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 AdS_3 (WAdS_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.
Highlights
The spacelike warped Ad S3 black hole is a solution of the generalized minimal massive gravity (GMMG) that has been introduced in the paper [6]
GMMG is a modification of the minimal massive gravity (MMG) [7] that is an interesting theory in the context of Ad S/C F T correspondence where introduces a bulk theory with positive-energy propagating modes [6]
Entanglement entropy can be considered as a test for W Ad S3/W C F T conjecture, where we will study this test in the framework of GMMG model. In another term we investigate the holographic entanglement entropy and its first law in the context of W Ad S3/W C F T correspondence for asymptotically warped Ad S3 solution of GMMG model
Summary
The spacelike warped Ad S3 black hole is a solution of the generalized minimal massive gravity (GMMG) that has been introduced in the paper [6]. This property of the theory will be evident in the entanglement entropy of an interval in the vacuum, where we review the result of [17] . In parallel to the field theory calculations we have done in this paper, we investigate the holographic entanglement entropy and the gravitational charge. In order to be able to reproduce the results of [17] in the WCFT, the authors of [19] have considered an additional parameter to the Rindler transformations They have found the result for the holographic entanglement entropy in dualities beyond the AdS/CFT. We provide a conclusion for the paper and we give a summary of our work on this class of non-AdS holography
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