Holographic Mutual Information for Singular Surfaces

We study corner contributions to holographic mutual information for entangling regions composed of a set of disjoint sectors of a single infinite circle in three-dimensional conformal field theories. In spite of the UV divergence of holographic mutual information, it exhibits a first order phase transition. We show that tripartite information is also divergent for disjoint sectors, which is in contrast with the well-known feature of tripartite information being finite even when entangling regions share boundaries. We also verify the locality of corner effects by studying mutual information between regions separated by a sharp annular region. Possible extensions to higher dimensions and hyperscaling violating geometries is also considered for disjoint sectors.Comment: 35 pages, 25 Figures, v2: presentation improved, v3: matches published version in JHE

Complexity Growth with Lifshitz Scaling and Hyperscaling Violation

Using complexity=action proposal we study the growth rate of holographic complexity for Lifshitz and hyperscaling violating geometries. We will consider both one and two sided black branes in an Einstein-Maxwell-Dilaton gravitational theory. We find that in either case Lloyd's bound is violated and the rate of growth of complexity saturates to a value which is greater than twice the mass of the corresponding black brane. This value reduces to the mass of the black brane in the isotropic case. We show that in two sided black brane the saturation happens from above while for one sided black brane it happens from below.Comment: 17 pages, 4 figures, v2: typos corrected, references added, v3: Minor corrections, New counter terms added that also contribute to the rate of complexity growth. The conclusion is not changed, now 19 pages, v4: matches published versio