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mitchell porter

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- geometric unity

Eric Weinstein finally released a video of his 2013 Oxford talk on "geometric unity". There are many fans and skeptics out there, looking in vain for a genuinely informed assessment of the idea.

I admit that so far I have only skimmed the transcript of the video, being very pressed for attention and time these days. But I come away with the impression of a four-manifold, with some kind of a connection and some kind of fermion bundle, and then mostly he counts degrees of freedom and hopes that this will give the fermions and gauge fields of the standard model.

But one thing that caught my attention, is his remark in the 2020 introduction, at 28 minutes, that Witten's 1994 quantum-field construction of Donaldson theory (a branch of pure math) could also be obtained from Weinstein's starting point; and that Weinstein's model could also have given rise to the Seiberg-Witten equations.

Not only are those rather strong claims, but they might actually help us arrive at a more nuanced grasp of what Weinstein's idea is. As you may read here, Witten obtained Donaldson theory by starting with an N=2 field theory, then "topologically twisting" it to obtain a topological QFT; and Seiberg-Witten equations may be obtained in a different limit. Weinstein doesn't employ supersymmetry, so one has to wonder what he's thinking, but maybe this can still help us zero in on what his idea is.

I admit that so far I have only skimmed the transcript of the video, being very pressed for attention and time these days. But I come away with the impression of a four-manifold, with some kind of a connection and some kind of fermion bundle, and then mostly he counts degrees of freedom and hopes that this will give the fermions and gauge fields of the standard model.

But one thing that caught my attention, is his remark in the 2020 introduction, at 28 minutes, that Witten's 1994 quantum-field construction of Donaldson theory (a branch of pure math) could also be obtained from Weinstein's starting point; and that Weinstein's model could also have given rise to the Seiberg-Witten equations.

Not only are those rather strong claims, but they might actually help us arrive at a more nuanced grasp of what Weinstein's idea is. As you may read here, Witten obtained Donaldson theory by starting with an N=2 field theory, then "topologically twisting" it to obtain a topological QFT; and Seiberg-Witten equations may be obtained in a different limit. Weinstein doesn't employ supersymmetry, so one has to wonder what he's thinking, but maybe this can still help us zero in on what his idea is.