Dirac Operator Zero-modes on a Torus

Details Dirac Operator Zero-modes on a Torus Dirac Operator Zero-modes on a Torus

2005-06-30

arxiv.org/abs/hep-th/0506259v1

Annals Phys. 322 (2007) 460-488

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, 2 figures

Scientific paper

We study Dirac operator zero-modes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In a suitable torus coordinates the zero-mode wave functions can be related to holomorphic functions of the complex torus coordinates. We construct the zero-mode wave functions that satisfy the twisted periodic conditions. The chirality and the degeneracy of the zero-modes are uniquely determined by the gauge background and are consistent with the index theorem.

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