Exact relations between the conductivities and their connection to the chemical composition of QCD matter

We present exact relations between the diffusion coefficients or conductivities, ${\kappa }_{q{q}^{\prime }}/T={\sigma }_{q{q}^{\prime }}$, of strongly interacting matter. We show that once the diagonal entries are known in two different charge representations, the off-diagonal coefficients are functions of the diagonal entries once isospin symmetry applies. As an important example, we infer the conductivities on the basis of available calculations from lattice quantum chromodynamics and argue that these computations suffer under the approximations made to achieve them. Further, we argue that the representation of the conductivities with respect to the conserved quark flavors may deliver more insight into the chemical composition of strongly interacting matter.