On small Dirac Neutrino Masses in String Theory

We study how tiny Dirac neutrino masses consistent with experimental constraints can arise in string theory SM-like vacua. We use as a laboratory 4d N=1 type IIA Calabi--Yau orientifold compactifications, and in particular recent results on Yukawa couplings at infinite field-space distance. In this regime we find Dirac neutrino masses of the form m_ν g_ν H, with gν the gauge coupling of the massive $U(1)$ under which the right-handed neutrinos νR are charged, and which should be in the range gν 10⁻¹⁴-10⁻¹² to reproduce neutrino data. The neutrino mass suppression occurs because the right-handed neutrino kinetic term behaves as Kνν 1 /gν². At the same time a tower of νR-like states appears with characteristic scale m₀ gν²MP 0.1-500 eV, in agreement with Swampland expectations. Two large hidden dimensions only felt by the νR sector arise at the same scale, while the string scale is around Mₛ g_ν MP 10-700 TeV. Some phenomenological implications and model building challenges are described. As a byproduct, independently of the neutrino issue, we argue that a single large dimension in the context of SM-like type IIA Calabi--Yau orientifolds leads to too small Yukawa couplings for quarks and charged leptons.