Abstract
Considering a higher dimensional Lorentz group as the symmetry of the tangent space, we unify gravity and gauge interactions in a natural way. The spin connection of the gauged Lorentz group is then responsible for both gravity and gauge fields, and the action for the gauged fields becomes part of the spin curvature squared. The realistic group which unifies all known particles and interactions is the SO(1, 13) Lorentz group whose gauge part leads to SO(10) grand unified theory and contains double the number of required fermions in the fundamental spinor representation. We briefly discuss the Brout-Englert-Higgs mechanism which breaks the SO(1, 13) symmetry first to SO(1, 3) × SU(3) × SU(2) × U(1) and further to SO(1, 3) × SU(3) × U(1) and gives very heavy masses to half of the fermions leaving the others with light masses.
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References
S. Weinberg, Generalized theories of gravity and supergravity in higher dimensions, in the proceeding of 5th Workshop on Grand Unification, K. Kang et al. eds., World Scientific, Singapore (1984).
A.H. Chamseddine and V. Mukhanov, Gravity with de Sitter and unitary tangent groups, JHEP 03 (2010) 033 [arXiv:1002.0541] [INSPIRE].
A.H. Chamseddine and J. Fröhlich, SO(10) unification in noncommutative geometry, Phys. Rev. D 50 (1994) 2893 [hep-th/9304023] [INSPIRE].
C. Misner, K. Thorne and J. Wheeler, Gravitation, Freeman and Company (1993).
A.H. Chamseddine and A. Connes, Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I, Fortsch. Phys. 58 (2010) 553 [arXiv:1004.0464] [INSPIRE].
R. Percacci, The Higgs phenomenon in quantum gravity, Nucl. Phys. B 353 (1991) 271 [arXiv:0712.3545] [INSPIRE].
F. Nesti and R. Percacci, Graviweak unification, J. Phys. A 41 (2008) 075405 [arXiv:0706.3307] [INSPIRE].
F. Nesti and R. Percacci, Chirality in unified theories of gravity, Phys. Rev. D 81 (2010) 025010 [arXiv:0909.4537] [INSPIRE].
R. Greene, Isometric embeddings of Riemannian and pseudo-Riemannian manifolds, Mem. Amer. Math. Soc. 97 (1970).
M.L. Gromov and V.A. Rokhlin, Embeddings and immersions in Riemannian geometry, Uspekhi Mat. Nauk 25 (1970) 1 [Russ. Math. Surv. 25 (1970) 1].
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ArXiv ePrint: 1602.02295
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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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Chamseddine, A.H., Mukhanov, V. On unification of gravity and gauge interactions. J. High Energ. Phys. 2016, 20 (2016). https://doi.org/10.1007/JHEP03(2016)020
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DOI: https://doi.org/10.1007/JHEP03(2016)020