  We explore theoretically how the coupling to cavity vacuum fields affects the
electron transport in quantum conductors due to the counter-rotating-wave terms
of light-matter interaction. We determine the quantum conductance in terms of
the transmission coefficients predicted by an effective electron Hamiltonian.
The coupling between bare electronic states is mediated by virtual processes
involving intermediate states with one electron (or one hole) on top of the
Fermi sea and one virtual cavity photon. We study the behavior of the quantum
conductance in the presence of artificial or disordered single-particle
potentials, as well as a spatially varying cavity mode. As illustrative
examples, we apply our theory to 1D conductors and to disordered 2D quantum
Hall systems. We show how the cavity vacuum fields can lead to both large
enhancement or suppression of electron conductance in the ballistic regime, as
well as modification of the conductance quantization and fluctuations.
