Topological model for domain walls in (super-)Yang-Mills theories

We derive a topological action that describes the confining phase of (super-)Yang--Mills theories with gauge group $SU(N)$, similar to the work recently carried out by Seiberg and collaborators. It encodes all the Aharonov--Bohm phases of the possible nonlocal operators and phases generated by the intersection of flux tubes. Within this topological framework we show that the world volume theory of domain walls contains a Chern--Simons term at level N also seen in string theory constructions. The discussion can also illuminate dynamical differences of domain walls in the supersymmetric and nonsupersymmetric framework. Two further analogies, to string theory and the fractional quantum Hall effect, might lead to additional possibilities to investigate the dynamics.