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Stripe Instabilities of Geometries with Hyperscaling Violation

We study the dynamical stripe instabilities on the geometries with hyperscaling violation in the IR, which asymptotically approach AdS_4 in the UV. The instabilities break the translational invariance spontaneously and are induced by the axion term ~ a F \wedge F in the bulk action. We first study the perturbation equations in the probe limit, and find that there is a strong correlation between the stripe instabilities caused by the axion term and parameters of the theories which determine the IR hyperscaling violation. Contrary to the IR AdS_2 case, the effect of the axion term for the stripe instabilities can be enhanced/suppressed at low temperature depending on the parameters. For a certain one-parameter family of the hyperscaling violation, we find the onset of the stripe instability analytically in the axion coupling tuned model. For more generic parameter range of hyperscaling violation, we study the instability onset by searching for the zero mode numerically on the full geometries. We also argue that quite analogous results hold, after taking into account the graviton fluctuation, i.e., beyond the probe limit.