Exact lattice supersymmetry

We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at non-zero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and on 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. (C) 2009 Elsevier B.V. All rights reserved.