Abstract
The notion of a holographic entropy cone has recently been introduced and it has been proven that this cone is polyhedral. However, the original definition was fully geometric and did not strictly require a holographic duality. We introduce a new definition of the cone, insisting that the geometries used for its construction should be dual to states of a CFT. As a result, the polyhedrality of this holographic cone does not immediately follow. A numerical evaluation of the Euclidean action for the geometries that realize extremal rays of the original cone indicates that these are subdominant bulk phases of natural path integrals. The result challenges the expectation that such geometries are in fact dual to CFT states.
Highlights
JHEP10(2017)069 an important result of [10] was the proof that the number of inequalities implied by the RT prescription is finite for any number of regions, but all inequalities are linear and with integer coefficients
The result challenges the expectation that such geometries are dual to CFT states
The solutions we are interested in are multiboundary wormholes with N + 1 asymptotic boundaries with a set of constraints on the size of the horizons and all internal cycles such that the geometries correspond to extremal rays of the metric entropy cone
Summary
We first review the definition of the quantum entropy cone for arbitrary quantum systems, and the definition given in [10] for the holographic context. Since any extremal ray of this candidate cone can be realized by some geometry, it follows from convexity that any other ray inside the cone can be realized geometrically This proves that for four regions there cannot be new RT inequalities and that the candidate previously constructed is MC4. We define the Ryu-Takayanagi cone (RT CN ) as the cone spanned by all holographic states, for an arbitrary number of CFTs and all possible choices of the N regions This is a convex cone, since given any two rays it contains any conical combination of them, obtained by rescaling the metric and taking the tensor product of the corresponding two states..
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