  The determination of transport coefficients plays a central role in
characterizing hot and dense nuclear matter. Currently, there are significant
discrepancies between various calculations of the electric conductivity of hot
hadronic matter. In the present work we calculate the electric conductivity of
hot pion matter by extracting it from the electromagnetic spectral function,
via its zero energy limit at vanishing 3-momentum, within the Vector Dominance
Model (VDM). Since within the VDM the photon couples to the hadronic currents
primarily through the $\rho$ meson, we use hadronic many-body theory to
calculate the $\rho$-meson's self-energy in hot pion matter, by dressing its
pion cloud with thermal $\pi$-$\rho$ and $\pi$-$\sigma$ loops including vertex
corrections to maintain gauge invariance. In particular, we analyze the
low-energy transport peak of the spectral function, extract its behavior with
temperature and compare to (the results of) existing approaches in the
literature.
