Dynamical gauge fields and anomalous transport at strong coupling

Abstract

Anomalous transport coefficients are known to be universal in the absence of dynamical gauge fields. We calculate the corrections to these universal values due to dynamical gluon fields at strong coupling, at finite temperature and finite density, using the holographic duality. We show that the consistent chiral magnetic and chiral vortical currents receive no corrections, while we derive a semi-analytic formula for the chiral separation conductivity. We determine these corrections in the large color, large flavor limit, in terms of a series expansion in the anomalous dimension ∆ of the axial current in terms of physical parameters ∆, temperature, electric and chiral chemical potentials and the flavor to color ratio N f Nc . Our results are applicable to a generic class of chiral gauge theories that allow for a holographic description in the gravity approximation. We also determine the dynamical gluon corrections to the chiral vortical separation current in a particular example in the absence of external axial fields. arXiv:1806.07138v2 [hep-th] 26 Feb 2019 R α βµν is the Riemann tensor of the background geometry. The anomaly coefficients a 1 , a 2 and a 4 are examples of the first type whereas a 3 is of the second type. All are known to be one loop exact [18].The purpose of our paper is to explore the contribution of the second, dynamical, type of anomalies to anomalous transport in strongly coupled chiral gauge theories. We study the problem using the AdS/CFT correspondence [19][20][21]. In particular we calculate, using AdS/CFT, the transport coefficients that characterize the anomalous transport properties of the system, including the contribution from the dynamical type anomalies.1 See the review [5] for a recent account.

Chiral hydrodynamics in strong external magnetic fields

“…The behavior of the dimensionless ratio η 2 /s as a function of the magnetic fieldB is depicted in figure 11. 52 As expected, the ratio η 2 /s = 3/(8π) for vanishing JHEP04(2021)078 Note the behavior similar to η /s, namely that for γ = 2/ √ 3 there is a distinctly different behavior from the case γ = 0: for the largest three displayed chemical potentials, i.e. forμ ≥ 5, the value of the transport coefficient η 2 /s increases withB, while it always decreases for γ = 0. magnetic field and quadratically deviates from that value for small magnetic fields up toB = 1.…”

“…These (DC) conductivities have been shown to be exact in a multitude of holographic models [48,49], and based on field theory arguments [47]. (Non-)renormalization of these chiral conductivities was addressed holographically [50][51][52] and field theoretically [53]. The frequency dependent (AC) chiral conductivities have been discussed in [54][55][56], and from the field theory side in [19].…”

Higher-form symmetries, anomalous magnetohydrodynamics, and holography

“…It is thus very natural to expect that the bulk operation equivalent to "gauging" on the boundary is to perform a bulk Poincaré duality on the bulk 1-form potential V 1 , replacing it with a 2-form B 2 . Similar operations have a long history in AdS/CFT, and may be viewed as a higher-form generalization of [29]; see [30,31] for applications of such holographic operations in hydrodynamics. Also, see [32,33] for recent work in a similar holographic context.…”

Chiral hydrodynamics in strong external magnetic fields

“…Note that the Hall viscosity η has units of temperature T 3 , and hence η /T 3 is dimensionless. 50 Moreover, c 10 has the same units as T 2 implying that c 10 /T 2 is dimensionless.…”

“…These (DC) conductivities have been shown to be exact in a multitude of holographic models [47,48], and based on field theory arguments [44]. Nonrenormalization of these chiral conductivities was addressed holographically [49,50] and field theoretically [51]. The frequency dependent (AC) chiral conductivities have been discussed in [52][53][54], and from the field theory side in [16].…”