Computation of the relation between the bare lattice coupling and the $\overline{MS}$ coupling in SU($N$) gauge theories to two loops

The perturbation expansion of the $\overline{MS}$ coupling in the SU(N) gauge theory in powers of the bare lattice coupling is extended to two-loop order. A discussion of our results has already been published elsewhere. We here describe the calculation in some detail. It relies on the background field technique and a recently introduced coordinate space method to evaluate lattice Feynman integrals