Holographic OPE coefficients from AdS black holes with matters

Abstract

Abstract 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 $$ \overline{z} $$ 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.