The quadratic growth of Krylov spread complexity in the BTZ black hole
- URL: http://arxiv.org/abs/2608.09922v1
- Date: Mon, 10 Aug 2026 17:58:15 GMT
- Title: The quadratic growth of Krylov spread complexity in the BTZ black hole
- Abstract summary: We provide an analysis of a partition-function construction of Krylov spread complexity for thermofield-double states.<n>We show that the classical limit is reliable only when taken after the complexity has been reconstructed.<n>The construction provides a systematic route from black-hole thermodynamics to Krylov dynamics.
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- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The boundary quantity that captures the growth of black-hole interiors quantified by holographic complexity remains unknown beyond 2d dilaton gravity. We provide a critical analysis of a partition-function construction of Krylov spread complexity for thermofield-double states that provides a dimension-independent boundary reconstruction from semiclassical holographic partition functions, while developing the present dynamical and bulk construction for the BTZ saddle. In the double-scaled Sachdev-Ye-Kitaev model, where exact and semiclassical results can be compared, we show that the classical limit is reliable only when taken after the complexity has been reconstructed; taking this limit at the level of individual Lanczos coefficients discards essential information. Applying the construction to a large-central-charge two-dimensional conformal field theory above the Hawking-Page temperature dual to a Bañados-Teitelboim-Zanelli black hole, we find an intermediate departure from early-time quadratic growth followed by behavior compatible with a return toward asymptotically quadratic growth, rather than the linear late-time behavior of the volume and the standard finite-functional complexity = anything class. We then match this boundary behavior to a generalized complexity = anything bulk object built from an infinite series of extrinsic-curvature invariants. The construction provides a systematic route from black-hole thermodynamics to Krylov dynamics and can naturally be extended to higher-dimensional holographic black holes.
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