Zero Sound in Effective Holographic Theories

TL;DR

This paper explores zero sound modes and Fermi-liquid-like behavior in effective holographic theories with Einstein-Maxwell-Dilaton actions, analyzing thermodynamics, Green's functions, and conductivity in various dimensions.

Contribution

It provides a detailed analysis of zero sound and Fermi-liquid features in holographic models with anisotropic scaling, including conditions for linear specific heat and quasi-particle excitations.

Findings

Identification of zero sound modes in holographic theories.

Conditions for linear specific heat in probe D-brane setups.

Observation of quasi-particle excitations in certain parameter regimes.

Abstract

We investigate zero sound in $D$-dimensional effective holographic theories, whose action is given by Einstein-Maxwell-Dilaton terms. The bulk spacetimes include both zero temperature backgrounds with anisotropic scaling symmetry and their near-extremal counterparts obtained in 1006.2124 [hep-th], while the massless charge carriers are described by probe D-branes. We discuss thermodynamics of the probe D-branes analytically. In particular, we clarify the conditions under which the specific heat is linear in the temperature, which is a characteristic feature of Fermi liquids. We also compute the retarded Green's functions in the limit of low frequency and low momentum and find quasi-particle excitations in certain regime of the parameters. The retarded Green's functions are plotted at specific values of parameters in $D=4$, where the specific heat is linear in the temperature and the quasi-particle excitation exists. We also calculate the AC conductivity in $D$-dimensions as a by-product.