Holographic holes in higher dimensions

Abstract

Abstract:We extend the holographic construction of [1] from AdS 3 to higher dimensions. In particular, we show that the Bekenstein-Hawking entropy of codimension-two surfaces in the bulk with planar symmetry can be evaluated in terms of the 'differential entropy' in the boundary theory. The differential entropy is a certain quantity constructed from the entanglement entropies associated with a family of regions covering a Cauchy surface in the boundary geometry. We demonstrate that a similar construction based on causal holographic information fails in higher dimensions, as it typically yields divergent results. We also show that our construction extends to holographic backgrounds other than AdS spacetime and can accommodate Lovelock theories of higher curvature gravity.

Comments on Jacobson’s “entanglement equilibrium and the Einstein equation”

“…Entanglement is now recognized to play an important role in the emergence of space (and space-time) in quantum gravity with calculations from a variety of different approaches [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Of course, one of the most natural frameworks where this connection can be investigated is the AdS/CFT correspondence [15,16].…”

“…We are interested in the regime where the radius of the sphere R is much smaller than the dS curvature scale L. 11 Then the leading curvature correction in the OPE expansion is…”

“…A similar discussion applies for a deformed CFT, where we may expect that O ∆ vacuum = 0. In this case, we may write Further, let us add that the contribution to δS IR proportional to the trace of the stress tensor δ T a a also comes from the modular Hamiltonian, since again it is linear in the 11 We have chosen coordinates such that with L → ∞, eq. (3.5) reduces to the standard flat space expression (3.2).…”

Twist operators in higher dimensions

“…Recently, entanglement entropy and related theoretical tools have received considerable attention in areas ranging from condensed matter physics, e.g., [1][2][3][4][5] to quantum gravity, e.g., [6][7][8][9][10][11][12]. In particular, holographic entanglement entropy [13][14][15][16] is now playing an important role in developing our understanding of gauge/gravity duality.…”

Exploring the tensor networks/AdS correspondence

“…To remedy the problem, we explore the 1 Interested readers are referred to [13,14] for a comprehensive review on tensor networks and its diverse applications in various branches of theoretical physics. Also we list out some references [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] where the connection between reconstruction of bulk spacetime and entanglement in the context of holography have been explored. This list is by no means complete and the readers are encouraged to check the citations of these papers and the references within.…”