Chiral field model and universality in three-dimensional space. I

A noncanonically renormalized $1/N$ expansion of the $O(N)$-invariant $(\varphi^2)_3^2$ model is constructed in the high-and low-temperature phases, and also in the pre-asymptotic massless theory; it is free of infrared divergences in each individual diagram. It is shown that at the infrared-stable point of the renormalization group the pre-asymptotic $O(N)$-invariant $(\varphi^2)_3^2$ theory is identical with the conformally invariant critical chiral field theory. The proof of the existence of the critical limit is based exclusively on generalized relations of quantum chirality, as a result of which the chiral field model can be interpreted as universal in three-dimensional space.