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Flipped SU(5)
Encyclopedia
The Flipped SU model is a Grand Unified Theory
(GUT) theory first contemplated by Stephen Barr in 1982, and by Dimitri Nanopoulos
and others in 1984. Antoniadis, Ellis, Hagelin and Nanopoulos developed the supersymmetric flipped SU(5), derived from the deeper-level superstring.
Current efforts to explain the theoretical underpinnings for observed neutrino masses are being developed in the context of supersymmetric flipped SU(5).
Flipped SU(5) is not a fully unified model, because the U(1)y factor of the SM gauge group is within the U(1) 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.
[ SU(5)
× U(1)
χ ]/
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, N;
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 oscillation
s. There is also a
and/or 
called the Higgs fields which acquire a VEV, yielding the spontaneous symmetry breaking
to 
The SU(5) representations transform under this subgroup
as the reducible representation as follows:
.
and 
quark are respectively assigned to the 10 and 5 representation. In comparison with the standard SU(5), the flipped SU(5) can accomplish the spontaneous symmetry breaking using Higgs fields of dimension 10, while the standard SU(5) requires both a 5- and 45-dimensional Higgs.
The sign convention
for U(1)χ varies from article/book to article.
The hypercharge Y/2 is a linear combination (sum) of the
of SU(5) and χ/5.
There are also the additional fields 5-2 and
containing the electroweak Higgs doublets.
Calling the representations foe example,
and 240 is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableau
x or Dynkin diagrams with numbers on their vertices, and is a standard used by GUT
theorists.
Since the homotopy group
this model does not predict monopoles. See Hooft-Polyakov monopole.
invariant cubic polynomial in the superfields which has an R-charge of 2. It is a linear combination of the following terms:
The second column expands each term in index notation (neglecting the proper normalization coefficient). i and j are the generation indices. The coupling Hd 10i 10j has coefficients which are symmetric in i and j.
In those models without the optional φ sterile neutrinos, we add the nonrenormalizable couplings instead.
These couplings do break the R-symmetry.
Grand unification theory
The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...
(GUT) theory first contemplated by Stephen Barr in 1982, and by Dimitri Nanopoulos
Dimitri Nanopoulos
Dimitri Nanopoulos is a Greek physicist. He is one of the most regularly cited researchers in the world, cited more than 35,800 times over across a number of separate branches of science....
and others in 1984. Antoniadis, Ellis, Hagelin and Nanopoulos developed the supersymmetric flipped SU(5), derived from the deeper-level superstring.
Current efforts to explain the theoretical underpinnings for observed neutrino masses are being developed in the context of supersymmetric flipped SU(5).
Flipped SU(5) is not a fully unified model, because the U(1)y factor of the SM gauge group is within the U(1) factor of the GUT group. The addition of states below Mx in this model, while solving certain threshold correction issues in string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
, makes the model merely descriptive, rather than predictive.
The Model
The Flipped SU(5) model states that the gauge group is:Special unitary group
The special unitary group of degree n, denoted SU, is the group of n×n unitary matrices with determinant 1. The group operation is that of matrix multiplication...
× U(1)
Unitary group
In mathematics, the unitary group of degree n, denoted U, is the group of n×n unitary matrices, with the group operation that of matrix multiplication. The unitary group is a subgroup of the general linear group GL...
χ ]/
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, N; 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 oscillation
Neutrino oscillation
Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates...
s. There is also a
and/or called the Higgs fields which acquire a VEV, yielding the spontaneous symmetry breakingSpontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
to The SU(5) representations transform under this subgroup
Restricted representation
In mathematics, restriction is a fundamental construction in representation theory of groups. Restriction forms a representation of a subgroup from a representation of the whole group. Often the restricted representation is simpler to understand...
as the reducible representation as follows:
-
(uc and l) -
(q, dc and νc) -
(ec)
.Comparison with the standard SU(5)
The name "flipped" SU(5) arose in comparison to the "standard" SU(5) model of Georgi-Glashow, in which and quark are respectively assigned to the 10 and 5 representation. In comparison with the standard SU(5), the flipped SU(5) can accomplish the spontaneous symmetry breaking using Higgs fields of dimension 10, while the standard SU(5) requires both a 5- and 45-dimensional Higgs.The sign convention
Sign convention
In physics, a sign convention is a choice of the physical significance of signs for a set of quantities, in a case where the choice of sign is arbitrary. "Arbitrary" here means that the same physical system can be correctly described using different choices for the signs, as long as one set of...
for U(1)χ varies from article/book to article.
The hypercharge Y/2 is a linear combination (sum) of the
of SU(5) and χ/5.There are also the additional fields 5-2 and
containing the electroweak Higgs doublets.Calling the representations foe example,
and 240 is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableauYoung tableau
In mathematics, a Young tableau is a combinatorial object useful in representation theory. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties. Young tableaux were introduced by Alfred Young, a mathematician at...
x or Dynkin diagrams with numbers on their vertices, and is a standard used by GUT
theorists.
Since the homotopy group
Homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space...
this model does not predict monopoles. See Hooft-Polyakov monopole.
global internal symmetry
Z2 (matter parity) not related to U(1)R in any way for this particular modelchiral superfields
As complex representations:| label | description | multiplicity | SU(5)× U(1)χ rep |  rep |
U(1)R |
| 10H | GUT Higgs field | 1 | 101 | 0 |
 |
GUT Higgs field | 1 |  |
0 |
| Hu | electroweak Higgs field | 1 |  |
2 |
| Hd | electroweak Higgs field | 1 |  |
2 |
 |
matter fields | 3 |  |
|
| 0 | ||||
| 10 | matter fields | 3 | 101 | |
| 0 | ||||
| 1 | left-handed positron | 3 | 15 | |
| 0 | ||||
| φ | sterile neutrino (optional) | 3 | 10 | |
| 2 | ||||
| S | singlet | 1 | 10 | 2 |
Superpotential
A generic invariant renormalizable superpotential is a (complex) invariant cubic polynomial in the superfields which has an R-charge of 2. It is a linear combination of the following terms:The second column expands each term in index notation (neglecting the proper normalization coefficient). i and j are the generation indices. The coupling Hd 10i 10j has coefficients which are symmetric in i and j.
In those models without the optional φ sterile neutrinos, we add the nonrenormalizable couplings instead.
These couplings do break the R-symmetry.