Abstract
We analyze the running at one-loop of the gauge couplings in the spectral Pati-Salam model that was derived in the framework of noncommutative geometry. There are a few different scenarios for the scalar particle content which are determined by the precise form of the Dirac operator for the finite noncommutative space. We consider these different scenarios and establish for all of them unification of the Pati-Salam gauge couplings. The boundary conditions are set by the usual RG flow for the Standard Model couplings at an intermediate mass scale at which the Pati-Salam symmetry is broken.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev. D 11 (1975) 2856 [INSPIRE].
U. Aydemir, D. Minic, C. Sun and T. Takeuchi, Pati-Salam unification from non-commutative geometry and the TeV-scale W R boson, arXiv:1509.01606 [INSPIRE].
V.D. Barger, E. Ma and K. Whisnant, General analysis of a possible second weak neutral current in gauge models, Phys. Rev. D 26 (1982) 2378 [INSPIRE].
A.H. Chamseddine and A. Connes, Universal formula for noncommutative geometry actions: unification of gravity and the Standard Model, Phys. Rev. Lett. 77 (1996) 4868 [INSPIRE].
A.H. Chamseddine and A. Connes, The spectral action principle, Commun. Math. Phys. 186 (1997) 731 [hep-th/9606001] [INSPIRE].
A.H. Chamseddine and A. Connes, Why the Standard Model, J. Geom. Phys. 58 (2008) 38 [arXiv:0706.3688] [INSPIRE].
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].
A.H. Chamseddine and A. Connes, Resilience of the spectral Standard Model, JHEP 09 (2012) 104 [arXiv:1208.1030] [INSPIRE].
A.H. Chamseddine, A. Connes and M. Marcolli, Gravity and the Standard Model with neutrino mixing, Adv. Theor. Math. Phys. 11 (2007) 991 [hep-th/0610241] [INSPIRE].
A.H. Chamseddine, A. Connes and V. Mukhanov, Geometry and the quantum: basics, JHEP 12 (2014) 098 [arXiv:1411.0977] [INSPIRE].
A.H. Chamseddine, A. Connes and V. Mukhanov, Quanta of geometry: noncommutative aspects, Phys. Rev. Lett. 114 (2015) 091302 [arXiv:1409.2471] [INSPIRE].
A.H. Chamseddine, A. Connes and W.D. van Suijlekom, Beyond the spectral Standard Model: emergence of Pati-Salam unification, JHEP 11 (2013) 132 [arXiv:1304.8050] [INSPIRE].
D. Chang, R.N. Mohapatra and M.K. Parida, A new approach to left-right symmetry breaking in unified gauge theories, Phys. Rev. D 30 (1984) 1052 [INSPIRE].
T.P. Cheng, E. Eichten and L.-F. Li, Higgs phenomena in asymptotically free gauge theories, Phys. Rev. D 9 (1974) 2259 [INSPIRE].
V. Elias, Coupling constant renormalization in unified gauge theories containing the Pati-Salam model, Phys. Rev. D 14 (1976) 1896 [INSPIRE].
V. Elias, Gauge coupling constant magnitudes in the Pati-Salam model, Phys. Rev. D 16 (1977) 1586 [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 1. Wave function renormalization, Nucl. Phys. B 222 (1983) 83 [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 2. Yukawa couplings, Nucl. Phys. B 236 (1984) 221 [INSPIRE].
M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 3. Scalar quartic couplings, Nucl. Phys. B 249 (1985) 70 [INSPIRE].
W. McKay and J. Patera, Tables of dimensions, indices, and branching rules for representations of simple Lie algebras, Lect. Notes Pure Appl. Math. 69, Marcel Dekker Inc., New York U.S.A. (1981).
R. Mohapatra, Unification and supersymmetry. The frontiers of quark-lepton physics, third edition, Springer, New York U.S.A. (2003).
J.C. Pati and A. Salam, Lepton number as the fourth color, Phys. Rev. D 10 (1974) 275 [Erratum ibid. D 11 (1975) 703] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1507.08161
Rights and permissions
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.
About this article
Cite this article
Chamseddine, A.H., Connes, A. & van Suijlekom, W.D. Grand unification in the spectral Pati-Salam model. J. High Energ. Phys. 2015, 11 (2015). https://doi.org/10.1007/JHEP11(2015)011
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)011