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 .
Highlights
Of an external magnetic field B, a combination of QCD and QED anomalies result in generation of an electric current parallel to B
Authors of [3] presented an independent derivation of (1.1) by the physical requirement of non-negative entropy current. In this derivation anomalous transport was generalized to include the effects of relatives of the Chiral Magnetic Effect (CME) such as the Chiral Vortical Effect (CVE), that is, generation of an electric current in the presence of vorticity due to the gravitational anomaly [10, 11]
In this paper we address the question of renormalization of chiral magnetic and vortical conductivities in electric and heat currents and related in the holographic approach in a gravitational setting dual to a non-conformal, confining QFT at finite temperature
Summary
In [49] the authors found the following analytic solution to (2.1) for the following specific choices of the potentials:. One can think of the integration constant b as related to the dynamically generated mass scale in the dual theory, i.e. ΛQCD ∝ b. A generic solution to the Einstein-Maxwell-dilaton theory should correspond to a dual field theory that is characterized by three parameters in the grand canonical ensemble: ΛQCD, T and μ. The first option as it is more natural in application to QCD-like theories.13 In this specific model the chemical potential and the mass gap ΛQCD will be tied to each other. This unphysical fact is the price one has to pay to work with an analytic solution, which is a crucial technical simplification for the calculations . This relation clarifies the physical meaning of the integration constant c and it will be useful below when we calculate the energy and the free energy of the solution
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