I am looking at S-duality a bit, and was wondering if anyone had the answer to the following question. It is known that the supersymmetric Yang-Mills theory in 4 space dimensions is self-dual with gauge group or U(N) or SU(2). But is it known whether there are more Yang-Mills theories that are self-dual? On the other hand, is it known that some are not?

Any help much appreciated!

This post imported from StackExchange Physics at 2014-08-05 15:04 (UCT), posted by SE-user user30564