Asymptotic safety and local gauge invariance

[metroplex021]

Hi folks -- does anyone know of a good survey article on the topic of whether local gauge invariance is a requirement of a fundamental theory within QFT -- hence of an asymptotically safe theory?

I only have a few scattered remarks to this effect (by F. Wilczek mostly), so any good references or even statements of the state of play would be most appreciated!

 

[atyy]

Gauge invariance is not a fundamental requirement for a nonlinear relativistic quantum field theory that rigourously exists, at least not in all dimensions. For example, http://www.claymath.org/sites/default/files/yangmills.pdf (section 6.2) says there are rigourous nonlinear scalar fields in 2 and 3 dimensions. However they go on to discuss that in 4 dimensions the best candidate for a rigourous construction seems to be Yang-Mills, which is a gauge theory.

 

[metroplex021]

thank you very much, that is tremendously helpful!