Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero–Moser systems, and KZB equations
| Autor: | Andrey Levin, A. V. Zotov, M. A. Olshanetsky |
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| Rok vydání: | 2016 |
| Předmět: |
Physics
Pure mathematics Nonlinear Sciences - Exactly Solvable and Integrable Systems Generalization 010102 general mathematics FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Automorphism 01 natural sciences Higgs bundle High Energy Physics::Theory Elliptic curve Nonlinear Sciences::Exactly Solvable and Integrable Systems Simple (abstract algebra) 0103 physical sciences Lie algebra Higgs boson 010307 mathematical physics Exactly Solvable and Integrable Systems (nlin.SI) 0101 mathematics Mathematical Physics Spin-½ |
| Zdroj: | Theoretical and Mathematical Physics. 188:1121-1154 |
| ISSN: | 1573-9333 0040-5779 |
| DOI: | 10.1134/s0040577916080018 |
| Popis: | We construct twisted Calogero-Moser (CM) systems with spins as the Hitchin systems derived from the Higgs bundles over elliptic curves, where transitions operators are defined by an arbitrary finite order automorphisms of the underlying Lie algebras. In this way we obtain the spin generalization of the twisted D'Hoker- Phong and Bordner-Corrigan-Sasaki-Takasaki systems. As by product, we construct the corresponding twisted classical dynamical r-matrices and Knizhnik-Zamolodchikov-Bernard equations related to the automorphisms of the Lie algebras. Comment: 35 pages + 2 tables |
| Databáze: | OpenAIRE |
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