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

Abstract

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 $SU(8)\supset SU(3)\times SU(5)$, we find that the stable minimum of the potential breaks the original symmetry according to $SU(8)\supset SU(3)\times Sp(4)$. 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.

Comments: Latex, 15 pages. v3 to appear in Journal of Physics A: Mathematical and Theoretical