Bulk and Transhorizon Measurements in AdS/CFT

TL;DR

The paper develops a framework for reconstructing bulk operators in AdS/CFT, including interiors of AdS black holes, by mapping bulk fields to boundary CFT operators via the GKPW dictionary and Green's-function techniques. It extends the construction to spacetimes with horizons, arguing that interior information can be encoded in the boundary theory and that the bulk–boundary map can be intrinsic and region-dependent, with a careful treatment of locality, gauge constraints, and boundary conditions. A path-integral fold viewpoint and a survey of alternative approaches (holographic RG, correlators, Wilson loops, and probes) illuminate the robustness and limits of bulk reconstruction, especially behind horizons and in the presence of gravity. The work clarifies how black hole complementarity can be reconciled within a unified AdS/CFT framework and highlights the significance of nonlocal boundary observables, or precursors, for accessing interior bulk physics while acknowledging the subtleties of locality and boundary data dependence.

Abstract

We discuss the construction of bulk operators in asymptotically AdS spacetimes, including the interiors of AdS black holes. We use this to address the question "If Schrodinger's cat were behind the horizon of an AdS black hole, could we determine its state by a measurement in the dual CFT?"

Figures (5)

• Figure 1: Boundary constructions of the bulk operator in the center of AdS at time $\tau$, shown as cross sections through global AdS. The support is indicated in bold. a) An operator in the center of AdS, using the spacelike Green's function. b) An operator elsewhere on the timeslice, obtained by a conformal transformation. c) Using ordinary Cauchy evolution from $\tau$ to $\tilde{\tau}$, and then the spacelike Green's function.
• Figure 2: Formation and evaporation of an AdS black hole. The grey lines represent an ingoing null shell, formed by perturbing the CFT. Field operators behind the horizon are integrated backwards in the bulk to before the formation of the black hole, and then expressed in terms of CFT operators; these can be integrated forward e.g. to times $\tau$ or $\tau_{\rm m}$. The Penrose diagram is doubled to match Fig. 1.
• Figure 3: The mapping from operators in the bulk region that is spacelike with respect to $\tau_0$ to CFT operators at $\tau_0$ is independent of the Hamiltonian at other times. Because the operator at the marked position is really defined non-localy on a Cauchy surface for the diamond, it does not fit into any other diamond.
• Figure 4: a) CFT path integral with a fold, to insert the operator ${\cal O}(\tau,x)$ at time $\tau_0$. b) The fold unfolded, and extended into the bulk. Arrows indicate the direction of time.
• Figure 5: a) CFT path integral with a fold, to insert the operator ${\cal O}(\tau,x)$ at time $\tau_0$. On the gray segments time evolution is generated by $H'$. b) Bulk fields ($\circ$, $\bullet$) and their corresponding boundary operators. Insertion of $\circ$ appears to change the dynamics used to derive the map for $\bullet$. However, each boundary operator should be understood in terms of a folded geometry as in (a), so that $\circ$ is in a different bulk region.