On Information Loss in AdS$_3$/CFT$_2$

TL;DR

The paper investigates information loss in $AdS_3$/CFT$_2$ by focusing on the universal Virasoro vacuum block at large central charge $c$. It shows that Euclidean forbidden singularities and late-time Lorentzian decay signal unitarity-violation and that finite-$c$ nonperturbative effects universally resolve these singularities within the vacuum block, altering late-time behavior around $t_L \sim S_{BH}$. Using exact results for degenerate external operators and Borel-resummed $1/c$ expansions, it identifies information-restoring contributions from heavy states that correspond to classical AdS$_3$ saddles, suggesting a concrete link between CFT data and gravitational path integrals. The work thereby provides a concrete, model-independent mechanism for information recovery in holographic black-hole backgrounds and points toward a more precise formulation of the gravitational path integral in $AdS_3$.

Abstract

We discuss information loss from black hole physics in AdS$_3$, focusing on two sharp signatures infecting CFT$_2$ correlators at large central charge $c$: 'forbidden singularities' arising from Euclidean-time periodicity due to the effective Hawking temperature, and late-time exponential decay in the Lorentzian region. We study an infinite class of examples where forbidden singularities can be resolved by non-perturbative effects at finite $c$, and we show that the resolution has certain universal features that also apply in the general case. Analytically continuing to the Lorentzian regime, we find that the non-perturbative effects that resolve forbidden singularities qualitatively change the behavior of correlators at times $t \sim S_{BH}$, the black hole entropy. This may resolve the exponential decay of correlators at late times in black hole backgrounds. By Borel resumming the $1/c$ expansion of exact examples, we explicitly identify 'information-restoring' effects from heavy states that should correspond to classical solutions in AdS$_3$. Our results suggest a line of inquiry towards a more precise formulation of the gravitational path integral in AdS$_3$.

Figures (13)

• Figure 1: This figure suggests a heavy-light CFT correlator and its association with a light probe object interacting with a deficit angle or BTZ black hole background.
• Figure 2: This figure suggests the positions of OPE image singularities of CFT correlators. Black holes produce the pattern on the right, while the 'additional angles' discussed in section \ref{['sec:ExactVirasoroBlocks']} produce the pattern on the left. These singularities are forbidden in unitary four-point correlators. The heavy operators are located at $1$ and $\infty$, and the light probe operators are at $0$ and $z$ in the Euclidean plane.
• Figure 3: This figure provides a visualization of a space with an 'additional angle' totaling $4\pi$ around the origin. This suggests the spatial geometry created by a heavy degenerate operator with dimension $h_{2,1} = -\frac{c}{8}$ at large $c$. The $h_{r,1}$ always produce a total angle equal to the integer $r$ times $2 \pi$.
• Figure 4: This figure shows the behavior of a degenerate Virasoro vacuum block near a forbidden singularity for various values of the central charge $c$. We have specifically plotted $\log | {\cal V}_{2,1} |$ with $h_L = 1$ as a function of the variable $\log(z-1)$ in the vicinity of $z=2$.
• Figure 5: The figure on the left indicates the positions of the operators and the forbidden singularities (green stars) associated with the $\rho$-expansion of ${\cal V}_{3,1}$. The figure on the right displays the logarithm of the $2n^{\mathrm{th}}$ coefficient from equation (\ref{['eq:RhoExpansionDefinition31']}) for various values of $c$. At $c=\infty$ the coefficients grow exponentially for all $n$, leading to a forbidden singularity at $|\rho_\pm | = \frac{1}{\sqrt{3}}$. At finite $c$ the coefficients initially grow exponentially, but then fall back to sub-exponential behavior at large $n$.