# Bulk fields from the boundary OPE

Abstract : Previous work has established an equality between the geodesic integral of a free bulk field in AdS and the contribution of the conformal descendants of its dual CFT primary operator to the OPE of two other operators inserted at the endpoints of the geodesic. Working in the context of the AdS$_3$/CFT$_2$ correspondence, we extend this relation to include the $1/N$ corrections to the bulk field obtained by dressing it with i) a $U(1)$ current and ii) the CFT stress tensor. In the former case, we argue that the contribution of the Ka\v{c}-Moody descendants to the respective boundary OPE equals the geodesic integral of a particular $U(1)$-dressed bulk field, which is framed to the boundary via a split Wilson line. In the latter case, we compute the gravitational $1/N$ corrections to the bulk field in various gauges, and then write a CFT expression for a putative bulk field whose geodesic integral captures the contribution of Virasoro descendants to the OPE of interest. We comment on the bulk interpretation of this expression.
Type de document :
Pré-publication, Document de travail
t16/203 Added a detailed derivation of the bulk field in radial gauge, an appendix, references and variou.. 2017
Domaine :
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Littérature citée [20 références]

https://hal-cea.archives-ouvertes.fr/cea-01541457
Contributeur : Emmanuelle De Laborderie <>
Soumis le : lundi 19 juin 2017 - 10:53:54
Dernière modification le : jeudi 15 mars 2018 - 15:06:08
Document(s) archivé(s) le : vendredi 15 décembre 2017 - 16:16:54

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1610.08952.pdf
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### Identifiants

• HAL Id : cea-01541457, version 1
• ARXIV : 1610.08952

### Citation

Monica Guica. Bulk fields from the boundary OPE. t16/203 Added a detailed derivation of the bulk field in radial gauge, an appendix, references and variou.. 2017. 〈cea-01541457〉

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