Correction to Vector Fields
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Pure spinor formalism implies that supergravity equations in space-time are equivalent to the requirement that the worldsheet sigma-model satisfies certain properties. Here we point out that one of these properties has a particularly transparent geometrical interpretation. Namely, there exists an odd nilpotent vector field on some singular supermanifold, naturally associated to space-time. All supergravity fields are encoded in this vector field, as coefficients in its normal form. The nilpotence implies, modulo some zero modes, that they satisfy the SUGRA equations of motion.
Introduction
Notations
Setup for cohomological perturbation theory
Cohomology ofin the space of vector fields
Coefficients of normal form satisfy wave equations
Fermionic fields
Supersymmetries and dilatation
Acknowledgments
Higher spin conformal Killing tensors
Bibliography
main scratchpad notes letters vector-fields NSNS literature ps-pco JHEP reserve