Closed superforms, contracted with commuting Killing spinors on supersymmetric backgrounds, produce equivariantly closed polyforms; demonstrated in 4d N=2 conformal supergravity.
Explaining Pure Spinor Superspace
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In the pure spinor formalism for the superstring and supermembrane, supersymmetric invariants are constructed by integrating over five $\theta$'s in d=10 and over nine $\theta$'s in d=11. This pure spinor superspace is easily explained using the superform (or ''ectoplasm'') method developed by Gates and collaborators, and generalizes the standard chiral superspace in d=4. The ectoplasm method is also useful for constructing d=10 and d=11 supersymmetric invariants in curved supergravity backgrounds.
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Superform Approach to Equivariant Localization in Supergravity
Closed superforms, contracted with commuting Killing spinors on supersymmetric backgrounds, produce equivariantly closed polyforms; demonstrated in 4d N=2 conformal supergravity.