N=2 Super Yang–Mills and the XXZ spin chain

Abstract We analyse the renormalisation properties of composite operators of scalar fields in the N = 2 Super Yang–Mills theory. We compute the matrix of anomalous dimensions in the planar limit at one-loop order in the ’t Hooft coupling, and show that it corresponds to the Hamiltonian of an integrable XXZ spin chain with an anisotropy parameter Δ > 1 . We suggest that this parameter could be related to the presence of non-trivial two-form fluxes in the dual supergravity background. We find that the running of the gauge coupling does not affect the renormalisation group equations for these composite operators at one-loop order, and argue that this is a general property of gauge theories which is not related to supersymmetry.