  Following a proposal of Budczies and Zirnbauer, we investigate an alternative
lattice discretization of continuum ${\rm SU}(N_c)$ Yang-Mills theory in which
the self-interactions of the gauge field are induced by a path integral over
$N_b\ge N_c-1$ auxiliary bosonic fields which are coupled linearly to the gauge
field. In two dimensions there exists an analytic proof that the new
discretization reproduces Yang-Mills theory in its non-perturbative continuum
limit. We provide numerical evidence that this is also the case in three and
four dimensions and that, after a suitable matching of the free parameters, the
results of the induced theory agree with results from the ordinary plaquette
action up to lattice artifacts. The new discretization is ideally suited to
change the order of integration in the QCD path integral to arrive at
formulations in which the gauge fields have been integrated out. The resulting
theories might be amenable to methods previously used in the infinite-coupling
limit, and we briefly discuss possibilities to arrive at dual representations
of lattice QCD.
