Abstract
We study the magnetoconductivity induced by the axial anomaly via the chiral magnetic effect in strongly coupled holographic models. An important ingredient in our models is that the axial charge is non-conserved beyond the axial anomaly. We achieve this either by explicit symmetry breaking via a non-vanishing non-normalisable mode of an axially charged scalar or using a Stuckelberg field to make the AdS-bulk gauge field massive. The DC magnetoconductivites can be calculated analytically. They take a universal form in terms of gauge field mass at the horizon and quadratic dependence on the magnetic field. The axial charge relaxation time grows linearly with magnetic field in the large B regime. Most strikingly positive magnetoconductivity is still present even when the relaxation times are short τ5 ≈ 1/(πT) and the axial charge can not be thought of as an approximate symmetry. In the U(1) A explicit breaking model, we also observe that the chiral separation conductivity and the axial magnetic conductivity for the consistent axial current vanish in the limit of strong symmetry breaking.
Highlights
Background in the probe limitSince we are going to study the magneto response, we turn on a background magnetic field in the U(1)V sector
We study the magnetoconductivity induced by the axial anomaly via the chiral magnetic effect in strongly coupled holographic models
For our purpose of breaking the axial charge conservation symmetry explicitly at the boundary, we focus on solutions with nonzero M, which sources this explicit breaking of axial charge conservation
Summary
In this paper we shall turn on a non-zero source associated to the dual scalar operator in order to break the U(1)A symmetry explicitly, which introduces an axial charge dissipation mechanism in our system. With the mass term for the scalar field, the dual scalar operator has a scaling dimension ∆Φ = 2 ± 4 + m2s and to make sure that the scaling dimension of the axial current does not change, m2s has to be negative and above the BF bound The conformal dimension of the dual scalar operator is 3 and the corresponding source is of dimension 1. This reminds us to the four dimensional free massive fermion systems. Since the covariant current is the one which has been widely used in the framework of hydrodynamics, we will use the covariant current in most parts of our paper and briefly comment on the behaviour of the consistent current in subsection 2.3
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