The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields
Dolan, Brian P (2003) The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields. Journal of High Energy Physics, 0305 .
The spectrum and degeneracies of the Dirac operator are analysed on compact coset spaces when there is a non-zero homogeneous background gauge field which is compatible with the symmetries of the space, in particular when the gauge field is derived from the spin-connection. It is shown how the degeneracy of the lowest Landau level in the recently proposed higher dimensional quantum Hall effect is related to the Atiyah-Singer index theorem for the Dirac operator on a compact coset space.
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