Twisted Supersymmetric Gauge Theories and Orbifold Lattices

We examine the relation between twisted versions of the extended supersymmetric gauge theories and supersymmetric orbifold lattices. In particular, for the $\mathcal{N}=4$ SYM in $d=4$, we show that the continuum limit of orbifold lattice reproduces the twist introduced by Marcus, and the examples at lower dimensions are usually Blau-Thompson type. The orbifold lattice point group symmetry is a subgroup of the twisted Lorentz group, and the exact supersymmetry of the lattice is indeed the nilpotent scalar supersymmetry of the twisted versions. We also introduce twisting in terms of spin groups of finite point subgroups of $R$-symmetry and spacetime symmetry.Comment: 32 page

Exact Lattice Supersymmetry

We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of {\cal N}=4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems

Exact Lattice Supersymmetry

We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of {\cal N}=4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems

Lattice formulation of (2,2) supersymmetric gauge theories with matter fields

We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.Comment: 13 pages, 2 figures. Appendix added, references updated, typos fixe