Properties of CFTs dual to Charged BTZ black-hole

TL;DR

This paper investigates the properties of strongly coupled 1+1 dimensional conformal field theories with background charge via their dual charged BTZ black hole, analyzing correlators, conductivity, and fermionic behavior at zero and finite temperature.

Contribution

It provides a detailed analysis of correlators and fermionic properties in charged CFTs using holography, revealing non-Fermi-liquid behavior and finite spectral density features.

Findings

Correlation between log periodicity and spectral density of gapless modes

Vanishing real part of conductivity as frequency approaches zero

Fermion Green's function exhibits non-Fermi-liquid quasiparticle peaks

Abstract

We study properties of strongly coupled CFT's with non-zero background electric charge in 1+1 dimensions by studying the dual gravity theory - which is a charged BTZ black hole. Correlators of operators dual to scalars, gauge fields and fermions are studied at both T=0 and $T\neq 0$. In the $T=0$ case we are also able to compare with analytical results based on $ AdS_2$ and find reasonable agreement. In particular the correlation between log periodicity and the presence of finite spectral density of gapless modes is seen. The real part of the conductivity (given by the current-current correlator) also vanishes as $\omega \rightarrow 0$ as expected. The fermion Green's function shows quasiparticle peaks with approximately linear dispersion but the detailed structure is neither Fermi liquid nor Luttinger liquid and bears some similarity to a "Fermi-Luttinger" liquid. This is expected since there is a background charge and the theory is not Lorentz or scale invariant. A boundary action that produces the observed non-Luttinger-liquid like behavior ($k$-independent non-analyticity at $\omega=0$) in the Greens function is discussed.