Noncommutative Chern-Simons terms and the noncommutative vacuum

Abstract

It is pointed out that the space noncommutativity parameters $thet{a}^{\mu \nu }$ in noncommutative 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 noncommutative 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 nonstandard gauge theories can emerge around the new vacua.

10 pages, no figures; minor typos and references corrected

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