Fermi-like Liquid From Einstein-DBI-Dilaton System
arXiv:1209.3559
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 dimensional bulk spacetime: $s\sim T^{\f{δ(d-1)-θ}{z}}_H$, where and are the dynamical exponent and temperature in the field theory, respectively. is related to the scaling violation exponent, whereas 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 , we show the linear temperature dependence of the specific heat and inverse quadratic temperature dependence of the resistivity for and , which resembles that of the Fermi-like liquid. Whereas for and gives us a solution that is conformal to , 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
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