Local Operators from the Space of Vacua of Four Dimensional SUSY Gauge Theories
arXiv:1810.01192
Abstract
We construct local operators in short representations of supersymmetry algebras from polyvector fields on the quantum moduli space of vacua of supersymmetric gauge theories. These operators form a super Lie algebra under a natural bracket operation with structure constants determined by terms in the operator product expansion of the corresponding operators. We propose a formula for the superconformal index in terms of an index over polyvector fields on the moduli space of vacua. Along the way, we construct several models with moduli space of vacua corresponding to affine cones over smooth bases using the classical geometry of Severi varieties and the Landsberg-Manivel projective geometries corresponding to the Freudenthal magic square of exceptional Lie algebras. Curiously, we relate the Landsberg-Manivel projective geometries to the exceptional enhanced symmetry surprises of Dimofte and Gaiotto. Finally, we determine Beasley-Witten higher-derivative F-terms in new examples arising from Severi varieties and remark on their origin in classical projective duality.
arXiv comment38 pages
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