On volumes of subregions in holography and complexity

By Omer Ben-Ami, Dean Carmi. 2016

156 citations recorded by the source corpus.

A bstractThe volume of the region inside the bulk Ryu-Takayanagi surface is a codimension-one object, and a natural generalization of holographic complexity to the case of subregions in the boundary QFT. We focus on time-independent geometries, and study the properties of this volume in various circumstances. We derive a formula for computing the volume for a strip entangling surface and a general asymptotically AdS bulk geometry. For an AdS black hole geometry, the volume exhibits non-monotonic behaviour as a function of the size of the entangling region (unlike the behaviour of the entanglement entropy in this setup, which is monotonic). For setups in which the holographic entanglement entropy exhibits transitions in the bulk, such as global AdS black hole, geometries dual to confining theories and disjoint entangling surfaces, the corresponding volume exhibits a discontinuous finite jump at the transition point (and so do the volumes of the corresponding entanglement wedges). We compute this volume discontinuity in several examples. Lastly, we compute the codim-zero volume and the bulk action of the entanglement wedge for the case of a sphere entangling surface and pure AdS geometry.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4afb1bf2a52c0af8c2b7547fa460308898b1b5d1

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Citations in the corpus

Comments on holographic complexity (2016, background): “These ideas were first considered for time-independent geometries by [21] in the context of CV duality — see also [22].”
On the time dependence of holographic complexity (2017, background): “Thus, it is enough to (15)For a proposed generalization for the complexity of subsystems in terms of the co-dimension one volume enclosed by the Ryu-Takayanagi surface, see [27, 45, 46].”
Complexity of formation in holography (2016, background): “See also [44, 45] for proposed generalizations for subregions.”