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 [Formula: see text]. The Dirac neutrino naturally accompanies a [Formula: see text] symmetry that can be embedded in the anomaly-free [Formula: see text] global symmetry of the standard model. We point out that the swampland conjectures applied to a circle compactification with the [Formula: see text] symmetry twisting lead to further constraints. In particular, the [Formula: see text] symmetry must be broken down to [Formula: see text], [Formula: see text] or [Formula: see text] in the case of normal hierarchy, and [Formula: see text] 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.