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The Pfaffian in the Grassmannian...

From a post by David Guarrera at Imaginary Potential:

One example that I do understand, since I’ve read the paper many times, is Hori and Tong’s “proof” of Rodland’s Conjecture: that the Pfaffian in the Grassmannian G(2,7) lives on the same kahler moduli space as a hypersurface Calabi Yau in a Grassmannian. The proof uses beautiful physical intuition about the dynamics of non-abelian gauge theories in two dimensions.
However, you may think that the kahler moduli spaces of Calabi Yau’s are useless. Fair enough, I say. But they’re quite beautiful.

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