  We study pure SU(N) lattice gauge theory with a plaquette weight factor given
by an inverse determinant which can be written as an integral over auxiliary
bosonic fields (modifying a proposal of Budczies and Zirnbauer). We derive
conditions for the existence of a continuum limit and its equivalence to
Yang-Mills theory. Furthermore, we perturbatively compute the relation between
the coupling constants of the `induced' gauge action and the familiar Wilson
gauge action using the background-field technique. The perturbative relation
agrees well with numerical results for N=2 in three dimensions.
