Asymptotic boundary KZB operators and quantum Calogero-Moser spin chains
| Autor: | Reshetikhin, Nicolai, Stokman, Jasper |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | Asymptotic boundary KZB equations describe the consistency conditions of degenerations of correlation functions for boundary Wess-Zumino-Witten-Novikov conformal field theory on a cylinder. In the first part of the paper we define asymptotic boundary KZB operators for connected real semisimple Lie groups G with finite center. We prove their main properties algebraically using coordinate versions of Harish-Chandra's radial component map. We show that their commutativity is governed by a system of equations involving coupled versions of classical dynamical Yang-Baxter equations and reflection equations. We use the coordinate radial components maps to introduce a new class of quantum superintegrable systems, called quantum Calogero-Moser spin chains. A quantum Calogero-Moser spin chain is a mixture of a quantum spin Calogero-Moser system associated to the restricted root system of G and an one-dimensional spin chain with two-sided reflecting boundaries. The asymptotic boundary KZB operators provide explicit expressions for its first order quantum Hamiltonians. We also explicitly describe the Schr\"odinger operator. Comment: 39 pages |
| Databáze: | arXiv |
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