  Recently proposed de Sitter Swampland conjectures imply non-trivial
constraints on a scalar field potential in any effective field theory that
admits a quantum gravity completion. The original conjecture apparently
excludes many phenomenologically motivated scalar potentials with de Sitter
extrema, such as the perturbative Standard Model Higgs potential and the QCD
axion potential, as the viable low-energy theories. Subsequently, the refined,
weaker conjecture was proposed. However, the full effective potential, having
been defined as a Legendre transform, is necessarily convex. This ensures that
the original Swampland conjecture can actually be satisfied in
phenomenologically relevant models, providing no de Sitter vacua exist.
