Holography of charged dilatonic black branes at finite temperature

TL;DR

This work analyzes four-dimensional AdS Einstein-Maxwell-dilaton gravity with non-minimal couplings and potentials to obtain electrically and dyonically charged black branes with scalar hair. By combining numerical construction of CDBBs and DDBBs with holographic transport calculations, it reveals rich finite-temperature phenomena such as Drude-like AC conductivity, nonmonotonic DC behavior, Hall responses, and synchrotron resonances, as well as universal zero-temperature scaling $\sigma_{AC}(\omega) \sim \omega^2$ (and $\sigma_{DC}(T)\sim T^2$ for many cases). The results show a coherent interpolation between metal-like transport at finite $T$ and strongly repulsive charged plasmas at $T\to0$, governed by the IR behavior of $f(\phi)$ and $V(\phi)$. The dyonic sector adds a magnetic-field–driven phase structure with a critical line $T_c(B)$ and diamagnetic responses, offering a broad holographic framework for strongly coupled condensed-matter analogs and magnetotransport phenomena.

Abstract

We investigate bulk and holographic features of finite-temperature black brane solutions of 4D anti-de Sitter Einstein-Maxwell-dilaton-gravity (EMDG). We construct, numerically, black branes endowed with non trivial scalar hairs for broad classes of EMDG. We consider both exponential and power-law forms for the coupling functions, as well as several charge configurations: purely electric, purely magnetic and dyonic solutions. At finite temperature the field theory holographically dual to these black brane solutions has a rich and interesting phenomenology reminiscent of electron motion in metals: phase transitions triggered by nonvanishing VEV of scalar operators, non-monotonic behavior of the electric conductivities as function of the frequency and of the temperature, Hall effect and sharp synchrotron resonances of the conductivity in presence of a magnetic field. Conversely, in the zero temperature limit the conductivities for these models show a universal behavior. The optical conductivity has a power-law behavior as a function of the frequency, whereas the DC conductivity is suppressed at small temperatures.

Figures (14)

• Figure 1: The scalar operator ${\cal O}_+$ as a function of the temperature for several values of $\alpha$ when $\beta=-2$ (left panels) and several values of $\beta$ when $\alpha=2$ (right panels). In the upper panels and lower panels we have used models with $f(\phi)=e^{\alpha\phi}$ and with linear coupling $f(\phi)=1+\alpha\phi$, respectively. Results are qualitatively similar in the two cases.
• Figure 2: Left panel: scalar condensate for models with a power-law coupling function $f(\phi)=1+\alpha\phi^m\,$ as a function of the temperature. Markers correspond to the temperatures considered in Fig. \ref{['fig:PL_cond2']} (see Sect. \ref{['sect:zerot']}). Right panel: Difference in free energy between the AdS-RN black brane and the hairy black brane, $\Delta F=F_{RNBB}-F_{HBB}$ as a function of the temperature. When $\Delta F>0$ the dilatonic solution is energetically favored. We have considered $\alpha=2$ and $\beta=-2$.
• Figure 3: Left panels: real part of the AC conductivity as a function of the frequency for different temperatures for models with exponential coupling function $f(\phi)$ and potential $V(\phi)$ given by Eqs. (\ref{['f51']}). Right panels: DC conductivity as a function of the temperature for several values of $\alpha$. Top, middle and bottom panels refer to $\beta=0$, $\beta=-2$ and $\beta=\beta_{BF}=-9/4$ respectively.
• Figure 4: Left panels: real part of the AC conductivity as a function of the frequency for different temperatures for models with linear coupling function $f(\phi)$. $f(\phi)$ and $V(\phi)$ are given by Eq. (\ref{['f6']}) . Right panels: DC conductivity as a function of the temperature for several values of $\alpha$. Top, middle and bottom panels refer to $\beta=0$, $\beta=-2$ and $\beta=\beta_{BF}=-9/4$ respectively.
• Figure 5: Left panel: Real part of the conductivity as a function of the frequency for models with power-law coupling function $f(\phi)$ and potential $V(\phi)$ are given by Eq. (\ref{['f_powerlaw']}). We show $Re[\sigma]$ for different values of $m$ and for $T\sim0.015\sqrt{\rho}$ in the stable branch. Right panel: DC conductivity as a function of the temperature. Notice that we show the conductivity for solutions both in the stable and in the unstable branch.