Abstract
Abstract
Motivated by the Bekenstein–Hawkingformula and the area law behaviour of entanglement entropy, we propose that in any UV finite theory of quantum gravity with a smooth spacetime, the total entropy for a pure state in a co-dimension one spatial region, to leading order, is given by
S
=
A
4
G
N
, where A is the area of the co-dimension two boundary. In the context of Dp brane holography we show that for some specially chosen regions bulk entanglement can be mapped to ‘target space’ entanglement in the boundary theory. Our conjecture then leads to a precise proposal for target space entanglement in the boundary theory at strong coupling and large N. In particular, it leads to the conclusion that the target space entanglement would scale like O(N
2) which is quite plausible in a system with O(N
2) degrees of freedom. Recent numerical advances in studying the D0 brane system hold out the hope that this proposal can be tested in a precise way in the future.
Funder
Department of Science and Technology, Government of India
Infosys Foundation
Department of Atomic Energy, Government of India
National Science Foundation
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
23 articles.
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