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

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.

LaTeX, 22pp; v2: corrected mistakes, added explanations, new Section 7; v3: we show that the nilpotence of Q implies all SUGRA equations of motion, and discuss div Q in the Introduction

References in corpus (3)

• Superstring Scattering Amplitudes with the Pure Spinor Formalism
• Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism
• Superstrings in General Backgrounds