Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.
Hidden singularities and closed timelike curves in a proposed dual for Lifshitz-Chern-Simons gauge theories
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abstract
We point out that the metrics recently proposed by K. Balasubramanian and J. McGreevy \cite{BalaMcGreevyLifshitz} as gravitational duals to Lifshitz Chern-Simons gauge theories contain both a hidden null singularity and a region of closed timelike curves accessible to asymptotic observers. Like the singularity in the original Liftshitz spacetime given by Kachru, Liu, and Mulligan, this singularity does not include large $\alpha'$ or $g_s$ corrections and hence appears to be singular in string theory as well as classically.
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Holographic Krylov Complexity with Lifshitz Scaling and Hyperscaling Violation
Krylov complexity grows quadratically in pure Lifshitz backgrounds and its late-time exponent is controlled by the hyperscaling violation parameter, with a special oscillatory regime.