Non-abelian Toda theory on AdS2 and AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality
Abstract It was recently observed that boundary correlators of the elementary scalar field of the Liouville theory on AdS2 background are the same (up to a non-trivial proportionality coefficient) as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to...
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doaj-4e987bacfa5e468084b61a92be6397352020-11-25T03:26:08ZengSpringerOpenJournal of High Energy Physics1029-84792019-09-012019914210.1007/s13130-019-11219-yNon-abelian Toda theory on AdS2 and AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ dualityMatteo Beccaria0Hongliang Jiang1Arkady A. Tseytlin2Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento & INFNAlbert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of BernBlackett Laboratory, Imperial CollegeAbstract It was recently observed that boundary correlators of the elementary scalar field of the Liouville theory on AdS2 background are the same (up to a non-trivial proportionality coefficient) as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line. The same relation generalizes to the conformal abelian Toda theory: boundary correlators of Toda scalars on AdS2 are directly related to the correlation functions of the chiral W $$ \mathcal{W} $$ -symmetry generators in the Toda CFT and thus are essentially controlled by the underlying infinite-dimensional symmetry. These may be viewed as examples of AdS2/CFT1 duality where the CFT1 is the chiral half of a 2d CFT; we shall to this as AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ . In this paper we demonstrate that this duality applies also to the non-abelian Toda theory containing a Liouville scalar coupled to a 2d σ-model originating from the SL(2, ℝ)/U(1) gauged WZW model. Here the Liouville scalar is again dual to the chiral stress tensor T while the other two scalars are dual to the parafermionic operators V ± of the non-abelian Toda CFT. We explicitly check the duality at the next-to-leading order in the large central charge expansion by matching the chiral CFT correlators of (T, V +, V −) (computed using a free field representation) with the boundary correlators of the three Toda scalars given by the tree-level and one-loop Witten diagrams in AdS2.http://link.springer.com/article/10.1007/s13130-019-11219-yAdS-CFT CorrespondenceConformal and W Symmetry |
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DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Matteo Beccaria Hongliang Jiang Arkady A. Tseytlin |
spellingShingle |
Matteo Beccaria Hongliang Jiang Arkady A. Tseytlin Non-abelian Toda theory on AdS2 and AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality Journal of High Energy Physics AdS-CFT Correspondence Conformal and W Symmetry |
author_facet |
Matteo Beccaria Hongliang Jiang Arkady A. Tseytlin |
author_sort |
Matteo Beccaria |
title |
Non-abelian Toda theory on AdS2 and AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality |
title_short |
Non-abelian Toda theory on AdS2 and AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality |
title_full |
Non-abelian Toda theory on AdS2 and AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality |
title_fullStr |
Non-abelian Toda theory on AdS2 and AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality |
title_full_unstemmed |
Non-abelian Toda theory on AdS2 and AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality |
title_sort |
non-abelian toda theory on ads2 and ads 2 / cft 2 1 2 $$ {\mathrm{ads}}_2/{\mathrm{cft}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2019-09-01 |
description |
Abstract It was recently observed that boundary correlators of the elementary scalar field of the Liouville theory on AdS2 background are the same (up to a non-trivial proportionality coefficient) as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line. The same relation generalizes to the conformal abelian Toda theory: boundary correlators of Toda scalars on AdS2 are directly related to the correlation functions of the chiral W $$ \mathcal{W} $$ -symmetry generators in the Toda CFT and thus are essentially controlled by the underlying infinite-dimensional symmetry. These may be viewed as examples of AdS2/CFT1 duality where the CFT1 is the chiral half of a 2d CFT; we shall to this as AdS 2 / CFT 2 1 2 $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ . In this paper we demonstrate that this duality applies also to the non-abelian Toda theory containing a Liouville scalar coupled to a 2d σ-model originating from the SL(2, ℝ)/U(1) gauged WZW model. Here the Liouville scalar is again dual to the chiral stress tensor T while the other two scalars are dual to the parafermionic operators V ± of the non-abelian Toda CFT. We explicitly check the duality at the next-to-leading order in the large central charge expansion by matching the chiral CFT correlators of (T, V +, V −) (computed using a free field representation) with the boundary correlators of the three Toda scalars given by the tree-level and one-loop Witten diagrams in AdS2. |
topic |
AdS-CFT Correspondence Conformal and W Symmetry |
url |
http://link.springer.com/article/10.1007/s13130-019-11219-y |
work_keys_str_mv |
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