  We consider Wilson's SU(N) lattice gauge theory (without fermions) at
negative values of beta= 2N/g^2 and for N=2 or 3. We show that in the limit
beta -> -infinity, the path integral is dominated by configurations where links
variables are set to a nontrivial element of the center on selected non
intersecting lines. For N=2, these configurations can be characterized by a
unique gauge invariant set of variables, while for N=3 a multiplicity growing
with the volume as the number of configurations of an Ising model is observed.
In general, there is a discontinuity in the average plaquette when g^2 changes
its sign which prevents us from having a convergent series in g^2 for this
quantity. For N=2, a change of variables relates the gauge invariant
observables at positive and negative values of beta. For N=3, we derive an
identity relating the observables at beta with those at beta rotated by +-
2pi/3 in the complex plane and show numerical evidence for a Ising like first
order phase transition near beta=-22. We discuss the possibility of having
lines of first order phase transitions ending at a second order phase
transition in an extended bare parameter space.
