Holographic quantum liquids in 1+1 dimensions

TL;DR

We construct and analyze a holographic 1+1 dimensional quantum liquid from a D3-D3 defect CFT in an AdS-Schwarzschild background with finite density. The work derives the thermodynamics, introduces gauge-counterterms to handle 1+1D log divergences, and computes bosonic and fermionic spectral functions, revealing a dissipationless zero-sound mode alongside a purely dissipative mode. The mixed bosonic sector exhibits coupled excitations with a robust massless mode persisting under mixing, and the fermionic sector yields an effective Luttinger parameter K≈0.22–0.28, suggesting non-Fermi liquid behavior in this low-dimensional holographic setup. Conductivity analyses show characteristic high-temperature linear-in-T behavior and frequency-dependent signatures consistent with a Luttinger-liquid-like transport, highlighting the distinctive features of 1+1D holographic quantum liquids.

Abstract

In this paper we initiate the study of holographic quantum liquids in 1+1 dimensions. Since the Landau Fermi liquid theory breaks down in 1+1 dimensions, it is of interest to see what holographic methods have to say about similar models. For theories with a gapless branch, the Luttinger conjecture states that there is an effective description of the physics in terms of a Luttinger liquid which is specified by two parameters. The theory we consider is the defect CFT arising due to a probe D3 brane in the AdS Schwarzschild planar black hole background. We turn on a fundamental string density on the worldvolume. Unlike higher dimensional defects, a persistent dissipationless zero sound mode is found. The thermodynamic aspects of these models are considered carefully and certain subtleties with boundary terms are explained which are unique to 1+1 dimensions. Spectral functions of bosonic and fermionic fluctuations are also considered and quasinormal modes are analysed. A prescription is given to compute spectral functions when there is mixing due to the worldvolume gauge field. We comment on the Luttinger conjecture in the light of our findings.