What physics describes a $SU(N)$ theory with large $N$?

2017-11-29 13:10:31

Suppose that we have a system that can be described by $N$ (is a large number!) degree of freedom besides well-known degree of freedom like energy, momentum, spin, etc.. Now scattering processes are invariant under exchanges in these extra degree of freedom; then a $SU(N)$ gauge Group acts locally, such that an $SU(N)$ Yang-Mills theory arises. Can this Yang-Mills theory describe collective phenomena between even a huge number of particles? (I ask that question because I have seen a Statement about $SU(N)$ for large $N$ at the 8th page of http://people.brandeis.edu/~headrick/talks/EntanglementGeometry.pdf)

My ideas:

Suppose that a fermion state $\left|k_\mu,s\right>$ arose causally from the $n$-th Fermion of the same Kind with probability Amplitude $\left|k_\mu,s,n\right>$. If this state was generated causally by all of the Fermions, then we can express it as a linear combination

$$\left|k_\mu,s\right> = \sum_{n=1}^N \alpha_n \left|k_\mu,s,n\right>$$

with specific ca