nLab pure spinor

Contents

Ingredients

Dynkin label	sp. orth. group	spin group	pin group	semi-spin group
	SO(2)	Spin(2)	Pin(2)
B1	SO(3)	Spin(3)	Pin(3)
D2	SO(4)	Spin(4)	Pin(4)
B2	SO(5)	Spin(5)	Pin(5)
D3	SO(6)	Spin(6)
B3	SO(7)	Spin(7)
D4	SO(8)	Spin(8)		SO(8)
B4	SO(9)	Spin(9)
D5	SO(10)	Spin(10)
B5	SO(11)	Spin(11)
D6	SO(12)	Spin(12)
	$\vdots$	$\vdots$
D8	SO(16)	Spin(16)		SemiSpin(16)
	$\vdots$	$\vdots$
D16	SO(32)	Spin(32)		SemiSpin(32)

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

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

See also

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)

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]

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

Last revised on July 10, 2023 at 07:06:54. See the history of this page for a list of all contributions to it.