Justifying the Standard Model U(1) x SU(2) x SU(3) Symmetry in a Multi-fold Universe
Authors: Maes Stephane 
Published: October 2023

Group theory is a good way to study Particle Physics, when all the details are not known. U(1) x SU(2) x SU(3) is a good example as the symmetry group of the Standard Model (SM). It is well established, yet it is still a mystery why these symmetries, and why not a different or bigger group. It is what motivated efforts in the direction of Grand Unification Theories (GUTs).The paper starts with an analysis of multi-fold aspects inspired from the Geometric Unity (GU). The first stages of the GU approach are contrasted with the multi-fold space time matter induction approach. It leads to different ways to characterize the symmetries of the 4D spacetime in the embedding space: Two unoriented 7D space time, tagged to cover a left and a right chirality, undefined in 7D, and therefore a Spin(7,7) symmetry. Spin (7,7) can be reduced by symmetry breaking to Sl(2,ℂ) x U(1) x SU(2) x SU(3), via a whole bunch of different paths and possible interim symmetries. The first term corresponds to General Relativity (GR) in 4D with Lorentz symmetries, while the rest are the SM symmetries associated to Quantum Physics. This 7D space, with chiral labels, is a local 7D ε neighborhood seen from the 4D spacetime, through multi-fold entry, exit or mapping points, locally embedding it, without Physics in it and implementing space time matter induction and scattering in the 4D multi-fold spacetime, ensuring U(1) x SU(2) x SU(3) for the SM, and induction of the SM particles. Indeed, the doubling of the spacetime sharing time as 7D embedding space explains the algebra doubling on non-commutative geometry in 4D that also predicts the SM particles. Revisiting the multi-fold mechanisms, we explicitly detail why a multi-fold spacetime carries U(1) x SU(2) x SU(3) symmetries, in addition to Lorentz symmetry: U(1) is the symmetry of the paths on the multi-folds (as circles on the surface of 3D spheres), SU(2) is the axial symmetry of the multi-fold mechanisms, and SU(3) is the 3D symmetry for the multi-fold axis choices. These symmetries transfer to the embedding 7D space (ε neighborhood),generated by the multi-folds. Also, GR reigns in that space, Ricci flat or Einsteinian. This way, traversable wormholes, thanks to right-handed neutrinos, could implement multi-folds. Additional considerations on traversability of wormholes are also discussed, in particular introducing effects like Casimir without 7D Physics.Explaining why SM has the symmetry that it has is quite unique. As far as we know, it has not been possible so far to derive a convincing explanation for why, larger symmetry breaking result into a remaining U(1) x SU(2) x SU(3) symmetry for the SM. Most papers either show compatibility with U(1) x SU(2) x SU(3) symmetries that are then assumed, or how larger symmetries could lead to U(1) x SU(2) x SU(3); but in general, not why this symmetry.So far, the GUTs failures to provide such an explanation, made U(1) x SU(2) x SU(3) even more puzzling. Because of how tied the SM symmetries are to the multi-fold mechanisms, and the embedding ε space perception, it may be another hint that our universe could be well modeled with multi-folds. The absence of larger symmetries is also a way to explain why no GUTs or supersymmetry exist, and to confirm our past prediction for a fundamental particle desert above the energy scale of the multi-fold gravity electroweak symmetry breaking.The symmetries of the 4D spacetime, the SM and the 7D embedding space can also become first step towards more quantitative sketches of the multi-fold action, Lagrangian or Hamiltonian.A consequence of this paper is that GR, or the Hilbert Einstein action contains fully the Standard Model and therefore the Standard Model (SM) (with gravity, i.e., the SMG). And there is no need to invoke fine-tuning or multiverses to explain our universe.