Classification of gauge orbit types for SU(n)-gauge theories

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d less than or equal to 4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang-Mills theory with the Chern-Simons term proposed by Asorey et al. is discussed.