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Large p SYK from chord diagrams
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abstract
The p-body SYK model at finite temperature exhibits submaximal chaos and contains stringy-like corrections to the dual JT gravity. It can be solved exactly in two different limits: "large p" SYK $1 \ll p \ll N$ and "double-scaled" SYK $N,p \to \infty$ with $\lambda = 2 p^2/N$ fixed. We clarify the relation between the two. Starting from the exact results in the double-scaled limit, we derive several observables in the large p limit. We compute euclidean $2n$-point correlators and out-of-time-order four-point function at long lorentzian times. To compute the correlators we find the relevant asymptototics of the $U_{q}(su(1,1))$ 6j-symbol.
Forward citations
Cited by 3 Pith papers
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Twisted times, the Schwarzian and its deformations in DSSYK
The soft modes of double-scaled SYK are reparametrizations of twisted time coordinates; their effective action is the nonlinear Schwarzian, and deformations yield multi-field Liouville theories with computable low-ene...
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Probing the singularity at the holographic screen via $q$-holography
The probe-regime two-point function of sinh dilaton gravity matches the q-deformed Ward identity correlator, indicating an emergent quantum hyperbolic disk with SLq(2) isometry near the holographic boundary.
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Operator K-complexity in DSSYK: Krylov complexity equals bulk length
In the semiclassical limit of double-scaled SYK, Krylov complexity of an operator insertion equals total chord number, i.e., bulk wormhole length.
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