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arXiv · 2606.20220

Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity

Eleonora Alfinito·Matteo Beccaria
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Abstract

The quantum wormhole length in sine-dilaton gravity has been shown to equal the Krylov spread complexity in the double-scaled SYK model. In the infinite temperature limit, we compute the five-loop semiclassical expansion of DSSYK complexity by singular perturbation of the operator Liouville-type equations of motion, extending the existing one-loop results. The same method is applied to evaluate the Krylov variance and third-order cumulant, related to the connected two- and three-point functions of the length operator at coincident points. The small- and large-time behaviour of these observables is also studied. In particular, for the large-time slope of the wormhole linear growth, we determine the all-order resummation of the perturbative series, and the leading non-perturbative corrections.

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Eleonora Alfinito, Matteo Beccaria. 2026-06-18. Higher-loop wormhole length in sine-dilaton gravity from DSSYK Krylov complexity. https://arxiv.org/abs/2606.20220

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