  We consider constraints on $D$-dimensional theories in $M_D$, $dS_D$ and
$AdS_D$ backgrounds in the light of AdS swampland conjectures as applied to
their compactification in a circle. In particular we consider the non-SUSY AdS
instability conjecture and the AdS distance conjecture. For $M_D$ and $dS_D$
vacua the results may be summarized by a light fermion conjecture which states
that in theories with $\Lambda_D\geq 0$ and a positive first non-vanishing
supertrace $(-1)^{k+1}\text{Str} M^{2k}>0$, a surplus of light fermions with
mass $m_f\lesssim \Lambda_D^{1/D}$ must be present. On the contrary, the cases
of $M_D$ and $AdS_D$ can be made consistent with the mild but not the strong
version of the AdS Distance conjecture, since the KK tower in the lower $d$-dim
theory will scale as $m\lesssim \Lambda_d^{\alpha}$ with $\alpha=1/d$. The
above constraints also suggest that the Standard Model of particle physics
would be inconsistent in Minkowski space but consistent in dS if the lightest
neutrino is Dirac and lighter than the cosmological constant scale.
