Anomalous transport and holographic momentum relaxation

Christian Copetti,Eugenio Megías,Jorge Fernández-Pendás,Karl Landsteiner

doi:10.1007/jhep09(2017)004

Abstract

The chiral magnetic and vortical effects denote the generation of dissipationless currents due to magnetic fields or rotation. They can be studied in holographic models with Chern-Simons couplings dual to anomalies in field theory. We study a holographic model with translation symmetry breaking based on linear massless scalar field backgrounds. We compute the electric DC conductivity and find that it can vanish for certain values of the translation symmetry breaking couplings. Then we compute the chiral magnetic and chiral vortical conductivities. They are completely independent of the holographic disorder couplings and take the usual values in terms of chemical potential and temperature. To arrive at this result we suggest a new definition of energy-momentum tensor in presence of the gravitational Chern-Simons coupling.

Highlights

We study a holographic model with translation symmetry breaking based on linear massless scalar field backgrounds
The purpose of this work is to check this in a simple explicit example, and we find that the CME and CVE are completely insensitive to the holographic disorder parameters
We found the new form by allowing the extrinsic curvature to vary independently near the boundary

Summary

Holographic momentum relaxation

We will base our considerations on the Stuckelberg mechanism using massless scalar fields (Goldstone modes of translation symmetry breaking). For each spatial dimension we introduce a scalar field XI , I = 1, . In addition we introduce a Chern-Simons action and counterterm. The gauge variation of the Chern-Simons action is a total derivative and leads to the anomaly δS = d4x√−γǫijkl α 3. Ra bij is the intrinsic curvature on the boundary This form holds for finite holographic cutoff only if the counterterm SCSK is added to the action [6]. Momentum dissipation is implemented by giving the scalar fields a linear profile (note that there are only derivative couplings of XI ). Because the scalars couple only through derivatives, the field equations and solutions will still be formally translational invariant. In this simple theory the background does not depend on the charge disorder coupling J. It reduces to the solution found in [14]

Holographic energy-momentum tensor

DC conductivity We introduce the small perturbations

Chiral vortical conductivity

Conclusion and discussion