Electric conductivity in finite-density lattice gauge theory

We study the dependence of the electric conductivity on chemical potential in finite-density SU(2) gauge theory with Nf=2 flavors of rooted staggered sea quarks, in combination with Wilson-Dirac and Domain Wall valence quarks. We concentrate in particular on the vicinity of the chiral crossover, where we find the low-frequency electric conductivity to be most sensitive to small changes in chemical potential. Working in the low-density QCD-like regime with spontaneously broken chiral symmetry, we obtain an estimate of the first nontrivial coefficient of the expansion of conductivity $\sigma(T,\mu) = \sigma(T,0) *(1 + c(T) (\mu/T)^2 + O(\mu^4))$ in powers of $\mu$, which takes its maximal value $c(T) \approx 0.1(5)$ around the critical temperature. At larger densities and lower temperatures, the conductivity quickly grows towards the diquark condensation phase, and also becomes closer to the free quark result. As a by-product of our study we confirm the conclusions of previous studies with heavier pion that for SU(2) gauge theory the ratio of crossover temperature to pion mass $T_c/m_{\pi} \approx 0.4$ at $\mu=0$ is significantly smaller than in real QCD.