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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-303/3/a/solution