't Hooft suppression and holographic entropy

TL;DR

This paper investigates how corrections to the entanglement first law in holographic CFTs are suppressed by powers of N, demonstrating that bulk and boundary entropy relations align in the large-N limit for certain states.

Contribution

It provides a perturbative, replica-trick-free derivation of subleading holographic entanglement entropy corrections at all orders in 1/N, confirming the suppression of corrections in large-N CFTs.

Findings

$1/N$ counting matches bulk predictions

Sources with magnitude $ extepsilon N$ are non-singular

Derivation of subleading Ryu-Takayanagi corrections at all orders

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 $\epsilon N$ with $\epsilon$ fixed-but-small as $N\rightarrow \infty$. 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 $1/N$.