nLab higher spin geometry - contents

spin geometry, string geometry, fivebrane geometry …

Ingredients

• supergeometry

• higher differential geometry

Spin geometry

spin geometry

• spin group

  pin group

  semi-spin group

  central product spin group

  spin^c group

• spin representation,

  • spinor, fermion

  • charge conjugation matrix, Fierz identity

  • real spin representation

  • Dirac conjugate

  • Dirac spinor, Weyl spinor, Majorana spinor

• spin structure, spin^c structure

• spinor bundle

• Dirac operator

  • index theory, K-theory

• Dirac equation

• Dirac field

rotation groups in low dimensions:

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)

see also

• Spin(5).Spin(3)

• finite rotation groups

• ADE-classification

String geometry

string geometry

• string 2-group, string^c 2-group

• string structure, string^c structure

Fivebrane geometry

• fivebrane 6-group

• fivebrane structure

Ninebrane geometry

• ninebrane 10-group