Phase diagram of Yang-Mills theories in the presence of a θ term

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 the presence of an imaginary baryon chemical potential.