We consider constraints on $D$-dimensional theories in $M_D$, $dS_D$ and $AdS_D$ backgrounds the light of AdS swampland conjectures as applied to their compactification a circle. In particular we non-SUSY instability conjecture distance conjecture. For $M_D$ vacua results may be summarized by fermion which states that with $\Lambda_D\geq 0$ positive first non-vanishing supertrace $(-1)^{k+1}\te...

Recent studies on swampland conjectures (e.g. non-SUSY AdS conjecture or distance conjecture) predict that the (lightest) neutrino must be Dirac and mass cosmologically small [Formula: see text]. The naturally accompanies a text] symmetry can embedded in anomaly-free global of standard model. We point out applied to circle compactification with twisting lead further constraints. In particular, ...