Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2001-08-16
Phys.Rev.D65:094501,2002
Physics
High Energy Physics
High Energy Physics - Lattice
29 pages, 10 figures. New results at strong coupling added. Minor corrections to text and one reference added. Version to appe
Scientific paper
10.1103/PhysRevD.65.094501
We study the two-dimensional Wess-Zumino model with extended N=2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving {\it exactly} a single supersymmetric invariance at finite lattice spacing $a$. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to $O(ga^2)$ where $g$ is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the massgaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing.
Catterall Simon
Karamov Sergey
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