Symmetry breaking patterns for third-rank totally antisymmetric tensor representations of unitary groups

Some possible symmetry breaking patterns for unitary group gauge theoretic models based on Higgs scalars in the third-rank totally antisymmetric tensor representations of U(n) are studied. It is shown that spontaneous symmetry breaking may take place from SU(n) to SU(3)xSU(n-3) for all n, from SU(6) to SU(3)xSU(3), from SU(7) to G2, from SU(8) to SU(3) and from SU(9) to U(1)xU(1)xU(1)xU(1). The absolute minima are shown to be degenerate for n >= 9. (author)