Covariant Holographic Entropy Cone

Abstract: The holographic entropy cone classifies the possible entanglement structures of quantum states with a classical gravity dual. For static geometries, Bao et al. established that this cone is polyhedral by constructing a graph model from Ryu-Takayanagi (RT) surfaces on a time-symmetric slice. Extending this framework to general, time-dependent states governed by the Hubeny-Rangamani-Takayanagi (HRT) formula has remained an open problem, as the relevant extremal surfaces do not lie on a common spatial slice. We resolve this by constructing a graph model directly from the causal structure of entanglement wedges. By proving a key "no-short-cut" theorem, we show that minimization over graph cuts reduces to a consideration of cuts corresponding to unions of complete HRT surfaces, establishing the equivalence of the covariant and static holographic entropy cones. Consequently, all foundational results, including polyhedrality and the finite nature of entropy inequalities, extend to general holographic states.