The Fundamental Need for a SM Higgs and the Weak Gravity Conjecture

Understand

Compactifying the SM down to 3D or 2D one may obtain AdS vacua depending on the neutrino mass spectrum.

• It has been recently shown that, by insisting in the absence of these vacua, as suggested by {\it Weak Gravity Conjecture} (WGC) arguments, intriguing constraints on the value of the lightest neutrino mass and the 4D cosmological constant are obtained.
• For fixed Yukawa coupling one also obtains an upper bound on the EW scale $\left\langle H\right\rangle\lesssim {\Lambda_4^{1/4}} /{Y_{\nu_{i}}}$,where $\Lambda_4$ is the 4D cosmological constant and $Y_{\nu_{i}}$ the Yukawa coupling of the lightest (Dirac) neutrino.
• This bound may lead to a reassessment of the gauge hierarchy problem.