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

TL;DR

This paper investigates how a third rank antisymmetric tensor scalar field in the 56 representation of SU(8) induces symmetry breaking via the Coleman-Weinberg potential, resulting in a stable SU(8) ; Sp(4) breaking pattern.

Contribution

It demonstrates that the stable symmetry breaking pattern is SU(8) ; Sp(4), not the commonly expected SU(3) ; SU(5), using both numerical and analytical approaches.

Findings

The stable minimum breaks SU(8) to SU(3) ; Sp(4).

Goldstone boson and BEH mechanism structures are characterized.

Group-theoretic classification of residual states is provided.

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.