Fermion Zero Modes in Odd Dimensions

Details Fermion Zero Modes in Odd Dimensions Fermion Zero Modes in Odd Dimensions

2009-11-24

arxiv.org/abs/0911.4598v1

J.Phys.A43:095402,2010

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1088/1751-8113/43/9/095402

We study the zero modes of the Abelian Dirac operator in any odd dimension. We use the stereographic projection between a $(2n-1)$ dimensional space and a $(2n-1)$ sphere embedded in a $2n$ dimensional space. It is shown that the Dirac operator with a gauge field of uniform field strengths in $S^{2n-1}$ has symmetries of SU($n$)$\times$U(1) which is a subgroup of SO($2n$). Using group representation theory, we obtain the number of fermion zero modes, as well as their explicit forms, in a simple way.

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