 F-term hybrid inflation

The bilinear hybrid superpotential couples an inflaton $S$ to two waterfall fields $u,v$. In global supersymmetry, $V=|g{|}^2(|uv-\zeta {|}^2+|S{|}^2(|u{|}^2+|v{|}^2))$. The branch $u=v=0$ breaks supersymmetry and is transversely stable for $|S{|}^2>|\zeta |$, while the zero-energy branch $S=0$, $uv=\zeta$ is supersymmetric. A canonical Kähler potential in supergravity slightly lifts the inflationary valley. It must not be described as two isolated stationary minima of the full potential.