A note on scalar field theory in AdS3/CFT2

We consider a scalar field theory in AdSd+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the correspondin...

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Autor principal: Minces, P.
Formato: JOUR
Materias:
AdS/CFT correspondence
Duality
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0217751X_v25_n14_p2815_Minces
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0217751X_v25_n14_p2815_Minces
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spelling todo:paper_0217751X_v25_n14_p2815_Minces2023-10-03T15:10:35Z A note on scalar field theory in AdS3/CFT2 Minces, P. AdS/CFT correspondence Duality We consider a scalar field theory in AdSd+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions Δ- and Δ+, respectively, where Δ± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS 3/CFT2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results. © 2010 World Scientific Publishing Company. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0217751X_v25_n14_p2815_Minces
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic AdS/CFT correspondence
Duality
spellingShingle AdS/CFT correspondence
Duality
Minces, P.
A note on scalar field theory in AdS3/CFT2
topic_facet AdS/CFT correspondence
Duality
description We consider a scalar field theory in AdSd+1, and introduce a formalism on surfaces at equal values of the radial coordinate. In particular, we define the corresponding conjugate momentum. We compute the Noether currents for isometries in the bulk, and perform the asymptotic limit on the corresponding charges. We then introduce Poisson brackets at the border, and show that the asymptotic values of the bulk scalar field and the conjugate momentum transform as conformal fields of scaling dimensions Δ- and Δ+, respectively, where Δ± are the standard parameters giving the asymptotic behavior of the scalar field in AdS. Then we consider the case d = 2, where we obtain two copies of the Virasoro algebra, with vanishing central charge at the classical level. An AdS 3/CFT2 prescription, giving the commutators of the boundary CFT in terms of the Poisson brackets at the border, arises in a natural way. We find that the boundary CFT is similar to a generalized ghost system. We introduce two different ground states, and then compute the normal ordering constants and quantum central charges, which depend on the mass of the scalar field and the AdS radius. We discuss certain implications of the results. © 2010 World Scientific Publishing Company.
format JOUR
author Minces, P.
author_facet Minces, P.
author_sort Minces, P.
title A note on scalar field theory in AdS3/CFT2
title_short A note on scalar field theory in AdS3/CFT2
title_full A note on scalar field theory in AdS3/CFT2
title_fullStr A note on scalar field theory in AdS3/CFT2
title_full_unstemmed A note on scalar field theory in AdS3/CFT2
title_sort note on scalar field theory in ads3/cft2
url http://hdl.handle.net/20.500.12110/paper_0217751X_v25_n14_p2815_Minces
work_keys_str_mv AT mincesp anoteonscalarfieldtheoryinads3cft2
AT mincesp noteonscalarfieldtheoryinads3cft2
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