Understand
We study the landscape of lower-dimensional vacua of the SM coupled to gravity in the presence of the ``dark dimension'' of size $R_\perp$ in the micron range, focusing on the validity of the swampland conjecture forbidding the presence of non-SUSY AdS vacua in a consistent quantum gravity theory.
- We first adopt the working assumption that right-handed neutrinos propagate in the bulk, so that neutrino Yukawa couplings become tiny due to a volume suppression, leading to naturally light Dirac neutrinos.
- We show that the neutrino KK towers compensate for the graviton tower to maintain stable dS vacua found in the past, but neutrino oscillation data set restrictive bounds on $R_\perp$ and therefore the first KK neutrino mode is too heavy to alter the shape of the radon potential or the required maximum mass for the lightest neutrino to carry dS rather than AdS vacua found in the absence of the dark dimension, $m_{1,{\rm max}}\lesssim 7.63~{\rm meV}$.
- We also show that a very light gravitino (with mass in the meV range) could help relax the neutrino mass constraint $m_{1,{\rm max}} \lesssim 50~{\rm meV}$.