Abstract
We consider a five dimensional supersymmetric SO(10) GUT compactified on an S 1∕(Z 2 × Z 2 ′) orbifold where \(S^{1} \equiv \mathbb{R}^{1}/\mathcal{T}\) and \(\mathcal{T}\) is the action of translations by 4π R (see Sect. 14.2). The first orbifold, Z 2, under which y → −y, breaks 5D N = 1 supersymmetry (4D N = 2) to 4D N = 1. The other orbifold, Z 2 ′, under which y → −y +π R, breaks SO(10) down to the PS gauge group SU(4) C × SU(2) L × SU(2) R . The fundamental domain of the y direction is the line segment y ∈ [0, π R]. SO(10) gauge symmetry is present everywhere except at the point y = π R, which only has Pati-Salam gauge symmetry. Hence, we call the two inequivalent fixed points the “SO(10)” (y = 0) and “Pati-Salam” branes (y = π R) where each fixed point is a three-brane (3+1 dimensional spacetime). The Higgs mechanism on the PS brane completes the breaking of the PS gauge symmetry to the SM gauge group.
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Notes
- 1.
When considering differential running of the gauge couplings, a Higgs hypermultiplet in the bulk is effectively the same as a 4D 10 of SO(10) with light Higgs MSSM doublets and heavy Higgs triplets of mass M c . This setup admits gauge coupling unification as shown by Kim and Raby [317]. In particular, see the calculations leading to Eq. (3.13) of that paper. Effects from brane Higgs doublets would be felt up to M ∗ and would tend to inhibit unification since they drive the couplings apart rather than together.
- 2.
With dimension six operators for the third family, mixing between this family and the first two can induce proton decay. Assuming that the mixing is of order | V ub | or | V cb | and that the gauge bosons have mass at M c , naive calculations using formulae in [103] put the proton lifetime many orders of magnitude above current limits, since this leads to an effective gauge boson mass of order M c ∕(V cb V ub ) ≈ 6 × 1017 GeV.
- 3.
The SO(10) breaking mass term, M χ , can be due to an additional \(16,\overline{16}\) which obtain VEVs in the right-handed neutrino direction and couple, for example, as follows, \(\overline{\widetilde{16}}_{a}\langle 16\ \overline{16}\rangle 16_{a}^{{\prime}}\).
- 4.
Such terms given by the substitution Φ L → Φ R 2 or Φ R → Φ L 2 would lead to a Yukawa matrix structure different from the one desired and so should be forbidden by some symmetry.
- 5.
We have chosen to use the notation found in [146] to ease comparison between prior works and our own.
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Raby, S. (2017). SO(10) SUSY GUT in 5D. In: Supersymmetric Grand Unified Theories. Lecture Notes in Physics, vol 939. Springer, Cham. https://doi.org/10.1007/978-3-319-55255-2_15
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DOI: https://doi.org/10.1007/978-3-319-55255-2_15
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