’t Hooft suppression and holographic entropy

• DOI: 10.1007/jhep10(2015)059
• Publication Date: 2015-10-13T20:40:44Z
• Authors: William R. Kelly; Kevin Kuns; Donald Marolf
• Keywords: Hamiltonian (control theory); Replica trick

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