Anomalous magnetoresponse and the Stückelberg axion in holography

Abstract

We study the magnetoresponse with nonconserved currents in holography. Nonconserved currents are dual to massive vector fields in anti-de Sitter (AdS). We introduce the mass in a gauge invariant way via the Stückelberg mechanism. In particular we find generalizations of the chiral magnetic effect, the chiral separation effect and the chiral magnetic wave. Since the associated charge is not conserved we need to source it explicitly by a coupling, the generalization of the chemical potential. In this setup we find that in general the anomalous transport phenomena are still realized. The values we find for nonzero mass connect continuously to the values of the anomalous conductivities of the consistent currents, i.e. the proper chiral magnetic effect vanishes for all masses (as it does for the consistent current in the zero mass case) whereas the chiral separation effect is fully present. The generalization of the chiral magnetic wave shows that for small momenta there is no propagating wave but two purely absorptive modes (one of them diffusive). At higher momenta we recover the chiral magnetic wave as a combination of the two absorptive modes. We also study the negative magneto resistivity and find that it grows quadratically with the magnetic field. The chiral magnetic wave and the negative magneto resistivity are manifestations of the chiral magnetic effect that takes place when the (nonconserved) charge is allowed to fluctuate freely in contrast to the case where the charge is fixed by an explicit source. Since the (classical) Uð1Þ A symmetry of QCD is not at all a symmetry at the quantum level we also argue that using massive vectors in AdS to model the axial singlet current might result in a more realistic holographic model of QCD and should be a good starting point to investigate the dynamics of anomalous transport in the strongly coupled quark gluon plasma.

Collective modes of chiral kinetic theory in a magnetic field

“…Alternatively, D anom may also be interpreted as a diffusion constant arising from the collective motion (drift) of chiral charges by chiral magnetic wave of the speed v B with a relaxation rate τ We note that these features are also found in a recent work in AdS/CFT correspondence [39] where the authors introduced axial charge breaking (corresponding to inter-chiral transitions we consider) via a mass term for the axial gauge field in the holographic 5 dimensional space-time.…”

Horizon universality and anomalous conductivities

“…Indeed this mechanism was proposed as a holographic dual to anomalous theories with type II anomalies -that is, with a gluonic contribution to the anomaly equation (a 3 = 0 in equation (1.2))-in [48] and [55]. The bulk axion is dual to a theta-term in the field theory action.…”

“…The idea is that coupling χ to the axial field induces a non-trivial expectation value for Tr G ∧ G in (1.2). The anomaly term associated with this expectation value, a 3 , then induces a modification of the result for the anomalous transport coefficients [48,55]. In holographic constructions of QCD m A is usually proportional to the number of flavors in the theory, and one needs a calculation in the Veneziano limit to see the effect of this term [56].…”

Anomalous Transport: Holography, QCD and (Semi-)Metals

“…The magnetic field exists only for a short time span and the non-renormalization theorems are known not to hold when dynamical gauge field [19,23,24] (such as the gluon field of QCD) are present in contrast to external classical fields we have considered up to now. A holographic toy model and a first study of anomaly related transport in such a situation has recently been performed in [25,26]. Another point is somewhat clearer: there is no evidence for an axial gauge potential in nature.…”