 Flat-direction exception to the adjoint cubic stationarity bound

For a traceless Hermitian adjoint scalar with potential $-m^2\mathrm{tr}{\Phi }^2+a(\mathrm{tr}{\Phi }^2{)}^2+b\mathrm{tr}{\Phi }^4$, the stationary eigenvalues satisfy $4b{x}^3+(4a{R}^2-2m^2)x-\zeta =0$. The usual bound of three distinct eigenvalues requires this polynomial not to vanish identically. With $b=0$, $a,m>0$, every traceless matrix of squared norm $R^2=m^2/(2a)$ is a global minimum, including matrices with all eigenvalues distinct. In SU(5), this permits an unbroken maximal torus $U(1{)}^4$, outside the generic three-block classification.