Langlands duality in liouville-H3 + WZNW correspondence

We show a physical realization of the Langlands duality in correlation functions of H+ 3 WZNW model. We derive a dual version of the StoyanovkyRiabultTeschner (SRT) formula that relates the correlation function of the H+ 3 WZNW and the dual Liouville theory to investigate the level duality k - 2 → (...

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Autores principales: Giribet, G., Nakayama, Y., NicolÁs, L.
Formato: JOUR
Materias:
Area theorem
Conformal field theory
Duality symmetries
Higher curvature black holes
Negative temperature
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0217751X_v24_n16-17_p3137_Giribet
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_0217751X_v24_n16-17_p3137_Giribet2023-10-03T15:10:34Z Langlands duality in liouville-H3 + WZNW correspondence Giribet, G. Nakayama, Y. NicolÁs, L. Area theorem Conformal field theory Duality symmetries Higher curvature black holes Negative temperature We show a physical realization of the Langlands duality in correlation functions of H+ 3 WZNW model. We derive a dual version of the StoyanovkyRiabultTeschner (SRT) formula that relates the correlation function of the H+ 3 WZNW and the dual Liouville theory to investigate the level duality k - 2 → (k - 2)-1 in the WZNW correlation functions. Then, we show that such a dual version of the $H-3+$-Liouville relation can be interpreted as a particular case of a biparametric family of nonrational conformal field theories (CFT's) based on the Liouville correlation functions, which was recently proposed by Ribault. We study symmetries of these new nonrational CFT's and compute correlation functions explicitly by using the free field realization to see how a generalized Langlands duality manifests itself in this framework. Finally, we suggest an interpretation of the SRT formula as realizing the DrinfeldSokolov Hamiltonian reduction. Again, the Hamiltonian reduction reveals the Langlands duality in the H+ 3 WZNW model. Our new identity for the correlation functions of H+ 3 WZNW model may yield a first step to understand quantum geometric Langlands correspondence yet to be formulated mathematically. © 2009 World Scientific Publishing Company. Fil:Giribet, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:NicolÁs, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0217751X_v24_n16-17_p3137_Giribet
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Area theorem
Conformal field theory
Duality symmetries
Higher curvature black holes
Negative temperature
spellingShingle Area theorem
Conformal field theory
Duality symmetries
Higher curvature black holes
Negative temperature
Giribet, G.
Nakayama, Y.
NicolÁs, L.
Langlands duality in liouville-H3 + WZNW correspondence
topic_facet Area theorem
Conformal field theory
Duality symmetries
Higher curvature black holes
Negative temperature
description We show a physical realization of the Langlands duality in correlation functions of H+ 3 WZNW model. We derive a dual version of the StoyanovkyRiabultTeschner (SRT) formula that relates the correlation function of the H+ 3 WZNW and the dual Liouville theory to investigate the level duality k - 2 → (k - 2)-1 in the WZNW correlation functions. Then, we show that such a dual version of the $H-3+$-Liouville relation can be interpreted as a particular case of a biparametric family of nonrational conformal field theories (CFT's) based on the Liouville correlation functions, which was recently proposed by Ribault. We study symmetries of these new nonrational CFT's and compute correlation functions explicitly by using the free field realization to see how a generalized Langlands duality manifests itself in this framework. Finally, we suggest an interpretation of the SRT formula as realizing the DrinfeldSokolov Hamiltonian reduction. Again, the Hamiltonian reduction reveals the Langlands duality in the H+ 3 WZNW model. Our new identity for the correlation functions of H+ 3 WZNW model may yield a first step to understand quantum geometric Langlands correspondence yet to be formulated mathematically. © 2009 World Scientific Publishing Company.
format JOUR
author Giribet, G.
Nakayama, Y.
NicolÁs, L.
author_facet Giribet, G.
Nakayama, Y.
NicolÁs, L.
author_sort Giribet, G.
title Langlands duality in liouville-H3 + WZNW correspondence
title_short Langlands duality in liouville-H3 + WZNW correspondence
title_full Langlands duality in liouville-H3 + WZNW correspondence
title_fullStr Langlands duality in liouville-H3 + WZNW correspondence
title_full_unstemmed Langlands duality in liouville-H3 + WZNW correspondence
title_sort langlands duality in liouville-h3 + wznw correspondence
url http://hdl.handle.net/20.500.12110/paper_0217751X_v24_n16-17_p3137_Giribet
work_keys_str_mv AT giribetg langlandsdualityinliouvilleh3wznwcorrespondence
AT nakayamay langlandsdualityinliouvilleh3wznwcorrespondence
AT nicolasl langlandsdualityinliouvilleh3wznwcorrespondence
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