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Geodesics, one-point functions, and black hole perturbations
Phys. Rev. D 114, 026037 – Published 28 July, 2026
DOI: https://doi.org/10.1103/ktch-p9h8
Abstract
Holographic black holes exhibit a striking relation between thermal boundary one-point functions and bulk geodesic lengths. In the large conformal-dimension limit, the one-point function of a primary operator is given by the exponential of the geodesic length from its boundary insertion point to the horizon. We test the robustness of this relation under perturbations by considering a class of deformations of an Euclidean Bañados-Teitelboim-Zanelli (BTZ) black hole, working to first order in the perturbation. We find that, at leading order in the large conformal-dimension limit and to first order in the radial horizon-preserving perturbation, the logarithmic variation of the one-point function is governed by the variation of the renormalized boundary-to-horizon geodesic length. The result is established using Wentzel-Kramers-Brillouin (WKB) and saddle-point methods, and WKB expressions at large conformal dimensions are checked against the exact Green function and bulk-boundary propagator.
Physics Subject Headings (PhySH)
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