From the Dirac Operator to Wess-Zumino Models on Spatial Lattices

Details From the Dirac Operator to Wess-Zumino Models on Spatial Lattices From the Dirac Operator to Wess-Zumino Models on Spatial Lattices

2004-07-23

arxiv.org/abs/hep-th/0407207v1

Annals Phys. 316 (2005) 357-392

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, 3 figures

Scientific paper

10.1016/j.aop.2004.09.002

We investigate two-dimensional Wess-Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking lattice artifacts. We study the nonlocal and antisymmetric SLAC derivative which allows for chiral fermions without doublers and minimizes those artifacts. The supercharges of the lattice Wess-Zumino models are obtained by dimensional reduction of Dirac operators in high-dimensional spaces. The normalizable zero modes of the models with N=1 and N=2 supersymmetry are counted and constructed in the weak- and strong-coupling limits. Together with known methods from operator theory this gives us complete control of the zero mode sector of these theories for arbitrary coupling.

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