Analog of dimensional regularization for calculation of the renormalization-group functions in the $1/n$ expansion for arbitrary dimension of space

The renormalization of the massless (critical) $O_n$-symmetric nonlinear $\sigma$, model for arbitrary dimension $2<D<4$ of space is investigated. The introduction of analytic regularization makes it possible to calculate the renormalization constants and the anomalous dimensions directly in the framework of massless theory in the same way as in the $4-\varepsilon$ scheme of dimensional regularization of the $\varphi^4$.