Holographic entanglement entropy of anisotropic minimal surfaces in LLM geometries

We calculate the holographic entanglement entropy (HEE) of the ZkZk 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 μ02-order where μ0μ0 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 μ0μ0, they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with ZkZk 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 μ04-order for the symmetric droplet case.