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arXiv · 2103.15600

Normal form of nilpotent vector field near the tip of the pure spinor cone

Andrei Mikhailov·Dennis Zavaleta
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Abstract

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.

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Andrei Mikhailov, Dennis Zavaleta. 2021-03-29. Normal form of nilpotent vector field near the tip of the pure spinor cone. https://doi.org/10.1007/jhep07(2021)150

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