Holographic thermal correlators revisited. (English) Zbl 1521.81263
Summary: 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 M. Grinberg and J. Maldacena [J. High Energy Phys. 2021, No. 3, Paper No. 131, 31 p. (2021; Zbl 1461.83017)]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of \(T^nO_k\) (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.
MSC:
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
| 83C57 | Black holes |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 83E30 | String and superstring theories in gravitational theory |
| 81T28 | Thermal quantum field theory |
| 83E05 | Geometrodynamics and the holographic principle |
Citations:
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