Holographic Entropy Cone Beyond AdS/CFT (2502.03516v1)

Abstract: We extend all known area inequalities obeyed by Ryu-Takayanagi surfaces of AdS boundary regions -- the holographic entropy cone -- to static generalized entanglement wedges of bulk regions in arbitrary spacetimes. The generalized holographic entropy cone is subject to a mutual independence condition on the bulk regions: each bulk input region must be outside the entanglement wedge of the union of all others. The condition captures when gravitating regions involve fundamentally distinct degrees of freedom despite the nonlocality inherent in the holographic principle.

• The paper extends the holographic entropy cone by generalizing entanglement wedges to arbitrary spacetimes beyond the AdS/CFT framework.
• It utilizes contraction maps and graph theory to demonstrate that established entanglement inequalities, like strong subadditivity, apply to bulk regions.
• The study implies broader applications in quantum gravity, laying groundwork for exploring entanglement structures in dynamic gravitational systems.

Holographic Entropy Cone Beyond AdS/CFT

The paper "Holographic Entropy Cone Beyond AdS/CFT" authored by Raphael Bousso and Sami Kaya extends the framework of holographic area inequalities, primarily known from the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, to more generalized settings. It systematically tackles entanglement structures in spacetimes with and without asymptotic boundaries, thereby broadening the understanding and applicability of the holographic principle.

Theory and Framework

In the context of the AdS/CFT duality, Ryu-Takayanagi (RT) surfaces have been instrumental in establishing a connection between the geometric properties of a bulk spacetime and the entropic properties of a boundary quantum field theory. The holographic entropy cone encapsulates all area inequalities satisfied by these RT surfaces, which are significant in asserting the consistency of entanglement structures mapped by the boundary to the bulk of holographic theories.

Bousso and Kaya aim to extend these concepts to static generalized entanglement wedges in arbitrary spacetimes. Traditional entanglement wedges correspond to boundary regions in AdS spacetimes, but generalized entanglement wedges also assign such regions to arbitrary bulk regions within valid holographic frameworks. A significant component of the construction presented by the authors is the mutual independence condition imposed on the bulk regions, asserting that each region must lie outside the entanglement wedge of the union of all other regions. This introduces an essential constraint reflecting the non-local nature of degrees of freedom in gravitational systems, dovetailing with the foundational elements of quantum gravity.

Main Contributions

The key contributions of this research are:

1. Generalization of Holographic Entropy Inequalities: The paper successfully generalizes the holographic entropy cone by embodying generalized entanglement wedges, subject to fundamental independence conditions of the involved regions.
2. Proof Structure and Contraction Maps: By leveraging aspects of graph theory and considering contraction maps, the research achieves a breakthrough by proving that all entanglement inequalities that apply to boundary input regions also extend to those defined by bulk input regions.
3. Theoretical Implications: This holds particular importance as many holographic entropy inequalities, such as strong subadditivity and monogamy of mutual information, are now provably applicable to more dynamic spacetime configurations, advancing the understanding of quantum information dynamics in gravitational settings.

Implications and Future Directions

Practically, the expansion of the applicability of these inequalities suggests new avenues for exploring the entanglement structures of realistic gravitational systems, including black holes and cosmological settings. The theoretical framework supports the robustness of quantum gravity theories when extrapolated beyond the ideal isotropic and homogeneous configurations. Bousso and Kaya’s extension facilitates integration with recent developments, such as the paper of time-dependent entanglement wedges.

Looking forward, there remains significant exploration on the frontiers of non-static conditions and time-dependent spacetimes. Moreover, the investigation into the relations between non-locality in quantum gravity and the independence condition might yield promising insights into the fundamental makeup of spacetime geometry and quantum fields. Further research addressing the complete characterization of holographic entropy cones in broader settings will continue to elucidate the deep relations between entanglement, information, and spacetime.

In summary, this work represents a substantive theoretical advancement in quantum gravity and holography, presenting new methodologies and proving significant claims about the entropic properties of generalized spacetimes. This expansion transcends the specific AdS/CFT framework and provides a foundational basis for further theoretical exploration and potential empirical validation in varied gravitational contexts.