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Holographic entanglement entropy for noncommutative anti-de Sitter space

Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan

E-mail Address: momeni_d@enu.kz

E-mail Address: d.momeni@yahoo.com

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Muhammad Raza

Department of Mathematics, COMSATS Institute of Information Technology, Sahiwal 57000, Pakistan

State Key Lab of Modern Optical Instrumentation, Centre for Optical and Electromagnetic Research, Department of Optical Engineering, Zhejiang University, Hangzhou 310058, P. R. China

E-mail Address: mreza06@gmail.com

E-mail Address: mraza@zju.edu.cn

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, and

Ratbay Myrzakulov

Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan

E-mail Address: rmyrzakulov@gmail.com

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https://doi.org/10.1142/S0217732316500735Cited by:1 (Source: Crossref)

Abstract

A metric is proposed to explore the noncommutative form of the anti-de Sitter (AdS) space due to quantum effects. It has been proved that the noncommutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu–Takayanagi (RT) algorithm is then applied to compute the entanglement entropy (EE) in dual CFT₂. This calculation can be exploited to compute ultraviolet–infrared (UV–IR) cutoff dependent central charge of the certain noncommutative CFT₂. This noncommutative computation of the EE can be interpreted in the form of the surface/state correspondence. We have shown that noncommutativity increases the dimension of the effective Hilbert space of the dual conformal field theory (CFT).

Keywords:

PACS: 11.25.Tq, 03.65.Ud, 74.62.-c

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