Electrical Conductivity of Quark-Gluon Plasma in Strong Magnetic Fields

TL;DR

This paper calculates the electrical conductivity of quark-gluon plasma in strong magnetic fields, revealing a large conductivity along the magnetic field due to chirality effects and mass sensitivity, with implications for heavy-ion collisions.

Contribution

It provides a one-loop quantum field theory calculation of conductivity in strong magnetic fields using the lowest Landau level approximation, including the effects of chirality and mass.

Findings

Conductivity diverges in the massless limit due to chirality conservation.

Conductivity along the magnetic field is significantly larger than at zero magnetic field.

Resummation of ladder diagrams confirms the leading-log order result.

Abstract

We compute the electrical conductivity of quark-gluon plasma in a strong magnetic field $B$ with quantum field theory at finite temperature using the lowest Landau level approximation. We provide the one-loop result arising from 1-to-2 scattering processes whose kinematics are satisfied by the (1+1) dimensional fermion dispersion relation. Due to the chirality conservation, the conductivity diverges in the massless limit, and is sensitive to the value of the current quark mass. As a result, we find that the conductivity along the direction of the magnetic field is quite large compared with the value at $B=0$, mainly because of the small value of the current quark mass. We show that the resummation of the ladder diagrams for the current-current correlator gives rise to only sub-leading contributions beyond the leading-log order, and thus verify our one-loop result at the leading-log accuracy. We also discuss possible implications for the relativistic heavy-ion collisions.