Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry

Abstract

We construct super Yang-Mills theories with $\mathcal{N}=2,4$ supersymmetries on the two-dimensional square lattice keeping one or two supercharges exactly. Along the same line as the previous paper \cite{sugino}, the construction is based on topological field theory formulation. In order to resolve the problem of degenerate classical vacua encountered in the previous paper, we consider two kinds of modifications of the action. For one of them, any supersymmetry breaking terms do not need to be introduced, and the formulations exactly realize some of supersymmetries at the lattice level. Our lattice actions flow to the desired continuum theories without any fine-tuning of parameters.

15 pages, no figure, LaTeX, (v2) published version in JHEP, (v3) minor corrections, (v4) 22 pages, reconsidered the vacuum degeneracy problem for SU(N), revised version

References in corpus (3)

• A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
• Exact Lattice Supersymmetry from Topological Field Theory
• Deconstruction, 2d lattice Yang-Mills, and the dynamical lattice spacing

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