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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.
Highlights
The chiral anomaly is an intriguing quantum mechanical phenomenon arising from an interplay between charge and chirality of massless particles such as chiral fermions
It has recently been appreciated that the chiral anomaly may induce interesting parity-odd transport phenomena in the plasmas of such particles [1,2,3,4,5]; at the lowest order in derivative expansion of hydrodynamics it has been shown that the second law of thermodynamics dictates the existence of such phenomena [6], including the chiral magnetic effect [3] and the chiral vortical effect [7,8]
Recent results from heavy-ion experiments at the RHIC [26,27,28,29,30] and the LHC [31] seem consistent with the predictions from chiral magnetic and vortical effects [32,33], and, quite interestingly, there has been a successful experimental test of the chiral magnetic effect in Dirac/Weyl semimetals that feature chiral fermionic excitations [39]
Summary
The chiral anomaly is an intriguing quantum mechanical phenomenon arising from an interplay between charge and chirality of massless particles such as chiral fermions. As was observed first by Jeon [57], in diagrammatic language, the nonanalytic behavior in the coupling dependence is signaled by the presence of pinch singularities in multiloop ladder diagrams of two-point correlation functions; this necessitates a resummation of all ladder graphs, by solving a Schwinger-Dyson-type equation, to get a leading log result. The necessary k~ dependence for P-odd correlation functions arises only from the spinor projection part of the fermion propagators With this important simplification, we are able to reduce the leading log part of the P-odd Schwinger-Dyson equation into a coupled set of second order differential equations, which can be solved numerically.
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