On Holography with Hyperscaling Violation

TL;DR

The paper investigates strongly coupled theories with hyperscaling violation using gravity duals that feature a Lifshitz-like metric with exponents $z$ and $\theta$ and a double Wick-rotated anisotropic background, focusing on entanglement entropy and various string probes as tools to read off field-theoretic properties.By applying holographic entanglement entropy methods and open/closed string analyses, it identifies conditions under which the entropy exhibits logarithmic area-law violations (notably at $\theta = d-1$ for anisotropic strips and at $\theta = d+z-2$ for isotropic strips), signaling potential Fermi-surface-like physics and intermediate-energy effective descriptions.The results show rich, direction-dependent dynamics: Wilson-loop potentials can be power-law or logarithmic depending on parameter relations, drag forces arise even at zero temperature due to anisotropy, rotating/open-string configurations yield worldsheet horizons and energy-loss rates, and closed-string configurations reveal distinctive E–S relations and quantization patterns, all highlighting the role of hyperscaling violation in holographic observables.Overall, the study provides a detailed map of how hyperscaling-violating backgrounds influence entanglement, external-object response, and string spectra, with implications for modeling nonrelativistic or strongly correlated systems in an intermediate-energy regime; finite-temperature extensions are suggested as future work.

Abstract

We study certain features of strongly coupled theories with hyperscaling violation by making use of their gravitational duals. We will consider models with an anisotropic scaling in time or in one of spatial directions. In particular for the case where the anisotropic scaling is along a spatial direction we will compute the holographic entanglement entropy and show that for specific values of the parameters it exhibits a logarithmic violation of the area law. We will also probe the backgrounds by different closed and open strings which in turn can be used to read, for example, effective potential of an external object, drag force and etc.

Figures (3)

• Figure 1: $\rho$ as a function of $r$ for the cases of $z=2$ and $\theta=\frac{3d}{4},\frac{d}{2},0$ which are shown by dashed, dotted and thin curves, respectively. In order to compare our results with that of AdS case ($z=1, \theta=0$), we have also plotted this case which is shown by a thick curve. Note that to solve the equation we have set the initial date as $\omega=\Pi_\phi=1$.
• Figure 2: Here we have plotted $\rho$ as a function of $\phi$ for the cases of $z=1, \theta=0$ (left), $z=2, \theta=0$ (middle) and $z=2, \theta= \frac{d}{2}$ (right). The function is projected in to $x_1-x_2$ plane, where $\rho$ and $\phi$ are polar coordinates of this place. Here we have set $\omega=\Pi_\phi=1$.
• Figure 3: Here we have plotted $\rho_{*}$ as a function of $L=\Pi_\phi\omega$ for the case of $z=2, \theta=0$. Essentially this is the energy loss rate in terms of the radius of circle the external object moves.