Causal Structures and Nonlocality in Double Holography

TL;DR

The paper analyzes causal structures in double holography, revealing that the bulk AdS/BCFT causal structure is compatible with BCFT causality, in line with a generalized Gao-Wald mechanism. It further shows that the intermediate picture requires a distinctive nonlocal, IR-dominant propagation across the end-of-the-world brane to remain consistent with bulk causality, as evidenced by geodesic analyses and microcausality of operator commutators. By introducing and examining tentative entanglement wedges and detailed subregion mappings across BCFT, bulk, and intermediate pictures, the work highlights breakdowns in conventional subregion dualities and domain of dependence, driven by IR-sensitive nonlocality. The results suggest a fundamental link between nonlocality in the intermediate picture and topology-change effects (wormholes) in the gravitational path integral, with implications for information flow in black hole evaporation and the broader quantum gravity landscape.

Abstract

Double holography plays a crucial role in recent studies of Hawking radiation and information paradox by relating an intermediate picture, in which a dynamical gravity living on an end-of-the-world brane is coupled to a non-gravitational heat bath, to a much better-understood BCFT picture as well as a bulk picture. In this paper, causal structures in generic double holographic setups are studied. We find that the causal structure in the bulk picture is compatible with causality in the BCFT picture, thanks to a generalization of the Gao-Wald theorem. On the other hand, consistency with the bulk causal structure requires the effective theory in the intermediate picture to contain a special type of superluminal and nonlocal effect which is significant at long range or IR. These are confirmed by both geometrical analysis and commutators of microscopic fields. Subregion correspondences in double holography are discussed with the knowledge of this nonlocality. Possible fundamental origins of this nonlocality and its difference with other types of nonlocality will also be discussed.

Figures (16)

• Figure 1: The three equivalent pictures of a doubly holographic model. The asymptotic boundary $\Sigma$ and the end-of-the-world brane $Q$ are shown in grey and blue, respectively. The bulk region ${\cal M}$ is shaded.
• Figure 2: No shortcut should be allowed in the bulk ${\cal M}$ (shaded) when considering signal propagations on the asymptotic boundary $\Sigma$ (shown in grey). The solid line shows a null geodesic on $\Sigma$. The dashed line shows a time-like/null geodesic in ${\cal M}$ connecting two space-like separated (with respect to $\Sigma$) points on $\Sigma$, which should not have existed.
• Figure 3: A time slice $\tau = {\rm const.}$ of the vacuum configuration in the $(\tau,r,\phi)$ coordinate (left) and the $(\tau,\eta,\rho)$ coordinate (right) respectively. The asymptotic boundary $\Sigma$ is shown in grey and the end-of-the-world brane $Q$ is shown in blue. The dotted curve shows the asymptotic boundary of global AdS$_3$. The bulk region ${\cal M}$ is surrounded by ${\cal M} = \Sigma \cup Q$. Here, tension $T$ is positive in this figure so that the larger portion of pure AdS$_3$ is identified as the bulk ${\cal M}$.
• Figure 4: The orange dotted curves in the left panel show some null geodesics launching from $p:(\tau,r,\phi) = (-\pi/2,\infty,-\pi/2)$ in global AdS$_3$. All such geodesics reach $q: (\tau,r,\phi) = (\pi/2,\infty,\pi/2)$. The right panel shows the projection onto a time slice.
• Figure 5: Projection of the null geodesics connecting $p$ and the observer $\mathcal{R}$ on to a time slice for different situations. The orange dotted curves are the the fastest paths in the bulk ${\cal M}$. The green dotted curves are the fastest paths on the boundary $\partial{\cal M} = \Sigma \cup Q$. The shortest path on the boundary $\partial{\cal M}$ is omitted if it coincides that in the bulk ${\cal M}$.