The Ising model and planar N=4 Yang-Mills



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Gómez, César and Gunnesson, Johan and Hernández Redondo, Rafael (2008) The Ising model and planar N=4 Yang-Mills. Journal of physics A: Mathematical and theoretical, 41 (27). ISSN 1751-8113

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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 ±, 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 twodimensional Ising model, and the long-range variables x ± 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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© 2008 IOP Publishing Ltd. We are grateful to N. Dorey, F. Ferrari, J. Minahan and R. Roiban for comments and discussions. C. G. is also grateful to the Isaac Newton Institute for Mathematical Sciences for hospitality while this work was being completed. The work of J. G. is supported by a Spanish FPU grant and by a European fellowship through MRTN-CT-2004-005104. This work is also partially supported by the Spanish DGI under contracts FPA2003-02877 and FPA2003-04597 and by the CAM project HEPHACOS P-ESP-00346.

Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:45476
Deposited On:09 Jan 2018 12:38
Last Modified:09 Jan 2018 12:38

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