AdS Swampland Conjectures and Light Fermions

TL;DR

This paper explores constraints from AdS swampland conjectures on theories with different cosmological backgrounds, proposing a light fermion conjecture linking light fermions to positive cosmological constant scenarios and discussing implications for the Standard Model.

Contribution

It introduces a light fermion conjecture relating light fermions to positive cosmological constant theories and analyzes their consistency with swampland conjectures across various backgrounds.

Findings

Light fermion conjecture for $ ext{Lambda}_D \\geq 0$ theories.

Consistency of $M_D$ and $AdS_D$ with mild AdS Distance conjecture.

Implication that the Standard Model could be inconsistent in Minkowski space.

Abstract

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.