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.

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

References in corpus (6)

• Supersymmetry on a Euclidean Spacetime Lattice II: Theories with Eight Supercharges
• Lifetime Differences and CP Violation Parameters of Neutral B Mesons at the Next-to-Leading Order in QCD
• A lattice study of the two-dimensional Wess Zumino model
• Non-positive fermion determinants in lattice supersymmetry
• The fermion determinant in (4,4) 2d lattice super-Yang-Mills
• Exact Lattice Supersymmetry from Topological Field Theory

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