Department of Physics, Washington University, St. Louis, MO 63130, USA;4. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA;1. Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA;2. Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, 402 North Blackford St, Indianapolis, IN 46202-3216, USA;1. BME-MTA Statistical Field Theory ‘Lend ület’ Research Group, Department of Theoretical Physics, Budapest University of Technology and Economics, 1111 Budapest, Műegyetem rkp. 3, Hungary;2. SISSA and INFN, Sezione di Trieste, via Bonomea 265, I-34136, Trieste, Italy;3. MTA-BME Quantum Dynamics and Correlations Group, Eötvös Loránd Research Network, 1111 Budapest, Műegyetem rkp. 3, Hungary |
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| Abstract: | We investigate the structure of the linear differential operators whose solutions determine the four-point correlations of primary operators in the d = 2 conformally invariant SU(2) α-model with Wess-Sumino term and the d = 2 critical statistical systems with central Virasoro charge smaller than one. Factorisation properties of the differential operators are related to a finite closure of the operator algebras. We recover the selection and fusion rules of Fateev, Zamolodchikov and Gepner, Witten for the SU(2) α-model. It is outlined how the results of the SU(2) model can be used for the identification of closed operator algebras in the statistical model. |
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