Dirac equation on a G_2 manifold

Abstract

We find a large family of solutions to the Dirac equation on a manifold of $G_2$ holonomy asymptotic to a cone over $S^3\times S^3$, 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 $S^3\times S^3$. The approach here is complementary to previous analyses using dualities and anomaly cancellation.

1+11 pages. LaTeX. Minor rewording in introduction and conclusion

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Cited by in corpus (2)

• Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
• Comments on M Theory Dynamics on G2 Holonomy Manifolds