Holographic entanglement entropy of anisotropic minimal surfaces in LLM geometries

Abstract

We calculate the holographic entanglement entropy (HEE) of the Z(k) orbifold of Lin-Lunin-Maldacena (LLM) geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern-Simons level k. By solving the partial differential equations analytically, we obtain the HEEs for all LLM solutions with arbitrary M2 charge and k up to mu(2)(0)-order where mu(0) is the mass parameter. The renormalized entanglement entropies are all monotonically decreasing near the UV fixed point in accordance with the F-theorem. Except the multiplication factor and to all orders in mu(0), they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with Z(k) orbifold in terms of the shape of Young diagrams modulo overall size. HEE of each family is a pure number independent of the 't Hooft coupling constant except the overall multiplication factor. We extend our analysis to obtain HEE analytically to mu(4)(0)-order for the symmetric droplet case. (C) 2016 The Author(s). Published by Elsevier B.V.