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On Generalized Pfaffians

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arxiv 2409.06871 v1 pith:ZWUGLVPO submitted 2024-09-10 math.AG hep-thmath.CO

Jacques Distler , Nathan Donagi , Ron Donagi This is my paper · ORCID
classification math.AGhep-thmath.CO
keywords conjecturedeterminantentriesotherpolynomialsquareadmitanti-symmetric
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abstract

The determinant of an anti-symmetric matrix $g$ is the square of its Pfaffian, which like the determinant is a polynomial in the entries of $g$. Studies of certain super conformal field theories (of class S) suggested a conjectural generalization of this, predicting that each of a series of other polynomials in the entries of $g$ also admit polynomial square roots. Among other consequences, this conjecture led to a characterization of the local Hitchin image for type D. Several important special cases had been established previously. In this paper we prove the conjecture in full.

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  1. Even More On Twisted $A_{2n}$ Class-S Theories

    hep-th 2024-11 conditional novelty 6.0 of 10

    An order-4 twist automorphism and local polynomial constraints determine the Coulomb branch Hitchin systems for twisted A_{2n} class-S punctures, with explicit Seiberg-Witten curves for examples.

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