Nilpotence Varieties

Abstract We consider algebraic varieties canonically associated with any Lie superalgebra, and study them in detail for super-Poincaré algebras of physical interest. They are the locus nilpotent elements (the projectivized parity reversal of) odd part algebra. Most these have appeared various guises previous literature, but we systematically here, from a new perspective: As natural moduli spaces parameterizing twists super-Poincaré-invariant theory. obtain classification all possible twists, as well systematic analysis unbroken symmetry twisted theories. The stratification varieties, identification strata action Lorentz R -symmetry emphasized. also include short unconventional exposition pure spinor superfield formalism, perspective twisting, demonstrate that it can be applied to construct familiar multiplets four-dimensional minimally supersymmetric In dimensions amount supersymmetry, this technique produces BRST or BV complexes theories Koszul complex maximal ideal over coordinate ring nilpotence variety, possibly tensored equivariant module ring. addition, remark on connection Chevalley–Eilenberg supertranslation algebra, give two applications related ideas: calculation cohomology (2, 0) algebra six dimensions, degenerate encoding type IIB supergravity multiplet.