Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model

We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2, ℝ)k WZNW model. In particular, the classical relations in SL(2, ℝ)k can be formulated as a classical Liouville hierarchy in terms of the isotopic coordinates, and their covariance is ea...

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Autores principales: Bertoldi, G., Bolognesi, S., Giribet, G., Matone, M., Nakayama, Y.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_05503213_v709_n3_p522_Bertoldi
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_05503213_v709_n3_p522_Bertoldi2023-10-03T15:34:18Z Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model Bertoldi, G. Bolognesi, S. Giribet, G. Matone, M. Nakayama, Y. We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2, ℝ)k WZNW model. In particular, the classical relations in SL(2, ℝ)k can be formulated as a classical Liouville hierarchy in terms of the isotopic coordinates, and their covariance is easily understood in the framework of the AdS3/ CFT2 correspondence. Conversely, we find a closed expression for the classical Liouville decoupling operators in terms of the so-called uniformizing Schwarzian operators and show that the associated uniformizing parameter plays the same role as the isotopic coordinates in SL(2, ℝ)k. The solutions of the jth classical decoupling equation in the WZNW model span a spin j reducible representation of SL(2, ℝ). Likewise, we show that in Liouville theory solutions of the classical decoupling equations span spin j representations of SL(2, ℝ), which is interpreted as the isometry group of the hyperbolic upper half-plane. © 2005 Elsevier B.V. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_05503213_v709_n3_p522_Bertoldi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2, ℝ)k WZNW model. In particular, the classical relations in SL(2, ℝ)k can be formulated as a classical Liouville hierarchy in terms of the isotopic coordinates, and their covariance is easily understood in the framework of the AdS3/ CFT2 correspondence. Conversely, we find a closed expression for the classical Liouville decoupling operators in terms of the so-called uniformizing Schwarzian operators and show that the associated uniformizing parameter plays the same role as the isotopic coordinates in SL(2, ℝ)k. The solutions of the jth classical decoupling equation in the WZNW model span a spin j reducible representation of SL(2, ℝ). Likewise, we show that in Liouville theory solutions of the classical decoupling equations span spin j representations of SL(2, ℝ), which is interpreted as the isometry group of the hyperbolic upper half-plane. © 2005 Elsevier B.V. All rights reserved.
format JOUR
author Bertoldi, G.
Bolognesi, S.
Giribet, G.
Matone, M.
Nakayama, Y.
spellingShingle Bertoldi, G.
Bolognesi, S.
Giribet, G.
Matone, M.
Nakayama, Y.
Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model
author_facet Bertoldi, G.
Bolognesi, S.
Giribet, G.
Matone, M.
Nakayama, Y.
author_sort Bertoldi, G.
title Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model
title_short Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model
title_full Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model
title_fullStr Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model
title_full_unstemmed Zamolodchikov relations and Liouville hierarchy in SL(2, R)k WZNW model
title_sort zamolodchikov relations and liouville hierarchy in sl(2, r)k wznw model
url http://hdl.handle.net/20.500.12110/paper_05503213_v709_n3_p522_Bertoldi
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AT matonem zamolodchikovrelationsandliouvillehierarchyinsl2rkwznwmodel
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