The Ising model and planar N=4 Yang-Mills

Details The Ising model and planar N=4 Yang-Mills The Ising model and planar N=4 Yang-Mills

2007-11-21

arxiv.org/abs/0711.3404v2

J.Phys.A41:275205,2008

Physics

High Energy Physics

High Energy Physics - Theory

24 pages. v2: References added and minor typos corrected

Scientific paper

10.1088/1751-8113/41/27/275205

The scattering-matrix for planar Yang-Mills with N=4 supersymmetry relies on the assumption that integrability holds to all orders in perturbation theory. In this note we define a map from the spectral variables x^{\pm}, parameterizing the long-range magnon momenta, to couplings in a two-dimensional Ising model. Under this map integrability of planar N=4 Yang-Mills becomes equivalent to the Yang-Baxter equation for the two-dimensional Ising model, and the long-range variables x^{\pm} translate into the entries of the Ising transfer matrices. We explore the Ising correlation length which equals the inverse magnon momentum in the small momentum limit. The critical regime is thus reached for vanishing magnon momentum. We also discuss the meaning of the Kramers-Wannier duality transformation on the gauge theory, together with that of the Ising model critical points.

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