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.
- Differential and Algebraic Geometry
- Global Symmetries
- Solitons Monopoles and Instantons
ASJC Scopus subject areas
- Nuclear and High Energy Physics