Holographic entanglement entropy of anisotropic minimal surfaces in LLM geometries

Chanju Kim (Department of Physics, Ewha Womans University, Seoul, Republic of Korea) ; Kyung Kiu Kim (Department of Physics, College of Science, Yonsei University, Seoul, Republic of Korea) ; O-Kab Kwon (Department of Physics, BK21 physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon, Republic of Korea)

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.

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      "value": "We calculate the holographic entanglement entropy (HEE) of the <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub></math> orbifold of Lin\u2013Lunin\u2013Maldacena (LLM) geometries which are dual to the vacua of the mass-deformed ABJM theory with Chern\u2013Simons 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 <math><msubsup><mrow><mi>\u03bc</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math>-order where <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mn>0</mn></mrow></msub></math> 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 <math><msub><mrow><mi>\u03bc</mi></mrow><mrow><mn>0</mn></mrow></msub></math>, they are independent of the overall scaling of Young diagrams which characterize LLM geometries. Therefore we can classify the HEEs of LLM geometries with <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>k</mi></mrow></msub></math> 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 <math><msubsup><mrow><mi>\u03bc</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>4</mn></mrow></msubsup></math>-order for the symmetric droplet case."
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Published on:
02 June 2016
Publisher:
Elsevier
Published in:
Physics Letters B , Volume 759 C (2018)

Pages 395-401
DOI:
https://doi.org/10.1016/j.physletb.2016.05.095
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: