Probing holographic semi-local quantum liquids with D-branes

TL;DR

This paper investigates the dynamics of probe D-branes in semi-local holographic backgrounds, analyzing thermodynamics, Green's functions, and conductivity to understand quantum liquids with potential Fermi or Bose liquid behavior.

Contribution

It provides a detailed analysis of probe D-branes in semi-local backgrounds, revealing conditions for ground states, thermodynamic behavior, and quasi-particle excitations, extending holographic models of quantum liquids.

Findings

Entropy density vanishes at extremality, indicating a potential ground state.

AC conductivity exhibits different scaling behaviors depending on the ratio d/η.

No quasi-particle excitations are present when d/η ≥ 2.

Abstract

We study dynamics of probe D-branes in $(d+2)$-dimensional background with general semi-locality. The background is characterized by a parameter $\eta$ and is conformal to $AdS_{2}\times\mathbb{R}^{d}$. We discuss thermodynamics of the probe D-branes and find that the entropy density is vanishing in the extremal limit, which indicates that the background may correspond to the true ground state of the system. We also clarify the conditions under which the specific heat matches to the behavior of a Fermi liquid or a Bose liquid. We calculate the current-current and density-density retarded Green's functions, from which we can obtain the AC conductivity and the zero sound mode. The AC conductivity scales as $\omega^{-1}$ when $d/\eta<2$ and $\omega^{-2\eta/d}$ when $d/\eta>2$, while it contains a logarithmic term in $\omega$ when $d/\eta=2$. We also observe that there is no quasi-particle excitation when $d/\eta\geq2$ and classify the conditions under which the quasi-particle description is valid when $d/\eta<2$.