AdS swampland conjectures and light fermions

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 Λ_D ≥ 0 and a positive first non-vanishing supertrace ^{(- 1) k + 1}StrM^2k > 0, a surplus of light fermions with mass m_f ≲Λ_D^1/D must be present. For dS_D this is supported by both AdS swampland conjectures. 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 ≲ Λ_d^α with α = 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.