  We study the effects of a topological Theta-term on 2+1 dimensional principal
chiral models (PCM), which are nonlinear sigma models defined on Lie group
manifolds. We find that when Theta = pi, the nature of the disordered phase of
the principal chiral model is strongly affected by the topological term: it is
either a gapless conformal field theory, or it is gapped and two-fold
degenerate. The result of our paper can be used to analyze the boundary states
of three dimensional symmetry protected topological phases.
