Holographic DC conductivity and Onsager relations

Abstract

Within holography the DC conductivity can be obtained by solving a system of Stokes equations for an auxiliary fluid living on the black hole horizon. We show that these equations can be derived from a novel variational principle involving a functional that depends on the fluid variables of interest as well as the time reversed quantities. This leads to simple derivation of the Onsager relations for the conductivity. We also obtain the relevant Stokes equations for bulk theories of gravity in four dimensions including a ϑF ∧ F term in the Lagrangian, where ϑ is a function of dynamical scalar fields. We discuss various realisations of the anomalous Hall conductivity that this term induces and also solve the Stokes equations for holographic lattices which break translations in one spatial dimension.

S-duality, entropy function and transport in AdS4/CMT3

“…We move on to the heat current, considered (also with a topological term) from the point of view of transport coefficients in the presence of magnetization in [6]. The heat current itself was defined in [3].…”

“…The generalized Stokes equations are invariant under an S-duality transformation of the horizon data [2,6]. Indeed, consider the transformation…”

“…One is led to consider a system of gravity plus Abelian vector field, plus a scalar that defines the kinetic functions appearing in the Lagrangian. Transport in such systems has been considered in many papers, but here we will be mostly interested in the methods used in [1][2][3][4][5][6][7]. The question we want to ask is, what is the effect of S-duality on this bulk holographic theory on the transport coefficients for the holographic dual field theory?…”

Particle-vortex duality and theta terms in AdS/CMT applications

“…The AdS/CFT calculations using the membrane paradigm will be based on the original work of Iqbal and Liu [24] (see also [25]), as well as Kovtun, Son and Starinets [26] We we also treat quantum corrections to the gravitational action and the Maxwell and scalar fields in it, following the formalism of [27,28]. Within this context, the formalism for computing conductivities is based on [29,30]. We will also consider the membrane paradigm for the fluid/gravity correspondence defined in [31] (an early formulation is [32]).…”

Building magnetic hysteresis in holography

“…As a preliminary study toward ferromagnetism, we will consider a simple model to build spontaneous magnetization and the hysteresis curve using gauge/gravity duality [1,2] . In earlier studies, magnetized systems have already attracted much attention and have been studied numerous times in the holographic approach, e.g, [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”