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

Abstract

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.

Topics & Concepts