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Journal of High Energy Physics

, 2019:1 | Cite as

Holographic OPE coefficients from AdS black holes with matters

  • Yue-Zhou Li
  • Zhan-Feng MaiEmail author
  • H. Lü
Open Access
Regular Article - Theoretical Physics
  • 17 Downloads

Abstract

We study the OPE coefficients cΔ, 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 ΔL in an AdS black hole. We verify that the OPE coefficient cd,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 ΔL, although the OPE coefficients are not fully determined, we set up a framework to read off the coefficients γΔ,J of the log(z\( \overline{z} \)) terms that are associated with the anomalous dimensions of the exchange operators and obtain a general formula for γΔ,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 ΔL = d − 2. We derive the linear perturbation of such a scalar in the STU charged AdS black holes and obtain the explicit OPE coefficient cd−2,0. Finally, we analyse the asymptotic properties of scalar hairy AdS black holes and show how cd,0 can be nonzero with exchanging scalar operators in these backgrounds.

Keywords

AdS-CFT Correspondence Conformal Field Theory 

Notes

Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Center for Joint Quantum Studies and Department of Physics, School of ScienceTianjin UniversityTianjinChina

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