A principle of maximum ignorance for semiclassical gravity

TL;DR

<3-5 sentence high-level summary>The paper introduces a principle of maximum ignorance for semiclassical gravity, formalizing an ensemble of mixed states via random purifications and a state-averaging ansatz that preserves only coarse-grained, low-energy data. By constraining the ensemble with gravitational inputs such as overlap functions Z(τ1,τ2), the authors derive a Gaussian auxiliary ensemble whose mean reproduces semiclassical states while its off-diagonal fluctuations encode nonperturbative microstructure, exactly matching on-shell wormhole amplitudes in AdS/CFT. They demonstrate this explicitly for 3D gravity through punctured-torus and genus-two wormholes, and extend the framework to higher dimensions with PETS and large interiors, where interior backreaction is captured by envelope functions j0/j2 and the coarse-graining map reproduces exterior thermality. The work further argues for universality of the state-averaging construction, predicts new multi-boundary wormholes from higher cumulants, and discusses off-shell extensions and connections to operator-averaging in 3D gravity. Overall, wormholes emerge as manifestations of microscopic ignorance about the true quantum state given a fixed semiclassical bulk description.

Abstract

The principle of maximum ignorance posits that the coarse-grained description of a system is maximally agnostic about its underlying microscopic structure. We briefly review this principle for random matrix theory and for the eigenstate thermalization hypothesis. We then apply this principle in holography to construct ensembles of random mixed states. This leads to an ensemble of microstates which models our microscopic ignorance, and which on average reproduces the effective semiclassical physics of a given bulk state. We call this ensemble the state-averaging ansatz. The output of our model is a prediction for semiclassical contributions to variances and higher statistical moments over the ensemble of microstates. The statistical moments provide coarse-grained -- yet gravitationally non-perturbative -- information about the microstructure of the individual states of the ensemble. We show that these contributions exactly match the on-shell action of known wormhole configurations of the gravitational path integral. These results strengthen the view that wormholes simply parametrize the ignorance of the microstructure of a fundamental state, given a fixed semiclassical bulk description.

Figures (3)

• Figure 1: Three examples of gravitational overlaps of semiclassical states. Left: the thermofield double. Middle: a partially entangled thermal state. Right: a product state. The time-symmetric slice is indicated with a dashed line.
• Figure 2: The correlation function on $M$ can be expressed in terms of simpler correlation functions by cutting open the path integral and inserting a complete set of boundary states. This process is repeated until the observable can be expressed as a product of sphere three-point functions.
• Figure 3: The plumbing construction of the sphere six-point function and the torus two-point function.