From Self-Dual to Physical $\mathbb{C}P^{N-1}$: Anomalies, Boundary Stokes Phenomenon, and Global Structure of $θ$-vacua

We introduce a two-coupling generalization of $\mathbb{C}P^{N-1}$ model that continuously interpolates between the self-dual ($ε=0$) and the physical ($ε=g$) theories as a useful nonperturbative tool. At $ε\neq g$, this model possesses a chiral imbalance, which may be viewed as a real topological de