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

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

2004-05-28

arxiv.org/abs/hep-th/0405262v2

J.Geom.Phys. 54 (2005) 116-130

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 2 figures; v2: references added, misprints corrected

Scientific paper

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.

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