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

General

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)

For supergravity

On pure spinors in supergravity:

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

On manifestly supersymmetric action functionals for 11D supergravity via pure spinor superfields on superspace:

• Martin Cederwall: Towards a manifestly supersymmetric action for 11-dimensional supergravity, J. High Energ. Phys. 2010 117 (2010) [doi:10.1007/JHEP01(2010)117, arXiv:0912.1814]

• Martin Cederwall: $D=11$ supergravity with manifest supersymmetry, Mod. Phys. Lett. A 25 (2010) 3201–3212 [doi:10.1142/S0217732310034407, arXiv:1001.0112]

• Fabian Hahner, Ingmar Saberi: Eleven-dimensional supergravity as a Calabi-Yau twofold, Sel. Math. New Ser. 31 (2025) 38 [arXiv:2304.12371, doi:10.1007/s00029-025-01024-x]

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]