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A bstract We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator O k and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of T n O k (being T n the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way.
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Dressing bulk fields in AdS3
A bstract We study a set of CFT operators suitable for reconstructing a charged bulk scalar field ϕ in AdS 3 (dual to an operator $$ \mathcal{O} $$ O of dimension ∆ in the CFT) in the presence of a conserved spin- n current in the CFT. One has to sum a tower of smeared non-primary scalars $$ {\partial}_{+}^m{J}^{(m)} $$ ∂ + m J m , where J ( m ) are primaries with twist ∆ and spin m built from $$ \mathcal{O} $$ O and the current. The coefficients of these operators can be fixed by demanding that bulk correlators are well-defined: with a simple ansatz this requirement allows us to calculate bulk correlators directly from the CFT. They are built from specific polynomials of the kinematic invariants up to a freedom to make field redefinitions. To order 1/ N this procedure captures the dressing of the bulk scalar field by a radial generalized Wilson line.
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- Award ID(s):
- 1820734
- PAR ID:
- 10285035
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2020
- Issue:
- 10
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP10(2020)189
