Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape

TL;DR

This paper explores the vacuum structure of the Standard Model under compactification, linking the weak gravity conjecture and multiple point principle to predict neutrino properties and potential instabilities in the landscape.

Contribution

It investigates the implications of the weak gravity conjecture and multiple point principle on the Standard Model's vacuum landscape, predicting neutrino nature and masses.

Findings

Existence of a high-scale vacuum consistent with the measured Higgs mass.

Predicted neutrinos are Dirac with masses around 1-10 meV.

Potential instability sources for lower-dimensional vacua identified.

Abstract

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.