RT Journal Article
T1 The Ising model and planar N=4 Yang-Mills
A1 Gómez, César
A1 Gunnesson, Johan
A1 Hernández Redondo, Rafael
AB 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.
PB IOP Publishing Ltd
SN 1751-8113
YR 2008
FD 2008-07-11
LK https://hdl.handle.net/20.500.14352/52138
UL https://hdl.handle.net/20.500.14352/52138
LA eng
NO © 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.
NO Spanish FPU
NO European fellowship
NO Spanish DGI
NO CAM, Spain
DS Docta Complutense
RD 15 may 2024