Multiboundary wormholes and OPE statistics

TL;DR

The paper develops a bridge between chaotic OPE data in holographic 2D CFTs and bulk AdS3 gravity by leveraging typicality, crossing symmetry, and modular invariance. It derives universal higher moments of heavy-heavy-light OPE coefficients from torus n-point functions using Virasoro crossing kernels, and shows these moments correspond to new multiboundary wormhole geometries in Virasoro TQFT, including three- and four-boundary examples that reproduce cubic and quartic OPE statistics. A generalized ETH framework emerges, with entropic suppression $g_n\sim e^{-(n-1)S}$ and non-Gaussian contractions linked to the Virasoro $6j$ symbol, interpreted as explicit gravity saddles. The work also explores light-matter corrections via bulk Wilson loops and outlines a recursive recipe for arbitrary $n$, while discussing open questions about bulk mapping class groups, saddle dominance, and potential connections to tensor models and off-shell topologies. Overall, the paper offers a coherent gravity-side realization of OPE ensembles in holographic CFT2s and expands the dictionary between crossing data and Euclidean wormhole geometries.

Abstract

We derive higher moments in the statistical distribution of OPE coefficients in holographic 2D CFTs, and show that such moments correspond to multiboundary Euclidean wormholes in pure 3D gravity. The n-th cyclic non-Gaussian contraction of heavy-heavy-light OPE coefficients follows from crossing symmetry of the thermal n-point function. We derive universal expressions for the cubic and quartic moments and demonstrate that their scaling with the microcanonical entropy agrees with a generalization of the Eigenstate Thermalization Hypothesis. Motivated by this result, we conjecture that the full statistical ensemble of OPE data is fixed by three premises: typicality, crossing symmetry and modular invariance. Together, these properties give predictions for non-factorizing observables, such as the generalized spectral form factor. Using the Virasoro TQFT, we match these connected averages to new on-shell wormhole topologies with multiple boundary components. Lastly, we study and clarify examples where the statistics of heavy operators are not universal and depend on the light operator spectrum. We give a gravitational interpretation to these corrections in terms of Wilson loops winding around non-trivial cycles in the bulk.

Figures (10)

• Figure 1: The three basic crossing moves that relate conformal block decompositions in different channels. From left to right, the moves are called fusion, modular S-transform and braiding.
• Figure 2: The sequence of moves relating the necklace and OPE channel for the torus four-point function. Depicted below each surface is the corresponding trivalent diagram representing the pair-of-pants decomposition.
• Figure 3: Glueing along the inner torus boundaries in blue produces the punctured-torus wormhole.
• Figure 4: Heegaard splitting of the three-boundary wormhole.
• Figure 5: The Heegaard splitting described in this section leads to a three-boundary torus wormhole, whose conical defect lines meet in a bulk three-point vertex. The bulk has non-trivial topology (not shown in this figure), arising from the glueing of genus-two handlebodies.