Contents

group theory

# Contents

## Idea

$SO(12)$ is the special orthogonal group in dimension 12.

$Spin(12)$ is the spin group in dimension 12.

In the classification of simple Lie groups this is the entry D6.

Dynkin labelsp. orth. groupspin grouppin groupsemi-spin group
SO(2)Spin(2)Pin(2)
B1SO(3)Spin(3)Pin(3)
D2SO(4)Spin(4)Pin(4)
B2SO(5)Spin(5)Pin(5)
D3SO(6)Spin(6)
B3SO(7)Spin(7)
D4SO(8)Spin(8)SO(8)
B4SO(9)Spin(9)
D5SO(10)Spin(10)
B5SO(11)Spin(11)
D6SO(12)Spin(12)
$\vdots$$\vdots$
D8SO(16)Spin(16)SemiSpin(16)
$\vdots$$\vdots$
D16SO(32)Spin(32)SemiSpin(32)

## References

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### As a grand unified gauge group

Discussion as a gauge group in grand unified theory (see there):

• S. Rajpoot and P. Sithikong, Implications of the $SO(12)$ gauge symmetry for grand unification, Phys. Rev. D 23, 1649 (1981) (doi:10.1103/PhysRevD.23.1649)

• Takaaki Nomura and Joe Sato, Standard(-like) Model from an $SO(12)$ Grand Unified Theory in six-dimensions with $S^2$ extra-space, Nucl.Phys.B811:109-122, 2009 (arXiv:0810.0898)

• Takaaki Nomura, Physics beyond the standard model with $S^2$ extra-space, 2009 (pdf, pdf)

• Cheng-Wei Chiang, Takaaki Nomura, Joe Sato, Gauge-Higgs unification models in six dimensions with $S^2/\mathbb{Z}_2$ extra space and GUT gauge symmetry (arXiv:1109.5835)

Created on August 29, 2019 at 05:08:50. See the history of this page for a list of all contributions to it.