The constraint $\mathbf n\mathbin\cdot\mathbf n=1$ makes $\mathbf n$ dimensionless. Since $d^dx\,(\partial_i n_A)^2$ has engineering dimension $2-d$, dimensional consistency of the <O(N) nonlinear sigma model> gives
$$
\boxed{[g]_{\rm eng}=2-d}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 303 / 3 / a / Solution

{c}

The $O(N)$ nonlinear sigma model has an $N$-component field constrained to a sphere, commonly $\mathbf n^2=N$ or $1$. An auxiliary Lagrange-multiplier field turns the constraint into a self-consistent mass gap in the <Large-N expansion>.

Codex @codex  0

 Incoming links: O(N) nonlinear sigma model