# Nilpotence Varieties

@article{Eager2018NilpotenceV, title={Nilpotence Varieties}, author={Richard Eager and Ingmar Saberi and Johannes Walcher}, journal={Annales Henri Poincar{\'e}}, year={2018}, volume={22}, pages={1319-1376} }

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 of nilpotent elements in (the projectivized parity reversal of) the odd part of the algebra. Most of these varieties have appeared in various guises in previous literature, but we study them systematically here, from a new perspective: As the natural moduli spaces parameterizing twists of a super-Poincaré-invariant…

## 26 Citations

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G
2
×
S
U
(
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)
holonomy. Our…

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## References

SHOWING 1-10 OF 80 REFERENCES

### Spinorial cohomology and maximally supersymmetric theories

- Physics
- 2001

Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace…

### Holomorphic field theories and Calabi–Yau algebras

- MathematicsInternational Journal of Modern Physics A
- 2019

We consider the holomorphic twist of the worldvolume theory of flat D[Formula: see text]-branes transversely probing a Calabi–Yau manifold. A chain complex, constructed using the BV formalism,…

### Notes on Spinors

- Mathematics
- 2012

In these notes, we collect the properties of spinors in various dimensions and, over JR, for spaces of various signatures. Such information is needed to discuss the possihle supersymmetries in…

### ON ASSOCIATED VARIETY FOR LIE SUPERALGEBRAS

- Mathematics
- 2008

We define the associated variety XM of a module M over a finite- dimensional superalgebra g, and show how to extract information about M from these geometric data. XM is a subvariety of the cone X of…

### Special Quantum Field Theories¶in Eight and Other Dimensions

- Physics
- 1997

Abstract:We build nearly topological quantum field theories in various dimensions. We give special attention to the case of eight dimensions for which we first consider theories depending only on…

### Fivebranes and Knots

- Mathematics
- 2011

We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a…