We calculate the holographic entanglement entropy (HEE) of the Zk
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 μ0
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 μ0,
they are independent of the overall scaling of Young diagrams which
characterize LLM geometries. Therefore we can classify the HEEs of LLM
geometries with Zk 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.Comment: 15 pages, 1 figur