A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry

Abstract

We construct super Yang-Mills theories with extended supersymmetry on hypercubic lattices of various dimensions keeping one or two supercharges exactly. Gauge fields are represented by ordinary unitary link variables, and the exact supercharges are nilpotent up to gauge transformations. Among the models, we show that the desired continuum theories are obtained without any fine tuning of parameters for the cases $\mathcal{N}=2,4,8$ in two-dimensions.

Comments: 29 pages, 1 figure, LaTeX, (v2) problem on degenerate vacua discussed, renormalization arguments modified, (v3) explanations and references added, published version in JHEP