Английская Википедия:Flipped SU(5)
Шаблон:Short description The Flipped SU(5) model is a grand unified theory (GUT) first contemplated by Stephen Barr in 1982,[1] and by Dimitri Nanopoulos and others in 1984.[2][3] Ignatios Antoniadis, John Ellis, John Hagelin, and Dimitri Nanopoulos developed the supersymmetric flipped SU(5), derived from the deeper-level superstring.[4][5]
Some current efforts to explain the theoretical underpinnings for observed neutrino masses are being developed in the context of supersymmetric flipped Шаблон:Math.[6]
Flipped Шаблон:Math is not a fully unified model, because the Шаблон:Math factor of the Standard Model gauge group is within the Шаблон:Math factor of the GUT group. The addition of states below Mx in this model, while solving certain threshold correction issues in string theory, makes the model merely descriptive, rather than predictive.[7]
The model
The flipped Шаблон:Math model states that the gauge group is:
Fermions form three families, each consisting of the representations
- Шаблон:Math for the lepton doublet, L, and the up quarks Шаблон:Mvar;
- Шаблон:Math for the quark doublet, Q, the down quark, Шаблон:Mvar and the right-handed neutrino, Шаблон:Math;
- Шаблон:Math for the charged leptons, Шаблон:Mvar.
This assignment includes three right-handed neutrinos, which have never been observed, but are often postulated to explain the lightness of the observed neutrinos and neutrino oscillations. There is also a Шаблон:Math and/or Шаблон:Math called the Higgs fields which acquire a VEV, yielding the spontaneous symmetry breaking
The Шаблон:Math representations transform under this subgroup as the reducible representation as follows:
- <math>\bar{5}_{-3}\to (\bar{3},1)_{-\frac{2}{3}}\oplus (1,2)_{-\frac{1}{2}}</math> (uc and l)
- <math>10_{1}\to (3,2)_{\frac{1}{6}}\oplus (\bar{3},1)_{\frac{1}{3}}\oplus (1,1)_0</math> (q, dc and νc)
- <math>1_{5}\to (1,1)_1</math> (ec)
- <math>24_0\to (8,1)_0\oplus (1,3)_0\oplus (1,1)_0\oplus (3,2)_{\frac{1}{6}}\oplus (\bar{3},2)_{-\frac{1}{6}}</math>.
Comparison with the standard SU(5)
The name "flipped" Шаблон:Math arose in comparison to the "standard" Шаблон:Math Georgi–Glashow model, in which Шаблон:Mvar and Шаблон:Mvar quark are respectively assigned to the Шаблон:Math and Шаблон:Math representation. In comparison with the standard Шаблон:Math, the flipped Шаблон:Math can accomplish the spontaneous symmetry breaking using Higgs fields of dimension 10, while the standard Шаблон:Math typically requires a 24-dimensional Higgs.[8]
The sign convention for Шаблон:Math varies from article/book to article.
The hypercharge Y/2 is a linear combination (sum) of the following:
- <math>\begin{pmatrix}{1 \over 15}&0&0&0&0\\0&{1 \over 15}&0&0&0\\0&0&{1 \over 15}&0&0\\0&0&0&-{1 \over 10}&0\\0&0&0&0&-{1 \over 10}\end{pmatrix}\in \text{SU}(5), \qquad \chi/5.</math>
There are also the additional fields Шаблон:Math and Шаблон:Math containing the electroweak Higgs doublets.
Calling the representations for example, Шаблон:Math and Шаблон:Math is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableaux or Dynkin diagrams with numbers on their vertices, and is a standard used by GUT theorists.
Since the homotopy group
- <math>\pi_2\left(\frac{[SU(5)\times U(1)_\chi]/\mathbf{Z}_5}{[SU(3)\times SU(2)\times U(1)_Y]/\mathbf{Z}_6}\right)=0</math>
this model does not predict monopoles. See 't Hooft–Polyakov monopole.
Minimal supersymmetric flipped SU(5)
Spacetime
The Шаблон:Math superspace extension of Шаблон:Math Minkowski spacetime
Spatial symmetry
Шаблон:Math SUSY over Шаблон:Math Minkowski spacetime with R-symmetry
Gauge symmetry group
Global internal symmetry
Шаблон:Math (matter parity) not related to Шаблон:Math in any way for this particular model
Vector superfields
Those associated with the Шаблон:Math gauge symmetry
Chiral superfields
As complex representations:
| label | description | multiplicity | Шаблон:Math rep | Шаблон:Math rep | Шаблон:Math |
|---|---|---|---|---|---|
| Шаблон:Math | GUT Higgs field | Шаблон:Math | Шаблон:Math | + | Шаблон:Math |
| Шаблон:Math | GUT Higgs field | Шаблон:Math | Шаблон:Math | + | Шаблон:Math |
| Шаблон:Math | electroweak Higgs field | Шаблон:Math | Шаблон:Math | + | Шаблон:Math |
| Шаблон:Math | electroweak Higgs field | Шаблон:Math | Шаблон:Math | + | Шаблон:Math |
| Шаблон:Math | matter fields | Шаблон:Math | Шаблон:Math | - | Шаблон:Math |
| Шаблон:Math | matter fields | Шаблон:Math | Шаблон:Math | - | Шаблон:Math |
| Шаблон:Math | left-handed positron | Шаблон:Math | Шаблон:Math | - | Шаблон:Math |
| Шаблон:Mvar | sterile neutrino (optional) | Шаблон:Math | Шаблон:Math | - | Шаблон:Math |
| Шаблон:Mvar | singlet | Шаблон:Math | Шаблон:Math | + | Шаблон:Math |
Superpotential
A generic invariant renormalizable superpotential is a (complex) Шаблон:Math invariant cubic polynomial in the superfields which has an Шаблон:Math-charge of 2. It is a linear combination of the following terms:
<math>\begin{matrix} S&S\\ S 10_H \overline{10}_H & S 10_H^{\alpha\beta} \overline{10}_{H\alpha\beta}\\ 10_H 10_H H_d&\epsilon_{\alpha\beta\gamma\delta\epsilon}10_H^{\alpha\beta}10_H^{\gamma\delta} H_d^{\epsilon}\\ \overline{10}_H\overline{10}_H H_u&\epsilon^{\alpha\beta\gamma\delta\epsilon}\overline{10}_{H\alpha\beta}\overline{10}_{H\gamma\delta}H_{u\epsilon}\\ H_d 10 10&\epsilon_{\alpha\beta\gamma\delta\epsilon}H_d^{\alpha}10_i^{\beta\gamma}10_j^{\delta\epsilon}\\ H_d \bar{5} 1 &H_d^\alpha \bar{5}_{i\alpha} 1_j\\ H_u 10 \bar{5}&H_{u\alpha} 10_i^{\alpha\beta} \bar{5}_{j\beta}\\ \overline{10}_H 10 \phi&\overline{10}_{H\alpha\beta} 10_i^{\alpha\beta} \phi_j\\ \end{matrix} </math>
The second column expands each term in index notation (neglecting the proper normalization coefficient). Шаблон:Mvar and Шаблон:Mvar are the generation indices. The coupling Шаблон:Math has coefficients which are symmetric in Шаблон:Mvar and Шаблон:Mvar.
In those models without the optional Шаблон:Mvar sterile neutrinos, we add the nonrenormalizable couplings instead.
<math>\begin{matrix} (\overline{10}_H 10)(\overline{10}_H 10)&\overline{10}_{H\alpha\beta}10^{\alpha\beta}_i \overline{10}_{H\gamma\delta} 10^{\gamma\delta}_j\\ \overline{10}_H 10 \overline{10}_H 10&\overline{10}_{H\alpha\beta}10^{\beta\gamma}_i\overline{10}_{H\gamma\delta}10^{\delta\alpha}_j \end{matrix}</math>
These couplings do break the R-symmetry.
See also
References
- ↑ Шаблон:Cite journal
- ↑ Шаблон:Cite journal
- ↑ Stenger, Victor J., Quantum Gods: Creation, Chaos and the Search for Cosmic Consciousness, Prometheus Books, 2009, 61. Шаблон:ISBN
- ↑ Шаблон:Cite journal
- ↑ Freedman, D. H. "The new theory of everything", Discover, 1991, 54–61.
- ↑ Шаблон:Cite journal
- ↑ Barcow, Timothy et al., Electroweak symmetry breaking and new physics at the TeV scale World Scientific, 1996, 194. Шаблон:ISBN
- ↑ L.~F.~Li, ``Group Theory of the Spontaneously Broken Gauge Symmetries, Phys. Rev. D 9, 1723-1739 (1974) doi:10.1103/PhysRevD.9.1723
