Chaos in hyperscaling violating Lifshitz theories

• URL: http://arxiv.org/abs/2411.09667v1
• Date: Thu, 14 Nov 2024 18:37:28 GMT
• Title: Chaos in hyperscaling violating Lifshitz theories
• Authors: Nikesh Lilani,
• Abstract summary: We holographically study quantum chaos in hyperscaling-violating Lifshitz (HVL) theories (with charge) We present a detailed computation of the out-of-time ordered correlator (OTOC) via the shockwave analysis in the bulk HVL geometry with a planar horizon topology. We also analyze in detail, the behavior of $v_B$ with respect to the dynamical critical exponent (z), hyperscaling-violating parameter ($theta$), charge (Q) and the horizon radius ($r_h$)
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• Abstract: We holographically study quantum chaos in hyperscaling-violating Lifshitz (HVL) theories (with charge). Particularly, we present a detailed computation of the out-of-time ordered correlator (OTOC) via the shockwave analysis in the bulk HVL geometry with a planar horizon topology. We also compute the butterfly velocity ($v_{B}$) using the entanglement wedge reconstruction and find that the result matches the one obtained from shockwave analysis. Furthermore, we analyze in detail, the behavior of $v_{B}$ with respect to the dynamical critical exponent (z), hyperscaling-violating parameter ($\theta$), charge (Q) and the horizon radius ($r_{h}$). We interestingly find non-monotonic behavior of $v_{B}$ with respect to z (in the allowed region and for certain (not all) fixed, permissible values of $\theta$, Q and $r_{h}$) and $\theta$ (in the allowed region and for certain (not all) fixed, permissible values of z, Q and $r_{h}$). Moreover, $v_{B}$ is found to monotonically decrease with an increase in charge (for all permissible, fixed values of z, $\theta$ and $r_{h}$), whereas it is found to monotonically increase with $r_{h}$ (for all fixed, permissible values of z, $\theta$ and Q). Unpacking these features can offer some valuable insights into the chaotic nature of HVL theories.

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