Wilsonian RG-flow approach to holographic transport with momentum dissipation

Abstract

We systematically present a new approach for studying the coupled linear transport of holographic systems. In this approach, the set of equations for the linear perturbations can be reduced to a first-order nonlinear ordinary differential equation expressed as the radial (renormalization group) flow equation of the transport matrices. As an important application, we use this approach to compute the DC and AC conductivities of a holographic model with momentum dissipation, which can be easily read off from the nonlinear flow equations. This method also works for transport in the presence of an external magnetic field.arXiv:1702.05470v3 [hep-th]

Holographic RG flow of thermoelectric transport with momentum dissipation

“…The simple equation (28) is a matrix-form Riccati equation which has been derived previously in [21]. It should be noted that a key technique to build up Eq.…”

“…Recently, some of us studied the holographic RG flow for the strongly coupled systems with finite density and disorder [19][20][21], where the charge and energy transport are coupled and the transport coefficients are finite. The partial motivation of the work came from Ref.…”

“…[22], where the authors have not obtained the explicit flow when facing with the coupled transport. By introducing a square matrix of coupled sources, we illustrated that the coupled secondorder equations of linear perturbations can be reduced to a first-order matrix Riccati equation, which can have the direct physical meaning of the RG flow equation of twopoint correlation functions [21]. In addition, the boundary condition of the matrix Riccati equation can be simply determined by the regularity of correlation functions on the horizon.…”

“…In [19][20][21], however, the holographic RG flow was mainly used to study the DC transport on the boundary. In this paper, the first aim is to translate the matrix Riccati equation to the RG flow of AC thermoelectric conductivities, from which one can read the AC thermoelectric conductivities on the boundary.…”

Magnetothermoelectric DC conductivities from holography models with hyperscaling factor in Lifshitz spacetime

“…In presence of the magnetic field, the DC transport [54] gives more interesting results such as the Hall angle and the Nernst signal [55][56][57][58][59][60] if the magnetization currents are subtracted carefully to obtain radially independent quantities. A holographic Wilsonian renormalization group approach to momentum dissipated systems were also developed by one of the authors very recently [61].…”