Topological Symmetry of $N$ copies of Wilson-Fisher scalars

Question

I am studying the paper "More Abelian Dualities in 2+1 Dimensions".

https://arxiv.org/abs/1609.04012

On page 8, it says that $N$ copies of Wilson-Fisher scalars 

$$S[\vec{\phi}]=\sum_{i=1}^{N}\int d^{3}x\left\{|\partial_{\mu}\phi_{i}|^{2}-\alpha |\phi_{i}|^{4}\right\}$$

does not enjoy a global $U(N)$ symmetry, but $U(1)^{N}$ topological symmetries.

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I figured it out why $U(N)$ is not the symmetry, but why are $U(1)^{N}$ topological?