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

TL;DR

This paper calculates a second order transport coefficient related to the chiral anomaly in quark-gluon plasma at weak coupling, revealing a non-analytic dependence on the coupling and introducing a resummation method for accurate results.

Contribution

It introduces a diagrammatic resummation approach to compute a second order transport coefficient from the chiral anomaly, highlighting its non-analytic coupling dependence.

Findings

Transport coefficient scales as 1/(g^4 log(1/g)) at weak coupling.

Resummation of ladder diagrams is necessary for accurate leading log results.

Chiral magnetic current exhibits resistance to magnetic field changes, termed 'chiral induction effect'.

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.