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First law of entanglement entropy in topologically massive gravity

Long Cheng1,2, Ling-Yan Hung1,2,3, Si-Nong Liu1,2, and Hong-Zhe Zhou1,2

  • 1State Key Laboratory of Surface Physics and Department of Physics, Fudan University, 220 Handan Road, 200433 Shanghai, China
  • 2Center for Field Theory and Particle Physics, Fudan University, 220 Handan Road, 200433 Shanghai, China
  • 3Collaborative Innovation Center of Advanced Microstructures, Fudan University, 220 Handan Road, 200433 Shanghai, China

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Phys. Rev. D 94, 064063 – Published 22 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.064063

Abstract

In this paper we explore the validity of the first law of entanglement entropy in the context of topologically massive gravity (TMG). We find that the variation of the holographic entanglement entropy under perturbation from the pure anti–de Sitter background satisfies the first law upon imposing the bulk equations of motion in a given time slice, despite the appearance of instabilities in the bulk for generic gravitational Chern-Simons coupling μ. The Noether-Wald entropy is different from the holographic entanglement entropy in a general boosted frame. However, this discrepancy does not affect the entanglement first law.

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Phys. Rev. D 94, 064063– Published 22 September, 2016
  • Received 2 May 2016

© 2016 American Physical Society

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