Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries

Abstract

We calculate the holographic entanglement entropy (HEE) of the ${\mathbb{Z}}_k$ 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 ${\mu }_0^2$-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 ${\mathbb{Z}}_k$ 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 ${\mu }_0^4$-order for the symmetric droplet case.

15 pages, 1 figure