(Non)renormalization of anomalous conductivities and holography

Abstract

Abstract:The chiral magnetic and the chiral vortical effects are recently discovered phenomena arising from chiral gauge and gravitational anomalies that lead to generation of electric currents in presence of magnetic field or vorticity. The magnitude of these effects is determined by the anomalous conductivities. These conductivities can be calculated by the linear response theory, and in the strong coupling limit this calculation can be carried out by the holographic techniques. Earlier calculations in case of conformal field theories indicate non-renormalization of these conductivities where the holographic calculation agrees with the free field limit. We extend this holographic study to non-conformal theories exhibiting mass-gap and confinement-deconfinement type transitions in a holographic model based on the analytic black hole solution of Gao and Zhang. We show that radiative corrections are also absent in these non-conformal theories confirming indirect arguments of Jensen et al. in a direct and non-trivial fashion. There are various indications in field theory that such radiative corrections should arise when contribution of dynamical gluon fields to the chiral anomaly is present. Motivated by this, we seek for such corrections in the holographic picture and argue that such corrections indeed arise through mixing of the background and its fluctuations with the axion and the one-form fields that couple to the flavor and probe gauge branes through the Wess-Zumino terms. These corrections are non-vanishing when the flavor to color ratio N f /N c is finite, therefore they are only visible in the Veneziano limit at large N c .

Horizon universality and anomalous conductivities

“…However, this is a very special theory, and one is immediately prompted to analyze the situation in a more general class of theories, in particular theories with a mass gap and running gauge coupling. Such a study was undertaken very recently by one of the authors together with A. Jansen in [48]. In that paper the anomalous conductivities were calculated in a holographic setting that is dual to a non-conformal theory that exhibits a confinement-deconfinement transition.…”

“…However, when the result is expressed in terms of physical quantities such as the chemical potential µ 5 and temperature T , one again finds that the anomalous conductivities attain their universal values. In particular the chiral magnetic conductivity is again precisely given by (1.3) [48].…”

“…The non-trivial result obtained in [48] prompted us to seek for a generic, backgroundindependent mechanism to explain the universality of anomalous conductivities in the holographic setting. In a sense, in this paper we seek for the holographic analog of the nonrenormalization theorems in field theory, that we summarized above.…”

“…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.…”

Spontaneous chiral symmetry breaking and the chiral magnetic effect for interacting Dirac fermions with chiral imbalance

“…Apart from spontaneous chiral symmetry breaking, anomalous transport coefficients can receive purely radiative corrections if the corresponding currents/charges are coupled to dynamical gauge fields [27][28][29]. Since in Weyl semimetals the interactions are naturally associated with electric charges, one can expect that even perturbatively the CME current might receive some corrections.…”