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

The constraint $\mathbf{n}\cdot \mathbf{n}=1$ makes $\mathbf{n}$ dimensionless. Since $d^{d}x({\partial }_i{n}_A{)}^2$ has engineering dimension $2-d$, dimensional consistency of the O(N) nonlinear sigma model gives