A few months ago there were several math talks about how the Lie group E8 had been detected in some physics experiment. I recently looked up the original paper where this was announced,
"Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry", Science 327 (5962): 177–180, doi:10.1126/science.1180085
and was less than convinced by it. The evidence for the detection of E8 appears to be that they found a couple of peaks in some experiment, at points whose ratio is close to the golden ratio, which is apparently a prediction of some paper that I have not yet tracked down. The peaks are quite fuzzy and all one can really say is that their ratio is somewhere around 1.6. This seems to me to be a rather weak reason for claiming detection of a 248 dimensional Lie group; I would guess that a significant percentage of all experimental physics papers have a pair of peaks looking somewhat like this.
Does anyone know enough about the physics to comment on whether the claim is plausible? Or has anyone heard anything more about this from a reliable source? (Most of what I found with google consisted of uninformed blogs and journalists quoting each other.)
Update added later: I had a look at the paper mentioned by Willie Wong below, where Zamoldchikov predicts the expected masses. In fact he predicts there should be 8 peaks, and while the experimental results are consistent with the first 2 peaks, there are no signs of any of the other peaks. My feeling is that the interpretation of the experimental results as confirmation of an E8 symmetry is somewhat overenthusiastic.
Best Answer
This is a great question, but I don't think a reasonable answer can be given in this short space. So I wrote an expository note jointly with a colleague who was trained as a physicist. You can read it by following the link above -- comments are welcome.
But here are a couple of highlights:
One can argue about both of these points, of course. But these seem to be what the physicists claim and what they use in their papers.
To address Wadim's concerns about fringe science: Whether or not you find the E8 angle interesting or plausible, it seems that the experiment is interesting for entirely different reasons. The experimenters themselves claim that their main achievement is realizing this 1-dimensional quantum Ising model in the laboratory in a situation where the external field can be tuned to be above, below, or at the critical point. The Physics Today article on the subject paraphrases Subir Sachdev: