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