M-theory on G2 Manifolds Moduli to Phenomenology

Abstract

String theories are good candidates for unifying the Standard Model and general relativity. M theory is the non-perturbative limit of all string theories. Moreover, it has been shown that M theory should be compactified on $G_2$ manifold with ADE singularities. How this model deals with unsolved questions in physics is a good test for the validity of M theory. In this work, we will briefly cover the background in both math and physics for M theory compactified on $G_2$ manifold with ADE singularities. Then, we will discuss a linearized local model of this theory and use it to tackle physics questions such as quark mass hierarchy, neutrino mass, and proton decay. We see that in this model, geometrically the hierarchy of quark masses makes the solution for moduli very hard to find. This suggests a global model will be very predictive and testable through quark masses. Next, using the solution of the moduli, we compute neutrino Dirac mass terms and derive an estimation for neutrino masses. Notably, the masses of the two heavier light neutrinos are predicted to be about $0.05 text{ eV}$ and $0.009 text{ eV}$ ($0.05 text{ eV} $ and $0.05 text{ eV} $) for normal (inverted) hierarchy.