Using perturbations of the SU(N)_1 WZNW model, the authors derive the sign of the current-current interaction and conclude which theta-angled sigma models flow to a gapless CFT (flag, SU(N)/SO(N)) and which are gapped with two-fold degeneracy (CP^{N-1}, Grassmannian).
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Infrared properties of two-dimensional $\mathrm{SU}(N)/H$ nonlinear $\sigma$ models at nonzero $\theta$ angles
Using perturbations of the SU(N)_1 WZNW model, the authors derive the sign of the current-current interaction and conclude which theta-angled sigma models flow to a gapless CFT (flag, SU(N)/SO(N)) and which are gapped with two-fold degeneracy (CP^{N-1}, Grassmannian).