Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries

TL;DR

This paper analytically computes the holographic entanglement entropy for $ ext{LLM}$ geometries with $ ext{Z}_k$ orbifolds, revealing shape-dependent universal features and confirming the $F$-theorem near UV fixed points.

Contribution

It provides the first analytical calculation of HEE for all LLM solutions with arbitrary M2 charge and orbifold level, including higher-order mass deformations.

Findings

HEE decreases monotonically near UV fixed point.

HEE is independent of overall Young diagram scaling.

HEE is a shape-dependent universal number.

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.