Did a 1-dimensional magnet detect a 248-dimensional Lie algebra?
نویسندگان
چکیده
Y ou may have heard some of the buzz spawned by the recent paper [CTW+] in Science. That paper described a neutron scattering experiment involving a quasi-1-dimensional cobalt niobate magnet and led to rumors that E8 had been detected “in nature”. This is fascinating, because E8 is a mathematical celebrity and because such a detection seems impossible: it is hard for us to imagine a realistic experiment that could directly observe a 248-dimensional object such as E8. The connection between the cobalt niobate experiment and E8 is as follows. Around 1990, physicist Alexander Zamolodchikov and others studied perturbed conformal field theories in general; one particular application of this was a theoretical model describing a 1-dimensional magnet subjected to two magnetic fields. This model makes some numerical predictions that were tested in the cobalt niobate experiment, and the results were as predicted by the model. As the model involves E8 (in a way we will make precise in the section “Affine Toda Field Theory”), one can say that the experiment provides evidence for “E8
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