Coleman-Weinberg symmetry breaking in SU(8) induced by a third rank antisymmetric tensor scalar field

We study SU(8) symmetry breaking induced by minimizing the Coleman-Weinberg effective potential for a third rank antisymmetric tensor scalar field in the 56 representation. Instead of breaking {SU}(8)\supset {SU}(3)× {SU}(5), we find that the stable minimum of the potential breaks the original symmetry according to {SU}(8)\supset {SU}(3)× {Sp}(4). Using both numerical and analytical methods, we present results for the potential minimum, the corresponding Goldstone boson structure and BEH mechanism, and the group-theoretic classification of the residual states after symmetry breaking.