Nonperturbative effects of a topological theta term on principal chiral nonlinear sigma models in 2+1 dimensions

Cenke Xu and Andreas W. W. Ludwig

Accepted Tuesday Apr 23, 2013

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.