The gauge groups in Yang-Mills theory can be things like $O(10)$ or $SU(5)$ but continuing the pattern from real to complex, the next obvious thing would be quaternion matrices. A group like $U(4,H)$ where $H$ is the quaternions. This is another name for $Sp(4)$ (according to Wikipedia!).

A group like $U(4,H)$ I always thought would be interesting since it would be split $U(1,H)\times U(3,H)$ and $U(1,H)=SU(2)$ and $U(3,H)$ would have subgroup $SU(3)$.

But I have never seen a Yang-Mills theory with a compact symplectic gauge group so apparently there must be a good reason for that.

Do you know the reason? Is there a theoretical reason or an experimental reason?

This post imported from StackExchange Physics at 2016-09-20 21:55 (UTC), posted by SE-user zooby