Electrical conductivity of the quark-gluon plasma in the presence of strong magnetic fields

We compute the electrical conductivity of the strongly interacting medium in the presence of strong magnetic background fields, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>e</a:mi><a:mi>B</a:mi><a:mo>=</a:mo><a:mn>4</a:mn></a:math>, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>9</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:msup><c:mrow><c:mi>GeV</c:mi></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msup></c:mrow></c:math>, and for different values of the temperature, both in the confined and in the deconfined quark-gluon plasma (QGP) phase. The conductivity is obtained from the Euclidean lattice time correlator of the electrical current, computed on gauge configurations sampled from Monte-Carlo simulations of an improved staggered discretization of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>N</e:mi><e:mi>f</e:mi></e:msub><e:mo>=</e:mo><e:mn>2</e:mn><e:mo>+</e:mo><e:mn>1</e:mn></e:math> QCD. We perform the inverse Laplace transform of the correlator adopting a recently proposed version of the standard Backus-Gilbert procedure for the inversion. The results obtained in the QGP phase show a sizable enhancement of the conductivity in the direction parallel to the magnetic field, as well as a suppression in the direction orthogonal to it. The enhancement can interpreted through various different mechanisms, typically involving the chiral anomaly, among which the chiral magnetic effect (CME): for this reason we try to interpret our observations based on a CME-inspired , we extract the relaxation time of this process, extrapolate it to the continuum limit and compare it to previous results, finding it lower than expected in the explored range of temperatures.