q-Askey Deformations of Double-Scaled SYK

• URL: http://arxiv.org/abs/2605.13956v1
• Date: Wed, 13 May 2026 18:00:01 GMT
• Title: q-Askey Deformations of Double-Scaled SYK
• Abstract summary: We study families of deformations of the double-scaled SYK (DSSYK) model.<n>By increasing one of the deformation parameters, the models eventually exhibit discrete energy levels.<n>We discuss connections between our results and the emergence of baby universes in the bulk.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct families of deformations of the double-scaled SYK (DSSYK) model and investigate their bulk interpretation. We introduce microscopic deformations of the SYK model which, after ensemble averaging and in the double-scaling limit, are described by a transfer matrix encoding the recurrence relations of basic orthogonal polynomials in the q-Askey scheme. For certain families of deformations in the semiclassical limit at finite temperature, the chord number (encoding Krylov complexity) corresponds to the length of an Einstein-Rosen bridge connecting an End-Of-The-World brane to an anti-de Sitter asymptotic boundary. By increasing one of the deformation parameters, the models eventually exhibit discrete energy levels, signaling a new geometric transition in sine dilaton gravity. Via the SYK-Schur duality, Krylov complexity also admits a representation-theoretic interpretation as the spread of the SU(2) spin in the index of an $\mathcal{N}=2$ SU(2) gauge theory. We study the operator algebras of the deformed theories. The algebras can be type II$_1$ or type I$_\infty$ factors, depending on the operators that are included. The entanglement entropy between the type II$_1$ algebras for a pure state manifests as an extremal surface through the Ryu-Takayanagi formula. We discuss connections between our results and the emergence of baby universes in the bulk.

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