’t Hooft suppression and holographic entropy

Abstract

Recent works have related the bulk first law of black hole mechanics to the first law of entanglement in a dual CFT. These are first order relations, and receive corrections for finite changes. In particular, the latter is naively expected to be accurate only for small changes in the quantum state. But when Newton's constant is small relative to the AdS scale, the former holds to good approximation even for classical perturbations that contain many quanta. This suggests that -for appropriate states -corrections to the first law of entanglement are suppressed by powers of N in CFTs whose correlators satisfy 't Hooft large-N power counting. We take first steps toward verifying that this is so by studying the large-N structure of the entropy of spatial regions for a class of CFT states motivated by those created from the vacuum by acting with real-time single-trace sources. We show that 1/N counting matches bulk predictions, though we require the effect of the source on the modular hamiltonian to be non-singular. The magnitude of our sources is N with fixed-but-small as N → ∞. Our results also provide a perturbative derivation -without relying on the replica trick -of the subleading Faulkner-Lewkowycz-Maldacena correction to the Ryu-Takayagi and Hubeny-Rangamani-Takayanagi conjectures at all orders in 1/N .

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

“…The right hand side comes about due to the non commutativity of the two matrices in the log on the left hand side. That is, these are the usual nested commutator terms in the Baker-Campbell-Hausdorff formula keeping only terms to order O(δρ) (see also [62] for related discussion).…”

Bulk locality and entanglement swapping in AdS/CFT

“…The prominent role that entanglement entropy plays in these models of holography is reminiscent of the connection between boundary entanglement and bulk dynamics developed in [17][18][19][20][21][22]. We leave it to future work to fully implement these entanglement swapping operators in AdS/CFT and extract further lessons about the connection between entanglement and bulk physics.…”

Double‐trace deformations and entanglement entropy in AdS

“…However, explicit computations of quantum corrections dual to the 1/N expansions, pioneered by the works [6,7], have been limited to several specific examples. Among them, the quantum corrections play a crucial role in the entanglement entropy and mutual information [6,7] for multi intervals [8][9][10] in two dimensional CFTs and for its higher dimensional counterparts [11][12][13] (see also further related works [14][15][16][17][18][19][20][21] and for other aspects of quantum corrections to holographic entanglement entropy refer to [22][23][24][25][26] ).…”