From the Dirac Operator to Wess-Zumino Models on Spatial Lattices
arXiv:hep-th/0407207 · doi:10.1016/j.aop.2004.09.002
Abstract
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.
39 pages, 3 figures
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Cited by in corpus (17)
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- Low-dimensional Supersymmetric Lattice Models
- Complete supersymmetry on the lattice and a No-Go theorem: A simulation with intact supersymmetries on the lattice
- Simulations of super Yang-Mills theory in two dimensions
- Two-Dimensional Wess-Zumino Models at Intermediate Couplings
- Supersymmetry Breaking in Low Dimensional Models
- Supersymmetric nonperturbative formulation of the WZ model in lower dimensions
- Critical flavour number of the Thirring model in three dimensions
- Scaling and superscaling solutions from the functional renormalization group
- Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
- Supersymmetric Nonlinear O(3) Sigma Model on the Lattice
- Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms
- Optimised Dirac Operators on the Lattice: Construction, Properties and Applications
- Non-perturbative Methods in Supersymmetric Theories
- Lattice calculations on the spectrum of Dirac and Dirac-Kähler operators
- Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions