Dirac operator zeromodes on a torus
Abstract
We study Dirac operator zeromodes 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 suitable torus coordinates the zeromode wave functions can be related to holomorphic functions of the complex torus coordinates. Half of the twisted boundary conditions for the holomorphic part of the zeromode wave function can be made periodic or antiperiodic. The remaining half is until coordinate dependent but diagonal. We completely solve the twisted boundary conditions and construct the zeromode wave functions. The chirality and the degeneracy of the zeromodes are uniquely determined by the gauge background and are consistent with the index theorem.
 Publication:

Annals of Physics
 Pub Date:
 February 2007
 DOI:
 10.1016/j.aop.2006.02.013
 arXiv:
 arXiv:hepth/0506259
 Bibcode:
 2007AnPhy.322..460T
 Keywords:

 High Energy Physics  Theory
 EPrint:
 28 pages, 2 figures