Planar equivalence 2006

Planar equivalence between supersymmetric Yang-Mills theory and its orientifold daughters is a promising tool for explorations of nonperturbative aspects of quantum chromodynamics. Taking our 2004 review as a starting point, we summarize some recent developments in this issue. The most interesting processes in quantum chromodynamics (QCD) are those occurring at large distances, at strong coupling. The large distance dynamics determining such salient features as chiral symmetry breaking and color confinement are the realm of nonperturbative phenomena. Despite the practical importance of the issue and the fact that this is a very deep theoretical problem, very few analytic methods of calculations (of a limited scope) were developed over the years, for a recent review see [1]. The situation is much better in supersymmetric (SUSY) theories: certain quantities (which go under the name of F terms) can be calculated exactly, due to holomorphic dependences on various parameters. In particular, it is possible to calculate the exact value of the gluino condensate [2] in pure N = 1 super- Yang-Mills (SYM) theory (we will also refer to this theory as supersymmetric gluodynamics).