Dirac equation on a G2 manifold

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 develops 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.