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I am interested in scalar $O(N)$ gauge theory and what you can do with it. Is there a standard reference section in a textbook/monograph/paper/whatever that has a decent overview?

Wikipedia has a surprisingly okay treatment of some of the basics (https://en.wikipedia.org/wiki/Gauge_theory#An_example:_Scalar_O(n)_gauge_theory), with emphasis on it as a pedagogical example of a gauge field, but there is no reference to indicate whether this comes from a specific text.

The types of questions I am interested in: what (if anything) can you do with such a theory, i.e. is it useful for modelling anything in the real world? What do the propagators and other correlation functions look like/how do you compute them? What do the Feynman diagrams/perturbative expansions look like? What happens if you couple it to another scalar $O(N)$ gauge theory (with a different mass)?

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    $\begingroup$ For large $N$ stuff, a good reference is arxiv.org/abs/hep-th/9810198 $\endgroup$
    – Prahar
    Commented Jun 14 at 10:44
  • $\begingroup$ @Prahar that looks like it could be an answer :) $\endgroup$
    – Martin C.
    Commented Jun 15 at 7:47

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If you’re interested in the large N version of these models, then a good reference is https://arxiv.org/abs/hep-th/9810198

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