We study the transport coefficients, including the conductivities and shear viscosity of the nonrelativistic field theory dual to the Lifshitz black brane with multiple $U(1)$ gauge fields by virtue of the gauge/gravity duality. Focusing on the case of double $U(1)$ gauge fields, we systematically investigate the electric, thermal, and thermoelectric conductivities for the dual nonrelativistic field theory. In the large frequency regime, we find a nontrivial power law behavior in the electric alternating current conductivity when the dynamical critical exponent $z>1$ in ($2+1$)-dimensional field theory. The relations between this novel feature and the “symmetric hopping model” in condensed matter physics are discussed. In addition, we also show that the Kovtun-Starinets-Son bound for the shear viscosity to the entropy density is not violated by the additional $U(1)$ gauge fields and dilaton in the Lifshitz black brane.

• Received 11 March 2013

DOI:https://doi.org/10.1103/PhysRevD.87.086005