Fermionic zero modes in the vortex field in arbitrary dimensions and index of Dirac operator with Majorana-like interaction

Details Fermionic zero modes in the vortex field in arbitrary dimensions and index of Dirac operator with Majorana-like interaction Fermionic zero modes in the vortex field in arbitrary dimensions and index of Dirac operator with Majorana-like interaction

2011-10-31

arxiv.org/abs/1110.6911v2

Physics

High Energy Physics

High Energy Physics - Theory

30 pages

Scientific paper

In this work we consider fermionic zero modes in the external scalar and electromagnetic field forming the vortex on a sphere. We find the correspondence between the equations for the fermions in different dimensions, find their explicit expressions through the vortex fields in case of massless fermions, asymptotics near the poles in case of massive fermions and check the number of the solutions by proving index theorem for the fermions on a sphere. As a part of deriving the index, we write a detailed calculation of the Green function of the Heat equation.

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