Fermi-like Liquid From Einstein-DBI-Dilaton System

Understand

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: $s\sim T^{\f{\delta(d-1)-\theta}{z}}_H$, 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.