Abstract
We analyse the normalisable zero-modes of the Dirac operator on the TaubNUT manifold coupled to an abelian gauge field with self-dual curvature, and interpret them in terms of the zero modes of the Dirac operator on the 2-sphere coupled to a Dirac monopole. We show that the space of zero modes decomposes into a direct sum of irreducible SU(2) representations of all dimensions up to a bound determined by the spinor charge with respect to the abelian gauge group. Our decomposition provides an interpretation of an index formula due to Pope and provides a possible model for spin in recently proposed geometric models of matter.
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Jante, R., Schroers, B.J. Dirac operators on the Taub-NUT space, monopoles and SU(2) representations. J. High Energ. Phys. 2014, 114 (2014). https://doi.org/10.1007/JHEP01(2014)114
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DOI: https://doi.org/10.1007/JHEP01(2014)114