Fermi-like Liquid From Einstein-DBI-Dilaton System

Abstract

We have obtained an expression of the entropy density depending on the scale transformation of the spatial directions in the field theory. It takes the following form in $d+1$ dimensional bulk spacetime: $s\sim T^{\f{δ(d-1)-θ}{z}}_H$, where $z$ and $T_H$ are the dynamical exponent and temperature in the field theory, respectively. $\theta$ is related to the scaling violation exponent, whereas $\delta$ gives us the information about the scaling behavior of the spatial field theoretic direction. This we demonstrate by finding solutions to the Einstein-DBI-dilaton system in generic spacetime dimensions. Upon restricting to $d=3$, we show the linear temperature dependence of the specific heat and inverse quadratic temperature dependence of the resistivity for $z=2,\theta =0$ and $\delta =1$, which resembles that of the Fermi-like liquid. Whereas for $z=2,\theta =-2$ and $\delta =0$ gives us a solution that is conformal to $Ad{S}_2\otimes R^2$, which resembles with the non-Fermi-like liquid. Moreover, it shows the logarithmic violation of the entanglement entropy when the entangling region is of the strip type.

1+39 pages, LATEX, v2: Connection with the BI black holes made, associated references and acknowledgment added, v3: Solutions in arbitrary spacetime both at UV and IR, especially the scale symmetry violating solution, improved presentation, ref added, v4: More improvements and accepted for publication in JHEP

References in corpus (13)

• Towards a derivation of holographic entanglement entropy
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Non-relativistic holography
• A Non-Fermi Liquid from a Charged Black Hole; A Critical Fermi Ball
• Electron stars for holographic metallic criticality
• Thermodynamics and phase transitions in the Born-Infeld-anti-de Sitter black holes
• Zero Sound from Holography
• Electron star birth: A continuous phase transition at nonzero density
• Comments on Fermi Liquid from Holography
• Holographic Fermi surfaces and bulk dipole couplings
• A Note on Charged Black Holes in AdS space and the Dual Gauge Theories
• Generalized Attractors in Five-Dimensional Gauged Supergravity
• Entanglement Entropy at Finite Density from Extremal Black Holes