Two-dimensional ${\mathrm{CP}}^{N-1\mathrm{}}$ models are analyzed by means of the $\frac{1}{N}$ expansion, performed up to the first nonleading order. The expectation values of gauge- and renormalization-group-invariant quantities are computed in a regulated continuum version of the theory: renormalizability and absence of infrared divergences are explicitly verified. Special attention is devoted to open and closed loops of gauge fields and to their correlations. No single-particle mass for the "elementary" gauge-dependent fields can be consistently defined. The observable mass parameter is related to the lowest-energy bound state and shows a nonanalytic dependence on $\frac{1}{N}$. The qualitative picture of the ${\mathrm{CP}}^{N-1\mathrm{}}$ models resulting from the large-$N$ approximation is quantitatively confirmed in the $\frac{1}{N}$ expansion.

• Received 30 July 1991

DOI:https://doi.org/10.1103/PhysRevD.45.618