Supersymmetry on a lattice

Abstract

We develop Lagrangian and Hamiltonian lattice formulations of the Wess-Zumino model which preserve the superalgebra. We check that the lattice model passes into the continuum model in the zero-lattice-spacing limit, and obtain various perturbative results (nonrenormalization, effective-potential loop expansion) on the lattice. We study the phase structure with the one-loop effective potential and find dynamical symmetry breaking at large coupling in two dimensions, but not in four dimensions. Separately, we evaluate the strong-coupling limit in the Hamiltonian formulation and confirm the accuracy of the one-loop effective-potential predictions. Our methods should apply to certain other supersymmetric theories.