Fermi-like Liquid From Einstein-DBI-Dilaton System

We show the existence of a gravity dual of Fermi-like liquid in the classical limit. This we demonstrate by finding a Lifshitz type of black hole solution to the Einstein-DBI-Dilaton system in 3+1 dimensional spacetime. In particular, for $z=2$, we show the linear and inverse quadratic temperature dependence of the specific heat and the longitudinal conductivity, respectively. However, we did not see the logarithmic structure of the entropy when the entangling region is of the strip type because the metric components does not obey the relation, $g^d-2_xx(r)g_rr(r)=1/r^2$, where $d$ is the dimension of the field theory. We also find a new class of electrically charged black hole solution to the Einstein-DBI system in arbitrary spacetime dimension as well as a dyonic black hole in 3+1 dimensional spacetime.