No, string theory itself does not directly predict the rest mass of neutrinos. The prediction of neutrino masses and the discovery that neutrinos have non-zero rest masses came from experimental observations and subsequent theoretical developments in the field of particle physics, specifically through experiments such as the Super-Kamiokande and the Sudbury Neutrino Observatory.
However, string theory and its extensions can potentially provide a framework in which the origin and nature of neutrino masses can be understood. String theory proposes that all elementary particles, including neutrinos, arise from the vibrational modes of tiny, one-dimensional strings. The properties of these strings, such as their vibration patterns and interactions, can influence the masses of the particles they generate.
Various models within string theory, such as intersecting brane models or compactifications with specific geometries, have been proposed to incorporate the observed masses of neutrinos. These models introduce additional dimensions and specific arrangements of branes (higher-dimensional objects) in the theory, which can affect the masses and mixing of neutrinos. However, it's important to note that these models are still theoretical and require further development and experimental validation.
In summary, while string theory does not directly predict the rest mass of neutrinos, it offers a theoretical framework in which the origin and properties of neutrino masses can be explored. The actual determination of neutrino masses has relied on experimental observations and subsequent theoretical interpretations within the field of particle physics.