Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Holographic Entropy Cone   We initiate a systematic enumeration and classification of entropy
inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory
states with smooth holographic dual geometries. For 2, 3, and 4 regions, we
prove that the strong subadditivity and the monogamy of mutual information give
the complete set of inequalities. This is in contrast to the situation for
generic quantum systems, where a complete set of entropy inequalities is not
known for 4 or more regions. We also find an infinite new family of
inequalities applicable to 5 or more regions. The set of all holographic
entropy inequalities bounds the phase space of Ryu-Takayanagi entropies,
defining the holographic entropy cone. We characterize this entropy cone by
reducing geometries to minimal graph models that encode the possible cutting
and gluing relations of minimal surfaces. We find that, for a fixed number of
regions, there are only finitely many independent entropy inequalities. To
establish new holographic entropy inequalities, we introduce a combinatorial
proof technique that may also be of independent interest in Riemannian geometry
and graph theory.

30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int