Small Neutrino Mass from Large Compactification Volumes

We present an argument in which the scale $\sim 0.1\mathrm{eV}$ associated with neutrino masses naturally appears in a class of (very) large volume compactifications, being tied to a supersymmetry scale of ${10}^3\mathrm{GeV}$ and a string scale of ${10}^{11}\mathrm{GeV}$. The masses are of the Majorana type, and there is no right-handed neutrino within the low-energy field theory. The suppression scale ${10}^{14}\mathrm{GeV}$ is independent of the masses of the heavy states that are integrated out. These kinds of constructions appear naturally in type IIB flux compactifications. However, the arguments that lead to this result rely only on a few geometrical features of the compactification manifold and, hence, can be used independently of string theory.