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

P. Di Vecchia , A. Tanzini (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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 Delta>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 renormalization 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.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

P. Di Vecchia, A. Tanzini. N=2 Super Yang-Mills and the XXZ spin chain. Journal of Geometry and Physics, 2005, 54, pp.116-130. ⟨hal-00019927⟩