Second Order Transport Coefficient from Chiral Anomaly at Weak Coupling: Diagrammatic Resummation

Abstract

We compute one of the second order transport coefficients arising from the chiral anomaly in a high temperature weakly coupled regime of quark-gluon plasma. This transport coefficient is responsible for the CP-odd current that is proportional to the time derivative of the magnetic field, and can be considered as a first correction to the chiral magnetic conductivity at finite, small frequency. We observe that this transport coefficient has a non-analytic dependence on the coupling as $\sim 1/(g^4\log (1/g))$ at weak coupling regime, which necessitates a re-summation of infinite ladder diagrams with leading pinch singularities to get a correct leading log result: a feature quite similar to that one finds in the computation of electric conductivity. We formulate and solve the relevant CP-odd Schwinger-Dyson equation in real-time perturbation theory that reduces to a coupled set of second order differential equations at leading log order. Our result for this second order transport coefficient indicates that chiral magnetic current has some resistance to the time change of magnetic field, which may be called "chiral induction effect". We also discuss the case of color current induced by color magnetic field.

54 pages, 8 figures

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• Jet quenching parameter of quark-gluon plasma in strong magnetic field: Perturbative QCD and AdS/CFT correspondence
• Nonlinear Chiral Transport Phenomena
• Spin relaxation rate for heavy quarks in weakly coupled QCD plasma
• Second-order Charge Currents and Stress Tensor in Chiral System
• Chiral magnetic response to arbitrary axial imbalance
• Anomalous transport from holography: Part II
• Spin Polarized Photons from Axially Charged Plasma at Weak Coupling: Complete Leading Order
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• Non-static Analysis of the Anomalous Chiral Conductivities