Non-commutative Chern-Simons terms and the non-commutative vacuum

It is shown that the space noncommutativity parameters theta sup mu-nu in non-commutative gauge theory can be considered as a set of superselection parameters, in analogy with the theta-angle in ordinary gauge theories. As such, they do not need to enter explicitly into the action. A simple generic formula is then suggested to reproduce the Chern-Simons action in non-commutative gauge theory, which reduces to the standard action in the commutative limit but in general implies a cascade of lower-dimensional Chern-Simons terms. The presence of these terms in general alters the vacuum structure of the theory and non-standard gauge theories can emerge around the new vacua. (Author)