Bulk entanglement entropy and matrices

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.

Partial deconfinement at strong coupling on the lattice

“…The ideas proposed in refs. [50,51] may be related to this speculation. Partial deconfinement may also be related to other mechanisms of emergent geometry such as the ones in the Eguchi-Kawai model [52,53] or the IKKT matrix model [54][55][56][57], because the eigenvalue distribution plays an important role there as well.…”

A physical protocol for observers near the boundary to obtain bulk information in quantum gravity

“…Turning on weak gravitational effects changes this quantity from a finite value to 0. It would be interesting to understand the relationship of this result with the results of [38].…”

Gauge invariant target space entanglement in D-brane holography

“…In [1] four of us proposed that in gravitational theories which have holographic duals, such as the ones which arise in String Theory, such a precise notion indeed exists. The proposal is that in Dp brane holography for p < 3 this notion is provided by entanglement in the target space of the Yang-Mills theory on the brane.…”

“…We conjectured that when the state is the N brane bound state or its slightly heated up version, this von Neumann entropy is given by the Bekenstein formula A/4G where A is the area of the entangling surface in the dual black brane geometry. 1 In a complete theory of gravity one would expect that in any definition of geometric entanglement entropy the UV cutoff is automatic. Our conjecture therefore implies that the UV cutoff is provided by Netwon's constant, and not by e.g.…”

“…[18] had also conjectured that the entanglement entropy across an arbitrary surface in a theory of gravity saturates the Bekenstein bound. The reasoning of [1] is initi-…”