nLab SO(10)

Idea

$SO(10)$ is the special orthogonal group in dimension 10.

$Spin(10)$ is the spin group in dimension 10.

In the classification of simple Lie groups this is the entry D5.

Related concepts

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

References

General

(…)

As a grand unified gauge group

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

• Stefano Bertolini, Luca Di Luzio, Michal Malinský, Intermediate mass scales in the non-supersymmetric SO(10) grand unification: a reappraisal, Phys. Rev. D80:015013, 2009 (arXiv:0903.4049)

review:

• Howard Georgi, §24 in: Lie Algebras In Particle Physics, Westview Press (1999), CRC Press (2019) [doi:10.1201/9780429499210]

• Michal Malinský, 35 years of GUTs - where do we stand?, 2009 (pdf)

for non-superymmetric models:

• L. Lavoura and Lincoln Wolfenstein, Resuscitation of minimal $SO(10)$ grand unification, Phys. Rev. D 48, 264 (doi:10.1103/PhysRevD.48.264)

• Guido Altarelli, Davide Meloni, A non Supersymmetric SO(10) Grand Unified Model for All the Physics below $M_{GUT}$ (arXiv:1305.1001)

• Alexander Dueck, Werner Rodejohann, Fits to $SO(10)$ Grand Unified Models (arXiv:1306.4468)

• Chee Sheng Fong, Davide Meloni, Aurora Meroni, Enrico Nardi, Leptogenesis in $SO(10)$ (arXiv:1412.4776)

  (in view of leptogenesis)

• Tommy Ohlsson, Marcus Pernow, Fits to Non-Supersymmetric SO(10) Models with Type I and II Seesaw Mechanisms Using Renormalization Group Evolution (arXiv:1903.08241)

• Mainak Chakraborty, M.K. Parida, Biswonath Sahoo, Triplet Leptogenesis, Type-II Seesaw Dominance, Intrinsic Dark Matter, Vacuum Stability and Proton Decay in Minimal SO(10) Breakings (arXiv:1906.05601)

  Results indicating non-SUSY $SO(10)$ as self sufficient theory for neutrino masses, baryon asymmetry, dark matter, vacuum stability of SM scalar potential, origin of three gauge forces, and observed proton stability.

• Nobuchika Okada, Digesh Raut, Qaisar Shafi, Inflation, Proton Decay, and Higgs-Portal Dark Matter in $SO(10) \times U(1)_\pri$ (arXiv:1906.06869)

for supersymmetric models:

• Archana Anandakrishnan, B. Charles Bryant, Stuart Raby, LHC Phenomenology of $SO(10)$ Models with Yukawa Unification II (arXiv:1404.5628)

• Ila Garg, New minimal supersymmetric $SO(10)$ GUT phenomenology and its cosmological implications (arXiv:1506.05204)

On symmetry breaking in Spin(10)-grand unified theory to the exact standard model gauge group, via real normed division algebra (octonions, quaternions):

• Kirill Krasnov, Geometry of $Spin(10)$ Symmetry Breaking [arXiv:2209.05088]

• Nichol Furey, M. J. Hughes, Division algebraic symmetry breaking [arXiv:2210.10126]