F term breaking potential

1. Mar 2, 2013

$V=\sum^{N}_{i}|F_i|^2$
That is the expression for the scalar potential. Before you can find a minimum, you need to use the equation of motion for $F_i$, which leads to a dependence on the scalar fields, $F_i = f_i(\phi_j),$ so that $V = V(\phi_j)$. A minimum is the solution to $\partial V/\partial\phi_i=0$ with the correct properties on the 2nd derivatives.