arXiv:hep-th/0412283v1 23 Dec 2004 THE COMPLETE ONE–LOOP SPIN CHAIN FOR N =2 SUPER YANG–MILLS Paolo Di Vecchia NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark divecchi@alf.nbi.dk Alessandro Tanzini SISSA, via Beirut 2/4, 34014 – Trieste, Italy tanzini@sissa.it Abstract We show that the complete planar one–loop mixing matrix of the N =2 Super Yang–Mills theory can be obtained from a reduction of that of the N = 4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap. 1. INTRODUCTION AND DISCUSSION The study of the AdS/CFT correspondence in some particular subsec- tors characterised by large quantum numbers, started with [1], provided a new and very intuitive way to look at the duality between gauge and string theory. The basic idea is that in presence of large quantum num- bers one can give a semiclassical description of the string states. This semiclassical description is reproduced on the gauge theory side by the coherent states of a quantum mechanical model, which can be extracted from the study of a particular subsector of the dual gauge theory. More precisely, the original idea of Berenstein et al. [1] was to regard some gauge–invariant operators of N = 4 Super Yang–Mills (SYM) theory as a discretized version of the physical type IIB string on the plane–wave background. The BMN operators are single trace operators containing a large number of one of the complex scalar fields of N =4 SYM, with the insertion of few impurities given by the other fields of the N = 4 supermultiplet, each of them corresponding to a different excita- 1