  We study the phase diagram of non-Abelian pure gauge theories in the presence
of a topological theta term. The dependence of the deconfinement temperature on
theta is determined on the lattice both by analytic continuation and by
reweighting, obtaining consistent results. The general structure of the diagram
is discussed on the basis of large-N considerations and of the possible
analogies and dualities existing with the phase diagram of QCD in presence of
an imaginary baryon chemical potential.
