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

Understand

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.