Classification of conformal field theories based on Coulomb gases. Application to loop models |
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| Institution: | 1. School of Material and Metallurgy, University of Science and Technology Liaoning, Anshan 114051, China;2. Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China;3. School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China;4. School of Metallurgy, Northeastern University, Shenyang 110819, China;5. Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), Northeastern University, Shenyang 110819, China;1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China;2. Foshan Graduate School of Innovation, Northeastern University, Foshan 528312, China;3. Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China, Northeastern University, Shenyang 110819, China;4. Shenyang Aeroengine Research Institute, Aero Engine Corporation of China, Shenyang 110015, China |
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| Abstract: | We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of degenerate representations and for the closure of the vertex-operator algebra. The resulting classification contains, but is more general than, the standard one based on classical Lie algebras. We then apply the method to the Coulomb gas theory for the two-flavoured loop model of Jacobsen and Kondev. The purpose of the study is to clarify the relation between Coulomb gas models and conformal field theories with extended symmetries. |
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