Flipped SU(5)

The flipped model states that the gauge group is: : Fermions form three families, each consisting of the representations : for the lepton doublet, L, and the up quarks ; : for the quark doublet, Q, the down quark, and the right-handed neutrino, ; : for the charged leptons, . 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 and/or called the Higgs fields which acquire a VEV, yielding the spontaneous symmetry breaking : The representations transform under this subgroup as the reducible representation as follows: :\bar{5}_{-3}\to (\bar{3},1)_{-\frac{2}{3}}\oplus (1,2)_{-\frac{1}{2}} (uc and l) :10_{1}\to (3,2)_{\frac{1}{6}}\oplus (\bar{3},1)_{\frac{1}{3}}\oplus (1,1)_0 (q, dc and νc) :1_{5}\to (1,1)_1 (ec) :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}}. ==Comparison with the standard SU(5)==

The name "flipped" arose in comparison to the "standard" Georgi–Glashow model, in which and quark are respectively assigned to the and representation. In comparison with the standard , the flipped can accomplish the spontaneous symmetry breaking using Higgs fields of dimension 10, while the standard typically requires a 24-dimensional Higgs. The sign convention for varies from article/book to article. The hypercharge Y/2 is a linear combination (sum) of the following: :\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. There are also the additional fields and containing the electroweak Higgs doublets. Calling the representations for example, and 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 :\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 this model does not predict monopoles. See 't Hooft–Polyakov monopole. ==Minimal supersymmetric flipped SU(5)==

Spacetime The superspace extension of Minkowski spacetime Spatial symmetry SUSY over Minkowski spacetime with R-symmetry Gauge symmetry group Global internal symmetry (matter parity) not related to in any way for this particular model Vector superfields Those associated with the gauge symmetry Chiral superfields As complex representations: Superpotential A generic invariant renormalizable superpotential is a (complex) invariant cubic polynomial in the superfields which has an -charge of 2. It is a linear combination of the following terms: \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} The second column expands each term in index notation (neglecting the proper normalization coefficient). and are the generation indices. The coupling has coefficients which are symmetric in and . In those models without the optional sterile neutrinos, we add the nonrenormalizable couplings instead. \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} These couplings do break the R-symmetry. ==See also==