Perturbative distinguishability of black hole microstates from AdS/CFT correspondence

TL;DR

Addressing whether black hole microstates can be distinguished from thermal states via perturbative quantum gravity corrections in AdS$_3$/CFT$_2$, the work computes subsystem fidelity $F( ho_A, ho'_A)$ and Quantum Jensen-Shannon Divergence $J( ho_A, ho'_A)$ using twist-operator short-interval expansions and large-$c$ expansions to bound the subsystem trace distance $D( ho_A, ho'_A)$. For two primary microstates, leading corrections yield $F = 1 - rac{3 \pi^4 c \ell^4 (\epsilon_\phi-\epsilon_\psi)^2}{32 L^4} + o(\ell^4)$ and $J = \frac{2 \pi^4 c \ell^4 (\epsilon_\phi-\epsilon_\psi)^2}{15 L^4} + o(\ell^4)$, implying $O(c\ell^4) \lesssim D \lesssim O(c^{1/2}\ell^2)$; when comparing a microstate to a thermal state at the same energy, $F$ and $J$ scale as $F=1-\frac{7 \pi^8 c \ell^8 (22 \epsilon_\phi-1)^2 \epsilon_\phi^2}{512 (5 c+22) L^8}+o(\ell^8)$ and $J=\frac{32 \pi^8 c \ell^8 \epsilon_\phi^2 (22\epsilon_\phi-1)^2}{1575 (5 c+22) L^8}+o(\ell^8)$, giving $O(c^0 \ell^8) \lesssim D \lesssim O(c^0 \ell^4)$. These results establish perturbative distinguishability of black hole microstates within holographic CFTs and motivate generalized thermal ensembles and extensions to descendant states and higher dimensions.

Abstract

We establish direct evidence for the perturbative distinguishability between black hole microstates and thermal states using the AdS/CFT correspondence. In two-dimensional holographic conformal field theories, we obtain the subsystem fidelity and quantum Jensen-Shannon divergence, both of which provide rigorous lower and upper bounds for subsystem trace distance. This result demonstrates that perturbative quantum gravity corrections break semiclassical indistinguishability, thereby supporting the recovery of information even from a small amount of the Hawking radiation.