Title

Lattice Supersymmetry and Topological Field Theory

Author(s)/Creator(s)

Simon Catterall, Syracuse UniversityFollow

Document Type

Article

Date

1-28-2003

Language

English

Disciplines

Physics

Description/Abstract

It is known that certain theories with extended supersymmetry can be discretized in such a way as to preserve an exact fermionic symmetry. In the simplest model of this kind, we show that this residual supersymmetric invariance is actually a BRST symmetry associated with gauge fixing an underlying local shift symmetry. Furthermore, the starting lattice action is then seen to be entirely a gauge fixing term. The corresponding continuum theory is known to be a topological field theory. We look, in detail, at one example - supersymmetric quantum mechanics which possesses two such BRST symmetries. In this case, we show that the lattice theory can be obtained by blocking out of the continuum in a carefully chosen background metric. Such a procedure will not change the Ward identities corresponding to the BRST symmetries since they correspond to topological observables. Thus, at the quantum level, the continuum BRST symmetry is preserved in the lattice theory. Similar conclusions are reached for the two-dimensional complex Wess-Zumino model and imply that all the supersymmetric Ward identities are satisfied {\it exactly} on the lattice. Numerical results supporting these conclusions are presented.

Additional Information

18 pages, 2 figures More information at http://arxiv.org/abs/hep-lat/0301028

Recommended Citation

Catterall, Simon, "Lattice Supersymmetry and Topological Field Theory" (2003). Physics - All Scholarship. 464.
https://surface.syr.edu/phy/464

Source

Harvested from Arxiv.org

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.