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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Detalles Bibliográficos
Autores principales: Giribet, Gastón Enrique, Nicolás, Lorena
Publicado: 2009
Materias:
Area theorem
Conformal field theory
Duality symmetries
Higher curvature black holes
Negative temperature
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0217751X_v24_n16-17_p3137_Giribet
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
id paper:paper_0217751X_v24_n16-17_p3137_Giribet
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spelling paper:paper_0217751X_v24_n16-17_p3137_Giribet2023-06-08T15:21:09Z Langlands duality in liouville-H3 + WZNW correspondence Giribet, Gastón Enrique Nicolás, Lorena 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0217751X_v24_n16-17_p3137_Giribet 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, Gastón Enrique
Nicolás, Lorena
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.
author Giribet, Gastón Enrique
Nicolás, Lorena
author_facet Giribet, Gastón Enrique
Nicolás, Lorena
author_sort Giribet, Gastón Enrique
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
publishDate 2009
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0217751X_v24_n16-17_p3137_Giribet
http://hdl.handle.net/20.500.12110/paper_0217751X_v24_n16-17_p3137_Giribet
work_keys_str_mv AT giribetgastonenrique langlandsdualityinliouvilleh3wznwcorrespondence
AT nicolaslorena langlandsdualityinliouvilleh3wznwcorrespondence
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