Holographic entanglement entropy and modular Hamiltonian in warped CFT in the framework of GMMG model

Abstract

We study some aspects of a class of non-AdS holography where the 3d bulk gravity is given by Generalized Minimal Massive Gravity (GMMG). We consider the spacelike warped $Ad{S}_3$ ($WAd{S}_3$) black hole solution of this model where the 2d dual boundary theory is the warped conformal field theory (WFCT). The charge algebra of the isometries in the bulk and the charge algebra of the vacuum symmetries at the boundary are compatible and this is an evidence for the duality conjecture. Further evidence for this duality is the equality of entanglement entropy and modular Hamiltonian on both sides of the duality. So we consider the modular Hamiltonian for the single interval at the boundary in associated to the modular flow generators of the vacuum. We calculate the gravitational charge in associated to the asymptotic Killing vectors that preserve the metric boundary conditions. Assuming the first law of the entanglement entropy to be true, we introduce the matching conditions between the variables in two side of the duality and we find equality of the modular Hamiltonian variations and the gravitational charge variations in two sides of the duality. According to the results of the present paper we can say with more sure that the dual theory of the warped $AdS3$ black hole solution of GMMG is a Warped CFT.

arXiv comment23 pages. Accepted for publication in EPJC

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