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arXiv:2609.16109

Boundary duals of bulk detectors

Jacqueline Caminiti, Robert C. Myers, Kelly Wurtz

hep-thquant-phSubmitted Sep 14, 2026• Announced Sep 16, 2026• 0 citations
v1 · Sep 14, 2026v2 · Sep 23, 2026
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Abstract

What is the boundary dual of an Unruh-DeWitt detector in anti-de Sitter space? We argue that this question is naturally answered by the HKLL reconstruction program. A local detector in the bulk can be associated with a smeared detector in the boundary, where the choice of smearing depends on the choice of HKLL kernel. We use this formalism to analyze entanglement harvesting in the Poincaré patch of AdS$_{3}$ for a bulk Unruh-DeWitt detector paired either with a boundary detector or with a second bulk detector. We compute the amount of harvesting in the standard way, namely by evaluating the two-detector density matrix to quadratic order in the coupling $λ$. Additionally, we address an apparent tension between microcausality for spacelike-separated bulk detectors and the fact that the dual HKLL detectors may directly overlap in the boundary theory.

Comments
59 pages + appendices, 9 figures

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What is the boundary dual of an Unruh-DeWitt detector in anti-de Sitter space? We argue that this question is naturally answered by the HKLL reconstruction program. A local detector in the bulk can be associated with a smeared detector in the boundary, where the choice of smearing depends on the choice of HKLL kernel. We use this formalism to analyze entanglement harvesting in the Poincaré patch of AdS3_{3}3​ for a bulk Unruh-DeWitt detector paired either with a boundary detector or with a second bulk detector. We compute the amount of harvesting in the standard way, namely by evaluating the two-detector density matrix to quadratic order in the coupling λλλ. Additionally, we address an apparent tension between microcausality for spacelike-separated bulk detectors and the fact that the dual HKLL detectors may directly overlap in the boundary theory.
Abstract We examine in (2+1)-dimensional anti-de Sitter (AdS) space the phenomena of entanglement harvesting — the process in which a pair of detectors (two-level atoms) extract entanglement from a quantum field through local interactions with the field. We begin by reviewing the Unruh-DeWitt detector and its interaction with a real scalar field in the vacuum state, as well as the entanglement harvesting protocol in general. We then examine how the entanglement harvested by a pair of such detectors depends on their spacetime trajectory, separation, spacetime curvature, and boundary conditions satisfied by the field. The harvested entanglement is interpreted as an indicator of field entanglement between the localized regions where the detectors interact with the field, and thus this investigation allows us to probe indirectly the entanglement structure of the AdS vacuum. We find an island of separability for specific values of the detectors’ energy gap and separation at intermediate values of the AdS length for which entanglement harvesting is not possible; an analogous phenomena is observed in AdS4, to which we compare and contrast our results. In the process we examine how the transition probability of a single detector, as a proxy for local fluctuations of the field, depends on spacetime curvature, its location in AdS space, and boundary conditions satisfied by the field.
We investigate entanglement harvesting in AdS4{\mathrm{AdS}}_{4}AdS4​. Applying the general results of [K. K. Ng, R. B. Mann, and E. Mart\'{\i}n-Mart\'{\i}nez, Phys. Rev. D 97, 125011 (2018)], we consider two scenarios: one where two particle detectors are geodesic, with equal redshift; and one where both are static, at unequal redshift. As expected, at large AdS length LLL, our results approximate flat space. However at smaller LLL we observe nontrivial effects for various field boundary conditions. Furthermore, in the static case we observe a novel feature of the entanglement as a function of switching time delay, which we attribute to different (coordinate) frequencies of the detectors. We also find an island of separability in parameter space, analogous to that observed in AdS3{\mathrm{AdS}}_{3}AdS3​, to which we compare and contrast our other results. The variety of features observed in both cases suggest further study in other spacetimes.
We analyze correlations between pairs of detectors quadratically coupled to real and complex scalar bosonic fields in 3+1 dimensions. This is a first step toward studying the entanglement structure of the fermionic vacuum through the entanglement harvesting protocol. We find that, while a single quadratically coupled Unruh-DeWitt presents no divergences, when one considers pairs of detectors there emerge persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire \nfrom the field. These divergences were not anticipated in previous studies. We characterize the divergences, discuss whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally find a UV-safe quantifier of harvested correlations.
Bulk reconstruction is a central problem in AdS/CFT, and entanglement wedge reconstruction is its subregion version. We argue that this subregion statement should be separated from the stronger holographic quantum error correction interpretation, in which one region-independent logical bulk operator has code-preserving representatives in several boundary regions. A simple locality argument shows that such a common reconstruction must commute with the code-preserving local algebras in the complementary regions. This is the mechanism realized in HaPPY-type codes: the erased regions are blind to a protected logical algebra. An ordinary finite NNN holographic CFT does not have such a protected invisible sector for supergravity fields. Its low-energy local observables, in particular, suitably smeared stress tensors, detect the physical support and gravitational dressing of ordinary bulk operators, up to possible center or superselection data. Thus, there is no such holographic quantum error correction and the N=∞N=\inftyN=∞ agreement of global and subregion HKLL formulae is a free-theory statement. What remains is entanglement wedge reconstruction without holographic quantum error correction, or subregion complementarity: each boundary region has its own code-preserving low-energy algebra and its own region-adapted bulk interpretation, rather than a shared logical operator.
We analyze correlations between pairs of particle detectors quadratically coupled to a real scalar field. We find that, while a single quadratically coupled detector presents no divergences, when one considers pairs of detectors, there emerge unanticipated persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire from the field. We have characterized such divergences, discussed whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally found a UV-safe quantifier of harvested correlations. Our results are relevant to future studies of the entanglement structure of the fermionic vacuum.