Abstract
We introduce additional holomorphic constraints in the $\mathrm{CP}(N\ensuremath{-}1)$ model and derive, in the $\frac{1}{N}$ expansion, the effective action for neutral and charged composite fields. Then we discuss in four dimensions the generalized $\mathrm{CP}(N\ensuremath{-}1)$ model with four-linear Lagrangian and additional constraints. We also present a supersymmetric generalization of the model.
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