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Krylov complexity in conformal field theory

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arxiv 2104.09514 v1 pith:GTJ7QSWD submitted 2021-04-19 hep-th cond-mat.stat-mech

classification hep-thcond-mat.stat-mech
keywords krylovcomplexitychaosfieldgrowthboundcftsconformal
verification ladder T0 review T1 audit T2 compute T3 formal
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Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time ordered correlator (OTOC). We study Krylov complexity in conformal field theories by considering arbitrary 2d CFTs, free field, and holographic models. We find that the bound on OTOC provided by Krylov complexity reduces to bound on chaos of Maldacena, Shenker, and Stanford. In all considered examples including free and rational CFTs Krylov complexity grows exponentially, in stark violation of the expectation that exponential growth signifies chaos.

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Cited by 7 Pith papers

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

  1. Holographic timelike complexity for de Sitter

    hep-th 2026-07 conditional novelty 6.0 of 10

    Timelike subregion volume complexity in de Sitter grows exponentially early and diverges hyperfast at a maximal duration; near the SdS black hole horizon the divergence is replaced by slower, claimed-nonlinear growth.

  2. Krylov-Space Memory Cores

    hep-th 2026-07 conditional novelty 6.0 of 10

    Anomalous initial states in otherwise thermalizing models leave compact, stationary low-depth Krylov-space cores—regions with persistent fluctuations, Gibbs mismatch, and current activity—while generic states do not.

  3. Quantum Cosmology in Krylov Space: Complexity and Entropy

    gr-qc 2025-11 conditional novelty 6.0 of 10

    In a sharply peaked Gaussian state of a flat FLRW universe with a massless scalar clock, Krylov state complexity grows as σ²(φ−φ0)²/4 and operator complexity is exactly twice that, in both Wheeler-DeWitt and loop quan...

  4. Butterfly effect and $\textrm{T}\overline{\textrm{T}}$-deformation

    hep-th 2025-05 conditional novelty 6.0 of 10

    For T\bar{T}-deformed BTZ black holes, the butterfly velocity is v_B = sqrt(1 - 8π² μ/β²), exceeding the Mezei-Stanford bound for μ<0 while the Lyapunov exponent stays at the maximal value 2π/β.

  5. The Information Content of Krylov Observables: A Machine Learning Approach

    hep-th 2026-07 conditional novelty 5.0 of 10

    Under chaos, the normalized Wigner negativity χ(t) carries information about the fine return dynamics that spread complexity C(t) cannot, with the asymmetry gap rising from +0.33 to +0.77 across the integrable-to-GUE ...

  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.

  7. Generalized Krylov Complexity

    hep-th 2025-07 conditional novelty 5.0 of 10

    The paper defines generalized Krylov complexity for multi-generator unitary evolutions, computes it for U(1)xU(1), a U(1)xU(1) subgroup of SO(10), and SU(2), and introduces a weighted version.

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