Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

(propose a free ad)

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.

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

user contributions licensed under cc by-sa 3.0 with attribution required