Toward classification of conformal theories |
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| Institution: | 1. School of Mathematics and Statistics, Henan University, Kaifeng, 475004, China;2. Institute of Contemporary Mathematics, Henan University, Kaifeng 475004, China;3. Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA;1. School of Physics, Northwest University, Xi’an, Shaanxi 710069, China;2. National Key Laboratory of Photoelectric Technology and Functional Materials (Culture Base), and Institute of Photonics and Photon-Technology, Northwest University, Xi’an, Shaanxi 710069, China |
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| Abstract: | By studying the representations of the mapping class groups which arise in 2D conformal theories we derive some restrictions on the value of the conformal dimension hi of operators and the central charge c of the Virasoro algebra. As a simple application we show that when there are a finite number of operators in the conformal algebra, the hi and c are all rational. |
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