nLab pure spinor

Idea

A pure spinor is a spinor with vanishing spinor-to-vector pairing

$$\overline{\psi} \Gamma^a \psi \;=\; 0 \,.$$

Related concepts

• Berkovits superstring

References

See also

• Wikipedia, Pure spinor

Discussion of superstring scattering amplitudes in terms of pure spinors:

• Carlos Mafra, Oliver Schlotterer, Towards the $n$-point one-loop superstring amplitude I: Pure spinors and superfield kinematics (arXiv:1812.10969)

• Carlos Mafra, Oliver Schlotterer, Towards the $n$-point one-loop superstring amplitude II: Worldsheet functions and their duality to kinematics (arXiv:1812.10970)

• Carlos Mafra, Oliver Schlotterer, Towards the $n$-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure (arXiv:1812.10971)

Relation to picture changing operators:

• Andrei Mikhailov, Dennis Zavaleta, Geometrical framework for picture changing operators in the pure spinor formalism (arXiv:2003.13995)

On pure spinors in supergravity:

• Martin Cederwall, Pure spinors in classical and quantum supergravity, in Handbook of Quantum Gravity (2023) [arXiv:2210.06141]

Relating the D'Auria-Fré formulation of supergravity to pure spinor-formalism:

• Pietro Antonio Grassi, Remarks on the Integral Form of $D=11$ Supergravity [arXiv:2304.01743]

On super multiplets via derived geometry on the pure spinor variety:

• Chris Elliott, Fabian Hahner, Ingmar Saberi: The Derived Pure Spinor Formalism as an Equivalence of Categories, SIGMA 19 (2023) 022 [arXiv:2205.14133, doi:10.3842/SIGMA.2023.022]

• Richard Eager, Simone Noja, Raphael Senghaas, Johannes Walcher: Adinkras and Pure Spinors [arXiv:2404.07167]

• Simone Noja: The Geometry of Pure Spinor Superfield Formalism, talk at CQTS (Dec 2024) [pdf]