The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields

Details The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields The Spectrum of the Dirac Operator on Coset Spaces with Homogeneous Gauge Fields

2003-04-04

arxiv.org/abs/hep-th/0304037v1

JHEP 0305 (2003) 018

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, typeset in LaTeX, uses youngtab.sty

Scientific paper

10.1088/1126-6708/2003/05/018

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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