Holographic RG flow of thermoelectric transport with momentum dissipation

Abstract

We construct the holographic renormalization group (RG) flow of thermoelectric conductivities when the translational symmetry is broken. The RG flow is probed by the intrinsic observers hovering on the sliding radial membranes. We obtain the RG flow by solving a matrix-form Riccati equation. The RG flow provides a high-efficient numerical method to calculate the thermoelectric conductivities of strongly coupled systems with momentum dissipation. As an illustration, we recover the AC thermoelectric conductivities in the Einstein-Maxwell-axion model. Moreover, in several homogeneous and isotropic holographic models which dissipate the momentum and have the finite density, it is found that the RG flow of a particular combination of DC thermoelectric conductivities does not run. As a result, the DC thermal conductivity on the boundary field theory can be derived analytically, without using the conserved thermal current.

Chaos and entanglement spreading in a non-commutative gauge theory

“…Therefore, the disruption of mutual information effectively provides a concrete realization of the butterfly effect in holographic theories [17]. This setup has been studied and extended in various directions in [53][54][55][56][57][58][59][60][61].…”

Chaos, diffusivity, and spreading of entanglement in magnetic branes, and the strengthening of the internal interaction

“…Some works in this direction include, for instance,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Duality and modular symmetry in the quantum Hall effect from Lifshitz holography

“…The result is given in equation (B.39), Interpreting the classical radial equation of motion as an RG equation was suggested in [58,59] and the relation to the c-theorem was studied in [60,61]. This version of the RG equation is obtained by expressing the radial equation of motion as a Riccati equation, [62]- [68]. An alternative formulation uses the radial Hamilton-Jacobi equation [69]- [71] (for the Hamilton-Jacobi equation in the context of Lifshitz geometry see [9]) and a Wilsonian approach was developed in [72]- [75] (it was argued in [76] that the classical radial equation of motion and the Wilsonian method are equivalent).…”