SO(N) gauge theories
Although it is SU(N) rather than SO(N) gauge theories that
appear in the Standard Model, there has been recent interest
in the latter because they provide a promising route to learn
something about the former at finite chemical potential.
In particular it is known that SO(2N) has no `sign/phase problem' at
finite chemical potential and that it and SU(N) have a common N=oo limit
(in the C=+ sector of the latter). Thus if SU(3) is close to SU(oo),
and if say SO(6) is close to SO(oo), then the calculable phase
diagram of SO(6) will tell us what are the essential features
of the phase diagram of SU(3), i.e. of QCD.
In addition SO(N) differs from SU(N) in its center and it is
interesting to see how it differs from SU(N). And noting that
SO(3) is just SU(2) in the adjoint representation, one can try to
address some ancient questions about the identity of the two continuum
limits.
There is quite a bit that one can say analytically, but ultimately one
turns to numerical calculations for a full answer. This is work with
Francis Bursa (Glasgow) and my student Richard Lau.
Last major update 2012