Quantum Chromodynamics (QCD) is a fundamental theory of nuclear interactions, describing nucleons as composite states of quarks and gluons. Heavy-ion collision experiments create a very hot and dense phase of nuclear matter, in which nucleons melt into a quark-gluon plasma. With more than 100 nucleons participating in each collision, the large numbers of produced quarks and gluons allow us to use hydrodynamics to describe the dynamics of QGP. Since nucleons and quarks are electrically charged, a hot QCD medium has nonzero electric conductivity and is also subject to strong magnetic field generated during the collision, which calls for a magneto-hydrodynamic description. Magneto-hydrodynamic equations require electric conductivity as a first-principle input. In particular, it is of direct importance for the lifetime of magnetic field.
We carried out the first numerical study of the density dependence of electric conductivity. While this study is hardly possible in real QCD because of the fermionic sign problem which makes the path integral weight non-positive and does not allow for Monte-Carlo simulations, we circumvented the sign problem by replacing the SU(3) gauge group of QCD with the SU(2) gauge group. The resulting SU(2) gauge theory is similar to QCD for small densities. Using SU(2) gauge theory, we found that the density dependence of electric conductivity is mostly close to that of free quarks, and becomes somewhat more pronounced in the vicinity of the chiral crossover which separates the hadronic and the quark-gluon plasma regimes (see Figure). Furthermore, quantum anomalies of gauge theory (violations of classical chiral symmetry at the quantum level) generate new terms in magneto-hydrodynamic equations, known as anomalous transport phenomena. We used SU(2) gauge theory with finite fermion density to study one of these phenomena, the generation of fermionic chirality flow along the magnetic field in dense plasma, dubbed the Chiral Separation Effect. Justifying some of the popular phenomenological approaches, we found that the strength of the Chiral Separation Effect is well described by the free quark gas approximation everywhere in the phase diagram except for the low-temperature, low-density regime.