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)×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