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Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries
- Publication Year :
- 2016
-
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.<br />Comment: 15 pages, 1 figure
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1605.00849
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.physletb.2016.05.095