Holographic Krylov Complexity with Lifshitz Scaling and Hyperscaling Violation

Abstract:Following the holographic proposal that identifies the growth rate of Krylov complexity with the proper radial momentum of an infalling massive probe, we study Krylov complexity in Lifshitz and hyperscaling-violating backgrounds. For pure Lifshitz geometries, we find quadratic complexity growth for all values of the dynamical exponent. For hyperscaling-violating backgrounds, we show that the hyperscaling-violating exponent directly controls the late-time growth exponent, with a special limiting case exhibiting oscillatory behavior with a logarithmic envelope. We also extend our analysis to top-down string constructions, confirming the robustness of the scaling behaviors obtained in the bottom-up approach. Our analysis establishes that the momentum-Krylov correspondence extends naturally to non-relativistic holographic settings and remains well-defined despite the causal pathologies of Lifshitz spacetimes.

arXiv:2606.31724 [hep-th]

(or arXiv:2606.31724v2 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2606.31724 Focus to learn more arXiv-issued DOI via DataCite

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