Lattice Sigma Models with Exact Supersymmetry
arXiv:hep-lat/0311042 · doi:10.1088/1126-6708/2004/05/044
Abstract
We show how to construct lattice sigma models in one, two and four dimensions which exhibit an exact fermionic symmetry. These models are discretized and {\it twisted} versions of conventional supersymmetric sigma models with N=2 supersymmetry. The fermionic symmetry corresponds to a scalar BRST charge built from the original supercharges. The lattice theories possess local actions and in many cases admit a Wilson term to suppress doubles. In the two and four dimensional theorie s we show that these lattice theories are invariant under additional discrete symmetries. We argue that the presence of these exact symmetries ensures that no fine tuning is required to achieve N=2 supersymmetry in the continuum limit. As a concrete example we show preliminary numerical results from a simulation of the O(3) supersymmetric sigma model in two dimensions.
23 pages, 3 figures, formalism generalized to allow for explicit Wilson mass terms. New numerical results added. Version to be published in JHEP
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- Supersymmetric invariant theories