Dirac equation on a G₂ manifold

الأصل · EN

We find a large family of solutions to the Dirac equation on a manifold of G₂ holonomy asymptotic to a cone over S³ × S³, including all radial solutions. The behaviour of these solutions is studied as the manifold developes a conical singularity. None of the solutions found are both localised and square integrable at the origin. This result is consistent with the absence of chiral fermions in M-theory on the conifold over S³× S³. The approach here is complementary to previous analyses using dualities and anomaly cancellation.