Large-$N$ Solution and Effective Action of "Twisted-Mass'' Deformed $\mathbb{C}\mathbb{P}(N-1)$ Model

We study effective dynamics of the non-supersymmetric two-dimensional $\mathbb{C}\mathbb{P}(N-1)$ model in the large $N$ limit. This model is deformed by a mass term $m$ preserving ${\mathbb{Z}}_N$ symmetry of the Lagrangian. At small $m$ the theory is strongly coupled and resembles the undeformed $\mathbb{C}\mathbb{P}(N-1)$ model, while at large $m$ it is in a weakly coupled Higgs phase with spontaneously broken ${\mathbb{Z}}_N$. We find the phase transition point and discuss the fate of the kink-antikink ``mesons’’ at strong coupling. We also resolve an issue of instability that arose in previous studies of this model.