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: \( s\sim T_H^{{\frac{{\delta \left( {d-1} \right)-\theta }}{z}}} \), where z and T H are the dynamical exponent and temperature in the field theory, respectively. θ is related to the scaling violation exponent, whereas δ 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, θ = 0 and δ = 1, which resembles that of the Fermi-like liquid. Whereas for z = 2, θ = −2 and δ = 0 gives us a solution that is conformal to AdS 2 ⊗ 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.
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Pal, S.S. Fermi-like liquid from Einstein-DBI-dilaton system. J. High Energ. Phys. 2013, 7 (2013). https://doi.org/10.1007/JHEP04(2013)007
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DOI: https://doi.org/10.1007/JHEP04(2013)007