Further swampland constraint on Dirac Neutrino

Abstract

Recent studies on swampland conjectures (e.g. non-SUSY AdS conjecture or AdS distance conjecture) predict that the (lightest) neutrino must be Dirac and the mass must be cosmologically small $m<c{\Lambda }_{\text{cc}}^{1/4}\sim 10\text{meV}$. The Dirac neutrino naturally accompanies a $U(1)$ symmetry that can be embedded in the anomaly-free $U(1{)}_{B-L}$ global symmetry of the standard model. We point out that the swampland conjectures applied to a circle compactification with the $U(1)$ symmetry twisting lead to further constraints. In particular, the $U(1)$ symmetry must be broken down to ${\mathbb{Z}}_4$,${\mathbb{Z}}_8$ or ${\mathbb{Z}}_{10}$ in the case of normal hierarchy, and ${\mathbb{Z}}_4$ in the case of inverted hierarchy, providing evidence for the absence of continuous global symmetry in quantum gravity. We also predict a more constrained upper bound of the neutrino mass for each case.

Comments: 11 pages, main results appeared in master's thesis of the first author