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arXiv · 1312.4879

Dirac operators on the Taub-NUT space, monopoles and SU(2) representations

Rogelio Jante·Bernd Schroers
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Abstract

We analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT 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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Rogelio Jante, Bernd Schroers. 2013-12-19. Dirac operators on the Taub-NUT space, monopoles and SU(2) representations. https://doi.org/10.1007/jhep01(2014)114

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