Holography of Charged Dilaton Black Holes (0911.3586v4)

Abstract: We study charged dilaton black branes in $AdS_4$. Our system involves a dilaton $\phi$ coupled to a Maxwell field $F_{\mu\nu}$ with dilaton-dependent gauge coupling, ${1\over g^2} = f^2(\phi)$. First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques. The near horizon geometries in the simplest cases, where $f(\phi) = e^{\alpha\phi}$, are Lifshitz-like, with a dynamical exponent $z$ determined by $\alpha$. The black hole thermodynamics varies in an interesting way with $\alpha$, but in all cases the entropy is vanishing and the specific heat is positive for the near extremal solutions. We then compute conductivity in these backgrounds. We find that somewhat surprisingly, the AC conductivity vanishes like $\omega^2$ at T=0 independent of $\alpha$. We also explore the charged black brane physics of several other classes of gauge-coupling functions $f(\phi)$. In addition to possible applications in AdS/CMT, the extremal black branes are of interest from the point of view of the attractor mechanism. The near horizon geometries for these branes are universal, independent of the asymptotic values of the moduli, and describe generic classes of endpoints for attractor flows which are different from $AdS_2\times R^2$.

• The paper identifies extremal and near-extremal black brane solutions by analyzing dilaton-gauge couplings and Lifshitz-like near-horizon geometries.
• It demonstrates that near-extremal black branes exhibit vanishing entropy and positive specific heat, highlighting distinctive thermodynamic behavior.
• The study reveals that AC conductivity universally declines as ω² at zero temperature, linking holographic models to quantum critical phenomena.

Overview of "Holography Of Charged Dilaton Black Holes"

The paper "Holography Of Charged Dilaton Black Holes" by Goldstein et al. provides a detailed investigation into the holographic properties of charged dilaton black branes in a four-dimensional asymptotically anti-de Sitter (AdS) space. This work explores the intricate relationships between dilaton fields, gauge fields, and their coupling dependencies, emphasizing the nuances of extremal and near-extremal black brane solutions. The paper exemplifies a convergence of methods from both analytical and numerical realms to elucidate complex gravitational phenomena within the framework of the AdS/CFT correspondence.

Key Findings

One of the principal achievements of this research is the identification of solutions for extremal and near-extremal black branes by examining dilaton-black brane configurations. With a focus on cases where the gauge coupling $f(\phi) = e^{\alpha\phi}$, the near-horizon geometries exhibit Lifshitz-like characteristics, with the dynamical exponent $z$ determined by the parameter $\alpha$. This relationship reflects the broader attractor mechanism typically observed in black brane solutions, but under different universality conditions compared to standard models with an $AdS_2 \times R^2$ near-horizon geometry.

In terms of thermodynamics, the authors demonstrate an intriguing behaviour whereby the entropy vanishes, and the specific heat remains positive for near-extremal black branes. This result contrasts with other well-known charged black holes, where the large ground-state degeneracy poses challenges to aligning with thermodynamic principles.

A compelling outcome of the paper presented is the behavior of the AC conductivity within this black brane setting. At zero temperature, regardless of the value of $\alpha$, the AC conductivity diminishes as $\omega^2$. This finding indicates a level of universality not anticipated prior to this investigation, challenging previously held paradigms surrounding conductivity at quantum critical points.

Theoretical Implications & Future Directions

The results advance theoretical understanding within the broader context of the AdS/CMT (condensed matter theory) correspondence. The universality of results, especially the $\sigma(\omega) \sim \omega^2$ behavior in AC conductivity, serves as a pertinent conduit for linking holographic theories to condensed matter systems divisible by their ground state intricacies. This universality hints at deeper underpinnings within gravitational theories that are yet to be deciphered comprehensively.

The framework articulated by Goldstein et al. warrants further exploration into variants of the model, such as systems inclusive of axionic or multiple scalar fields which could enhance comprehension of holographic insulators or explore holographic superconductivity. Moreover, understanding finite temperature behavior as well as entanglement entropy in these models poses as consequential areas for subsequent examination.

While the paper provides a definitive stepping stone in modeling black branes with Lifshitz-like behavior, significant work remains in teasing out the distinctions between such theoretical constructs and observational phenomena, especially in terms of directly linking AdS/CFT models to actual condensed matter systems. Future research should endeavor to elucidate these connections and potentially link quantum critical models more directly to experimental observables.

In conclusion, the paper enriches the landscape of holographic studies with an intricate examination of charged dilaton black branes, posing new questions and establishing robust groundwork for advancing the dialogue between gravity theories and quantum critical matter.