The $CP^{N-1}$ model: Calculation of anomalous dimensions and the mixing matrices in the order $1/N$

In the first order in $1/N$ for arbitrary dimension $2<d<4$ of space for the $CP^{N-1}$ model quantized by means of the auxiliary fields $\varphi$ and $B$ ($\Phi$ is the principal field, go the auxiliary scalar field, and $B$ the auxiliary vector field) the following are calculated: 1) the matrix of renormalization constants and the corresponding matrix of the anomalous dimensions of the mixed operators $\varphi$ and $B^2$ of canonical dimension $2$; 2) the analogous matrices for the mixed operators $\varphi^2$ and $F_{\alpha\beta}F_{\alpha\beta}$ of canonical dimension $4$, which determine two correction exponents $\omega$; 3) the anomalous dimension $\gamma_\Phi$ in an arbitrary gauge.