nLab gauge-Higgs unification

Idea

In particle physics, gauge-Higgs unification (Manton 79, Hosotani 83) also known as the Hosotani mechanism (see Hosotani 12) refers to hypothetical models of particle physics where the Higgs field on 4d spacetimes arises as a component of a gauge field in higher dimensions, either after Kaluza-Klein compactification or by passage to a 4d asymptotic boundary in a Randall-Sundrum model or similar.

graphics grabbed from Lim 09

Gauge-Higgs unification is naturally combined with grand unification of gauge groups, whence one then also speaks of gauge-Higgs grand unification (e.g. Hosotani-Yamatsu 15). Also the Connes-Lott models realize gauge-Higgs unification, in a non-commutative geometric KK-compactification.

Attractive aspects of gauge-Higgs unification include the following:

1. a potential for providing a mechanism behind the Higgs-sector in the standard model of particle physics which could possibly solve the naturalness/hierarchy problem (e.g. Kaul 08, Csáki-Tanedo 13).

   As such, gauge-Higgs unification is a possible alternative to MSSM-models.

2. a mechanism for ruling out proton decay in GUT-models, see below.

Properties

No proton-decay

Gauge-Higgs grand unification is claimed to predict stability of the proton, hence no proton decay (Hosotani-Yamatsu 15, Furui-Hosotani-Yamatsu 16, Sec. 2.6 Hosotani 17, Section 6).

References

General

The mechanism is due to

• Nicholas Manton, A new six-dimensional approach to the Weinberg-Salam model, Nuclear Physics B Volume 158, Issue 1, 8 October 1979, Pages 141-153 (doi:10.1016/0550-3213(79)90192-5)

• Yutaka Hosotani, Dynamical Mass Generation by Compact Extra Dimensions, Phys. Lett. 126B (1983) 309-313 (spire:188768, doi:10.1016/0370-2693(83)90170-3)

• Yutaka Hosotani, Dynamics of non-integrable phases and gauge symmetry breaking, Annals of Physics Volume 190, Issue 2, March 1989, Pages 233-253 (doi:10.1016/0003-4916(89)90015-8)

and was revived with:

• H. Hatanaka, T. Inami, C.S. Lim, The Gauge Hierarchy Problem and Higher Dimensional Gauge Theories, Mod. Phys. Lett. A13 (1998) 2601-2612 (arXiv:hep-th/9805067)

Review:

• Yutaka Hosotani, Gauge-Higgs Unification Approach, AIP Conference Proceedings 1467, 208 (2012) (arXiv:1206.0552)

• Csaba Csáki, Philip Tanedo, Beyond the Standard Model, lectures at 2013 European School of High-Energy Physics, 2013 (doi:10.5170/CERN-2015-004.169)

Deatiled phenomenology:

• Naoyuki Haba, Kazunori Takenaga, Toshifumi Yamashita, Higgs mass in the gauge-Higgs unification, Phys. Lett. B615 (2005) 247-256 (arXiv:hep-ph/0411250)

• C. S. Lim, Precision Tests and CP Violation in Gauge-Higgs Unification, 2009 (slides pdf)

• Jason Carson, Nobuchika Okada, 125 GeV Higgs boson mass from 5D gauge-Higgs unification, Progress of Theoretical and Experimental Physics, Volume 2018, Issue 3, March 2018, 033B03 (doi:10.1093/ptep/pty018)

Discussion in view of naturalness/hierarchy problem:

• Romesh K. Kaul, Naturalness and Electro-weak Symmetry Breaking (arXiv:0803.0381)

In $Spin(11)$-GUT (“$SO(11)$”):

Discussion in Spin(11)-GUT (“SO(11)-GUT”):

• Yutaka Hosotani, Naoki Yamatsu, Gauge–Higgs grand unification, Progress of Theoretical and Experimental Physics, Volume 2015, Issue 11, November 2015 (arXiv:1504.03817, doi:10.1093/ptep/ptw116)

• Atsushi Furui, Yutaka Hosotani, Naoki Yamatsu, Toward Realistic Gauge-Higgs Grand Unification, Progress of Theoretical and Experimental Physics, Volume 2016, Issue 9, September 2016, 093B01 (arXiv:1606.07222)

• Yutaka Hosotani, Gauge-Higgs EW and Grand Unification, International Journal of Modern Physics AVol. 31, No. 20n21, 1630031 (2016) (arXiv:1606.08108)

• Yutaka Hosotani, New dimensions from gauge-Higgs unification (arXiv:1702.08161)

• Yutaka Hosotani, Naoki Yamatsu, Electroweak Symmetry Breaking and Mass Spectra in Six-Dimensional Gauge-Higgs Grand Unification (arXiv:1710.04811)

In $Spin(12)$-GUT (“$SO(12)$”):

Discussion in Spin(11)-GUT (“SO(11)-GUT”):

• 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, 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)