Abstract
We generalize the constructions for the multipartite reflected entropy in order to construct spacetimes capable of representing multipartite entanglement wedge cross sections of differing party number as Ryu-Takayanagi surfaces on a single replicated geometry. We devise a general algorithm for such constructions for arbitrary party number and demonstrate how such methods can be used to derive novel inequalities constraining mulipartite entanglement wedge cross sections.
Highlights
Background and definitionsLet M be an asymptotically locally AdS manifold in d + 1 spacetime dimensions that is holographically dual to a state of a CFT in d spacetime dimensions, which we can think of as existing at the boundary of the bulk alAdS spacetime, ∂M
We generalize the constructions for the multipartite reflected entropy in order to construct spacetimes capable of representing multipartite entanglement wedge cross sections of differing party number as Ryu-Takayanagi surfaces on a single replicated geometry
Consequence of this construction is that the surface corresponding to EW (A : B : C : D) in W becomes, in the replicated-and-glued geometry M0, a single geodesic anchored to two different copies of (D, A) that passes through W 1, W 2, W 3, and W 4
Summary
Let M be an asymptotically locally AdS (alAdS) manifold in d + 1 spacetime dimensions that is holographically dual to a state of a CFT in d spacetime dimensions, which we can think of as existing at the boundary of the bulk alAdS spacetime, ∂M. The key idea from the holographic construction above that we wish to focus on is that the bulk-anchored cross section ΓAB is realized as a conventional boundary-homologous minimal surface on a larger replicated manifold. [14, 15], map multipartite cross sections to minimal surfaces in even larger manifolds These constructions are only ever guaranteed to compute EW (A1 : A2 : · · · : An) alone as an entanglement entropy. While we focus on the static or time reflection-symmetric cases here, in principle there is no obstruction to working with a fully time-dependent spacetime M In such a setting, the minimal RT surface is replaced by the extremal Hubeny-Rangamani-Takayanagi (HRT) surface [21], and the entanglement wedge is a (d + 1)-dimensional bulk spacetime domain of dependence [22]. Within the covariant construction, one can still pick out a preferred bulk Cauchy surface that contains the HRT surface (a maximin surface [23]) so that cross sections may be computed and the gluing may be carried out according to the methods outlined above [14]
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