Holographic OPE coefficients from AdS black holes with matters

Yue-Zhou Li (Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300350, China) ; Zhan-Feng Mai (Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300350, China) ; H. Lü (Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin, 300350, China)

We study the OPE coefficients c Δ, J for heavy-light scalar four-point functions, which can be obtained holographically from the two-point function of a light scalar of some non-integer conformal dimension Δ L in an AdS black hole. We verify that the OPE coefficient c d,0 = 0 for pure gravity black holes, consistent with the tracelessness of the holographic energy-momentum tensor. We then study the OPE coefficients from black holes involving matter fields. We first consider general charged AdS black holes and we give some explicit low-lying examples of the OPE coefficients. We also obtain the recursion formula for the lowest-twist OPE coefficients with at most two current operators. For integer Δ L , although the OPE coefficients are not fully determined, we set up a framework to read off the coefficients γ Δ,J of the log(z z ¯ $$ \overline{z} $$ ) terms that are associated with the anomalous dimensions of the exchange operators and obtain a general formula for γ Δ,J . We then consider charged AdS black holes in gauged supergravity STU models in D = 5 and D = 7, and their higher-dimensional generalizations. The scalar fields in the STU models are conformally massless, dual to light operators with Δ L = d − 2. We derive the linear perturbation of such a scalar in the STU charged AdS black holes and obtain the explicit OPE coefficient c d−2,0. Finally, we analyse the asymptotic properties of scalar hairy AdS black holes and show how c d,0 can be nonzero with exchanging scalar operators in these backgrounds.

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      "surname": "L\u00fc", 
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  "abstracts": [
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      "source": "Springer", 
      "value": "We study the OPE coefficients c \u0394, J  for heavy-light scalar four-point functions, which can be obtained holographically from the two-point function of a light scalar of some non-integer conformal dimension \u0394 L  in an AdS black hole. We verify that the OPE coefficient c  d,0 = 0 for pure gravity black holes, consistent with the tracelessness of the holographic energy-momentum tensor. We then study the OPE coefficients from black holes involving matter fields. We first consider general charged AdS black holes and we give some explicit low-lying examples of the OPE coefficients. We also obtain the recursion formula for the lowest-twist OPE coefficients with at most two current operators. For integer \u0394 L , although the OPE coefficients are not fully determined, we set up a framework to read off the coefficients \u03b3 \u0394,J  of the log(z   <math> <mover> <mi>z</mi> <mo>\u00af</mo> </mover> </math>  $$ \\overline{z} $$ ) terms that are associated with the anomalous dimensions of the exchange operators and obtain a general formula for \u03b3 \u0394,J . We then consider charged AdS black holes in gauged supergravity STU models in D = 5 and D = 7, and their higher-dimensional generalizations. The scalar fields in the STU models are conformally massless, dual to light operators with \u0394 L  = d \u2212 2. We derive the linear perturbation of such a scalar in the STU charged AdS black holes and obtain the explicit OPE coefficient c  d\u22122,0. Finally, we analyse the asymptotic properties of scalar hairy AdS black holes and show how c  d,0 can be nonzero with exchanging scalar operators in these backgrounds."
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Published on:
25 December 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 9
Pages 1-43
DOI:
https://doi.org/10.1007/JHEP09(2019)001
arXiv:
1905.09302
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: