  Lattice gauge theory with a background gauge field is shown to be
renormalizable to all orders of perturbation theory. No additional counterterms
are required besides those already needed in the absence of the background
field. The argument closely follows the treatment given earlier for the case of
dimensional regularization by Kluberg-Stern and Zuber. It is based on the BRS,
background gauge and shift symmetries of the lattice functional integral.

High Energy Physics - Lattice