Wormholes from heavy operator statistics in AdS/CFT

TL;DR

The paper shows that higher-dimensional Euclidean AdS wormholes can encode the cumulants of correlation functions for an ensemble of heavy CFT operators modeled as a backreacting thin shell. By pairing an ETH-like ensemble with bulk backreaction, the authors derive microcanonical saddlepoint structures and construct wormhole geometries whose on-shell actions reproduce the cumulants of thermal correlators. They systematically connect bulk wormhole saddles to boundary ensemble statistics, including one-point variance, Hawking-Page-like transitions, and multi-boundary configurations for higher-point functions. The work also argues that such wormholes imply non-perturbative bulk violations of global symmetries unless the symmetry is gauged, illustrating a concrete holographic realization of these ideas in AdS/CFT.

Abstract

We construct higher dimensional Euclidean AdS wormhole solutions that reproduce the statistical description of the correlation functions of an ensemble of heavy CFT operators. We consider an operator which effectively backreacts on the geometry in the form of a thin shell of dust particles. Assuming dynamical chaos in the form of the ETH ansatz, we demonstrate that the semiclassical path integral provides an effective statistical description of the microscopic features of the thin shell operator in the CFT. The Euclidean wormhole solutions provide microcanonical saddlepoint contributions to the cumulants of the correlation functions over the ensemble of operators. We finally elaborate on the role of these wormholes in the context of non-perturbative violations of bulk global symmetries in AdS/CFT.

Figures (10)

• Figure 1: Geometry of the saddlepoint manifold $X$ for $\tau \in [0, \beta/2]$. The case $a)$ for $\tau <\tau_c$, in which the right patch $X^+$ does not include the tip of the right disk. The case $b)$ for $\tau >\tau_c$, in which the solution includes both tips.
• Figure 2: The different regions in the decomposition of the gravitational action $I[X]$. The green region $X_s$ accounts for the intrinsic contribution from the shell.
• Figure 3: The numerical value of the envelope function as a function of the energy difference $|\omega|$ for the thin shell operator in $d=2$. In this case the critical value is $\omega_c = Gm^2 \sim m$, independent of $\bar{E}$.
• Figure 4: The wormhole $X$ is deconstructed on the left figure. It corresponds to a portion of an Euclidean black hole, cut by the trajectories of two thin shells, which are then identified. On the right, the resulting $\mathbf{R}\times \mathbf{S}^1\times \mathbf{S}^{d-1}$ topology connecting both boundaries. The mass $M$ of the wormhole only depends on the combination $\beta+\beta'$.
• Figure 5: Renormalized action of the wormhole $\Delta I[X]$ as a function of the temperature, for $d=2$. The Hawking-Page transition at $\beta_{HP}=2\pi$ affects the normalization of the amplitude.