Double‐trace deformations and entanglement entropy in AdS

Abstract

We compute the bulk entanglement entropy of a massive scalar field in a Poincare AdS with the Dirichlet and Neumann boundary condition when we trace out a half space. Moreover, by taking into account the quantum back reaction to the minimal surface area, we calculate how much the entanglement entropy changes under a doubletrace deformation of a holographic CFT. In the AdS3/CFT2 setup, our result agrees with the known result in 2d CFTs. In higher dimensions, our results offer holographic predictions.

Entanglement Entropy Evolution under Double‐trace Deformation

“…The change of bulk entanglement entropy is positive which is consistent with pure Ad S 3 case [11] whose boundary theory is the zero temperature CFT. Note that the static BTZ black hole has the positive specific heat and is thermodynamically stable.…”

“…Under the double-trace deformation, there is a renormalization group flow starting from a UV fixed point where λ = 0. The end point of this flow is an IR fixed point where the boundary 1 This is defined as Neumann boundary condition CFT N in [11].…”

“…On the basis of the work of Miyagawa, Shiba and Takayanagi [11] who studied the holographic entanglement entropy evolution in the AdS space, we generalize the bulk entanglement evolution to the black hole background. The main purpose of this paper is to study an example where the quantum correction of entanglement entropy gives the leading contribution.…”

Entanglement entropy for free scalar fields in AdS

“…The subregion B in CFT is taken to be a half space in [19]. In the present paper, we take the subregion B as a ball with radius r 0 .…”

Aharonov-Bohm effect on entanglement entropy in conformal field theory

“…The entanglement entropy in the quantum field theory plays important roles in many fields of physics including the string theory [1][2][3][4][5][6][7][8][9][10][11][12], condensed matter physics [13][14][15], lattice gauge theories [16,17], and the physics of the black hole [18][19][20][21][22][23]. The entanglement entropy is a useful quantity which characterize quantum properties of given states.…”