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Spread complexity and the saturation of wormhole size

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arxiv 2412.02038 v1 pith:ZGDTENPG submitted 2024-12-02 hep-th quant-ph

Vijay Balasubramanian , Javier M. Magan , Poulami Nandi , Qingyue Wu This is my paper
classification hep-thquant-ph
keywords sizebasiscomplexityspreadbridgedssykkrylovlarge
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Recent proposals equate the size of Einstein-Rosen bridges in JT gravity to spread complexity of a dual, double-scaled SYK theory (DSSYK). We show that the auxiliary ``chord basis'' of these proposals is an extrapolation from a sub-exponential part of the finite-dimensional physical Krylov basis of a spreading thermofield double state. The physical tridiagonal Hamiltonian coincides with the DSSYK approximation on the initial Krylov basis, but deviates markedly over an exponentially large part of the state space. We non-perturbatively extend the identification of ER bridge size and spread complexity to the complete Hilbert space, and show that it saturates at late times. We use methods for tridiagonalizing random Hamiltonians to study all universality classes to which large N SYK theories and JT gravities can belong. The saturation dynamics depends on the universality class, and displays ``white hole'' physics at late times where the ER bridge shrinks from maximum size to a plateau. We describe extensions of our results to higher dimensions.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Comments on holographic spread complexity

    hep-th 2026-07 conditional novelty 7.0 of 10

    The momentum–spread-complexity relation requires generalized coherent states adapted to the spacetime symmetry algebra; semiclassical spreading alone cannot produce a momentum–complexity correspondence.

  2. York time in JT gravity

    hep-th 2025-05 conditional novelty 7.0 of 10

    In JT gravity, the Hartle-Hawking wavefunction satisfies a Schrodinger equation in York time with a Hermitian squeezing Hamiltonian, and York time evolution is a unitary change of the length basis rather than physical...

  3. The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$

    hep-th 2026-07 conditional novelty 6.0 of 10

    Normalized Krylov-Wigner negativity rate matches Krylov variance growth and equals tidal stretch rate R ∝ C P_ρ if and only if Δ=1 in AdS3.

  4. Resolving Black Hole Singularities in Jackiw-Teitelboim Gravity

    hep-th 2026-02 conditional novelty 6.0 of 10

    In JT gravity, the left confining potential required by spectral discreteness makes the wormhole length turn around and plateau, allowing boundary time to run past the would-be singularity and eliminating future horizons.

  5. Complexity of PXP scars revisited

    hep-th 2025-06 conditional novelty 6.0 of 10

    In the PXP model, the arch in the Lanczos coefficients is traced to a linear sl(3) part of the Hamiltonian, and the arch width is proposed as a signal distinguishing scarred from thermalizing states.

  6. Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity

    hep-th 2026-02 conditional novelty 5.0 of 10

    Reducing a graph walk to distance-layers reproduces Krylov/spread complexity, yielding analytic finite-q SYK Lanczos coefficients and hypercube complexity D sin²(t/D), with faster saturation than classical-walk circuits.

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