Intermediate scalings in holographic RG flows and conductivities

TL;DR

This paper constructs numerical holographic RG flow solutions with intermediate hyperscaling violation and Lifshitz scaling, revealing new ground states and analyzing optical conductivity scaling behaviors at zero temperature.

Contribution

It introduces a new class of finite density domain-wall solutions interpolating between two AdS4 fixed points with intermediate scalings, and studies their conductivity properties.

Findings

Identified intermediate hyperscaling violation regimes in holographic RG flows.

Found that IR fixed points avoid extensive zero-temperature entropy.

Demonstrated conductivity scaling controlled by IR and intermediate regimes.

Abstract

We construct numerically finite density domain-wall solutions which interpolate between two $AdS_4$ fixed points and exhibit an intermediate regime of hyperscaling violation, with or without Lifshitz scaling. Such RG flows can be realized in gravitational models containing a dilatonic scalar and a massive vector field with appropriate choices of the scalar potential and couplings. The infrared $AdS_4$ fixed point describes a new ground state for strongly coupled quantum systems realizing such scalings, thus avoiding the well-known extensive zero temperature entropy associated with $AdS_2 \times \mathbb{R}^2$. We also examine the zero temperature behavior of the optical conductivity in these backgrounds and identify two scaling regimes before the UV CFT scaling is reached. The scaling of the conductivity is controlled by the emergent IR conformal symmetry at very low frequencies, and by the intermediate scaling regime at higher frequencies.