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

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.