  The requirement for an ultraviolet completable theory to be well-behaved upon
compactification has been suggested as a guiding principle for distinguishing
the landscape from the swampland. Motivated by the weak gravity conjecture and
the multiple point principle, we investigate the vacuum structure of the
standard model compactified on $S^1$ and $T^2$. The measured value of the Higgs
mass implies, in addition to the electroweak vacuum, the existence of a new
vacuum where the Higgs field value is around the Planck scale. We explore two-
and three-dimensional critical points of the moduli potential arising from
compactifications of the electroweak vacuum as well as this high scale vacuum,
in the presence of Majorana/Dirac neutrinos and/or axions. We point out
potential sources of instability for these lower dimensional critical points in
the standard model landscape. We also point out that a high scale $AdS_4$
vacuum of the Standard Model, if exists, would be at odd with the conjecture
that all non-supersymmetric $AdS$ vacua are unstable. We argue that, if we
require a degeneracy between three- and four-dimensional vacua as suggested by
the multiple point principle, the neutrinos are predicted to be Dirac, with the
mass of the lightest neutrino O(1-10) meV, which may be tested by future CMB,
large scale structure and $21$cm line observations.
