We determine the structure of the hydrodynamics with conserved current, using the gauge/gravity duality of charged black-hole background. It turns out that even in the presence of the external electromagnetic field at the boundary, bulk Einstein equa
tion is equivalent to the boundary conservation of energy momentum tensor and that of current. As a consequence, the thermal conductivity and electric conductivity are calculated in terms of the parameters of the fundamental theory. We find that Wiedermann-Franz law hold with Lorentz number $1/e^2$
Recently the partial wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive explicitly
radial WKB series in the angular momentum cutoff for $d=2,3,4$ and 5 ($d$ is the spacetime dimension), which has uniform validity irrespectively of any specific values assumed for other parameters. Utilizing this series, precision evaluation of the renormalized functional determinant is possible with a relatively small number of low partial wave contributions determined separately. We illustrate the power of this scheme in numerically exact evaluation of the prefactor (expressed as a functional determinant) in the case of the false vacuum decay of 4D scalar field theory.
Our previously-developed calculational method (the partial wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be particularly effecti
ve when it is used in conjunction with a systematic WKB series for the large partial wave contribution to the effective action. By comparing these numerically exact calculations against the predictions based on the large mass expansion and derivative expansion, we discuss the validity ranges of the latter approximation methods.
