nLab
SO(32)

Contents

Contents

Idea

The special orthogonal group in dimension 32.

Properties

In string theory

In type I string theory, and more generally in type II string theory on toroidal orientifolds, RR-field tadpole cancellation implies that the gauge group is SO(32) (see there).

Under the duality between type I and heterotic string theory this translates to the semi-spin gauge group SemiSpin(32) of heterotic string theory.

Discussion of type-I string phenomenology and grand unified theory based on SO(32) type-I strings: (MMRB 86, Ibanez-Munoz-Rigolin 98, Yamatsu 17).

rotation groups in low dimensions:

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)

see also

References

Type I string phenomenology and discussion of GUTs based on SO(32) type I strings:

  • H.S. Mani, A. Mukherjee, R. Ramachandran, A.P. Balachandran, Embedding of SU(5)SU(5) GUT in SO(32)SO(32) superstring theories, Nuclear Physics B Volume 263, Issues 3–4, 27 January 1986, Pages 621-628 (doi:10.1016/0550-3213(86)90277-4)

  • Luis Ibáñez, C. Muñoz, S. Rigolin, Aspects of Type I String Phenomenology, Nucl.Phys. B553 (1999) 43-80 (arXiv:hep-ph/9812397)

  • Emilian Dudas, Theory and Phenomenology of Type I strings and M-theory, Class. Quant. Grav.17:R41-R116, 2000 (arXiv:hep-ph/0006190)

  • Naoki Yamatsu, String-Inspired Special Grand Unification, Progress of Theoretical and Experimental Physics, Volume 2017, Issue 10, 1 (arXiv:1708.02078, doi:10.1093/ptep/ptx135)

Created on May 15, 2019 at 11:30:04. See the history of this page for a list of all contributions to it.