Flipped SU(5)

Template: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]

In 2010, efforts to explain the theoretical underpinnings for observed neutrino masses were being developed in the context of supersymmetric flipped $SU(5)$ Script error: No such module "Check for unknown parameters"..^[6]

Flipped $SU(5)$ Script error: No such module "Check for unknown parameters". is not a fully unified model, because the $U(1) Y$ Script error: No such module "Check for unknown parameters". factor of the Standard Model gauge group is within the $U(1)$ Script error: No such module "Check for unknown parameters". 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 $SU(5)$ Script error: No such module "Check for unknown parameters". model states that the gauge group is:

(SU(5) \times U(1) χ)/ Z 5

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Fermions form three families, each consisting of the representations

5 -3

Script error: No such module "Check for unknown parameters". for the lepton doublet, L, and the up quarks Template:Mvar;

101

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N

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15

Script error: No such module "Check for unknown parameters". for the charged leptons, Template: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 $101$ Script error: No such module "Check for unknown parameters". and/or $10 -1$ Script error: No such module "Check for unknown parameters". called the Higgs fields which acquire a VEV, yielding the spontaneous symmetry breaking

(SU(5) \times U(1) χ)/ Z 5 \to (SU(3) \times SU(2) \times U(1) Y)/ Z 6

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The $SU(5)$ Script error: No such module "Check for unknown parameters". 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}}

(u^c and l)

1 0_{1} \to (3, 2)_{\frac{1}{6}} \oplus (\bar{3}, 1)_{\frac{1}{3}} \oplus (1, 1)_{0}

(q, d^c and ν^c)

1_{5} \to (1, 1)_{1}

(e^c)

2 4_{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" $SU(5)$ Script error: No such module "Check for unknown parameters". arose in comparison to the "standard" $SU(5)$ Script error: No such module "Check for unknown parameters". Georgi–Glashow model, in which Template:Mvar and Template:Mvar quark are respectively assigned to the $10$ Script error: No such module "Check for unknown parameters". and $5$ Script error: No such module "Check for unknown parameters". representation. In comparison with the standard $SU(5)$ Script error: No such module "Check for unknown parameters"., the flipped $SU(5)$ Script error: No such module "Check for unknown parameters". can accomplish the spontaneous symmetry breaking using Higgs fields of dimension 10, while the standard $SU(5)$ Script error: No such module "Check for unknown parameters". typically requires a 24-dimensional Higgs.^[8]

The sign convention for $U(1) χ$ Script error: No such module "Check for unknown parameters". varies from article/book to article.

The hypercharge Y/2 is a linear combination (sum) of the following:

(\begin{matrix} \frac{1}{15} & 0 & 0 & 0 & 0 \\ 0 & \frac{1}{15} & 0 & 0 & 0 \\ 0 & 0 & \frac{1}{15} & 0 & 0 \\ 0 & 0 & 0 & - \frac{1}{10} & 0 \\ 0 & 0 & 0 & 0 & - \frac{1}{10} \end{matrix}) \in SU (5), χ / 5 .

There are also the additional fields $5 -2$ Script error: No such module "Check for unknown parameters". and $52$ Script error: No such module "Check for unknown parameters". containing the electroweak Higgs doublets.

Calling the representations for example, $5 -3$ Script error: No such module "Check for unknown parameters". and $240$ Script error: No such module "Check for unknown parameters". 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

π_{2} (\frac{[S U (5) \times U (1)_{χ}] / 𝐙_{5}}{[S U (3) \times S U (2) \times U (1)_{Y}] / 𝐙_{6}}) = 0

this model does not predict monopoles. See 't Hooft–Polyakov monopole.

File:Proton decay3.svg

Dimension 6 proton decay mediated by the Template:Mvar boson

(3, 2)_{\frac{1}{6}}

in flipped

SU(5)

Script error: No such module "Check for unknown parameters". GUT

Minimal supersymmetric flipped SU(5)

Spacetime

The $N = 1$ Script error: No such module "Check for unknown parameters". superspace extension of $3 + 1$ Script error: No such module "Check for unknown parameters". Minkowski spacetime

Spatial symmetry

$N = 1$ Script error: No such module "Check for unknown parameters". SUSY over $3 + 1$ Script error: No such module "Check for unknown parameters". Minkowski spacetime with R-symmetry

Gauge symmetry group

$(SU(5) \times U(1) χ)/ Z 5$ Script error: No such module "Check for unknown parameters".

Global internal symmetry

$Z 2$ Script error: No such module "Check for unknown parameters". (matter parity) not related to $U(1) R$ Script error: No such module "Check for unknown parameters". in any way for this particular model

Vector superfields

Those associated with the $SU(5) \times U(1) χ$ Script error: No such module "Check for unknown parameters". gauge symmetry

Chiral superfields

As complex representations:

label	description	multiplicity	$SU(5) \times U(1) χ$ Script error: No such module "Check for unknown parameters". rep	$Z 2$ Script error: No such module "Check for unknown parameters". rep	$U(1) R$ Script error: No such module "Check for unknown parameters".
$10 H$ Script error: No such module "Check for unknown parameters".	GUT Higgs field	$1$ Script error: No such module "Check for unknown parameters".	$101$ Script error: No such module "Check for unknown parameters".	+	$0$ Script error: No such module "Check for unknown parameters".
$10 H$ Script error: No such module "Check for unknown parameters".	GUT Higgs field	$1$ Script error: No such module "Check for unknown parameters".	$10 -1$ Script error: No such module "Check for unknown parameters".	+	$0$ Script error: No such module "Check for unknown parameters".
$H u$ Script error: No such module "Check for unknown parameters".	electroweak Higgs field	$1$ Script error: No such module "Check for unknown parameters".	$52$ Script error: No such module "Check for unknown parameters".	+	$2$ Script error: No such module "Check for unknown parameters".
$H d$ Script error: No such module "Check for unknown parameters".	electroweak Higgs field	$1$ Script error: No such module "Check for unknown parameters".	$5 -2$ Script error: No such module "Check for unknown parameters".	+	$2$ Script error: No such module "Check for unknown parameters".
$5$ Script error: No such module "Check for unknown parameters".	matter fields	$3$ Script error: No such module "Check for unknown parameters".	$5 -3$ Script error: No such module "Check for unknown parameters".	-	$0$ Script error: No such module "Check for unknown parameters".
$10$ Script error: No such module "Check for unknown parameters".	matter fields	$3$ Script error: No such module "Check for unknown parameters".	$101$ Script error: No such module "Check for unknown parameters".	-	$0$ Script error: No such module "Check for unknown parameters".
$1$ Script error: No such module "Check for unknown parameters".	left-handed positron	$3$ Script error: No such module "Check for unknown parameters".	$15$ Script error: No such module "Check for unknown parameters".	-	$0$ Script error: No such module "Check for unknown parameters".
Template:Mvar	sterile neutrino (optional)	$3$ Script error: No such module "Check for unknown parameters".	$10$ Script error: No such module "Check for unknown parameters".	-	$2$ Script error: No such module "Check for unknown parameters".
Template:Mvar	singlet	$1$ Script error: No such module "Check for unknown parameters".	$10$ Script error: No such module "Check for unknown parameters".	+	$2$ Script error: No such module "Check for unknown parameters".

Superpotential

A generic invariant renormalizable superpotential is a (complex) $SU(5) \times U(1) χ \times Z 2$ Script error: No such module "Check for unknown parameters". invariant cubic polynomial in the superfields which has an $R$ Script error: No such module "Check for unknown parameters".-charge of 2. It is a linear combination of the following terms:

$\begin{matrix} S & S \\ S 1 0_{H} {\overline{10}}_{H} & S 1 0_{H}^{α β} {\overline{10}}_{H α β} \\ 1 0_{H} 1 0_{H} H_{d} & ϵ_{α β γ δ ϵ} 1 0_{H}^{α β} 1 0_{H}^{γ δ} H_{d}^{ϵ} \\ {\overline{10}}_{H} {\overline{10}}_{H} H_{u} & ϵ^{α β γ δ ϵ} {\overline{10}}_{H α β} {\overline{10}}_{H γ δ} H_{u ϵ} \\ H_{d} 1010 & ϵ_{α β γ δ ϵ} H_{d}^{α} 1 0_{i}^{β γ} 1 0_{j}^{δ ϵ} \\ H_{d} \bar{5} 1 & H_{d}^{α} {\bar{5}}_{i α} 1_{j} \\ H_{u} 10 \bar{5} & H_{u α} 1 0_{i}^{α β} {\bar{5}}_{j β} \\ {\overline{10}}_{H} 10 ϕ & {\overline{10}}_{H α β} 1 0_{i}^{α β} ϕ_{j} \end{matrix}$

The second column expands each term in index notation (neglecting the proper normalization coefficient). Template:Mvar and Template:Mvar are the generation indices. The coupling $H d 10 i 10 j$ Script error: No such module "Check for unknown parameters". has coefficients which are symmetric in Template:Mvar and Template:Mvar.

In those models without the optional Template:Mvar sterile neutrinos, we add the nonrenormalizable couplings instead.

$\begin{matrix} ({\overline{10}}_{H} 10) ({\overline{10}}_{H} 10) & {\overline{10}}_{H α β} 1 0_{i}^{α β} {\overline{10}}_{H γ δ} 1 0_{j}^{γ δ} \\ {\overline{10}}_{H} 10 {\overline{10}}_{H} 10 & {\overline{10}}_{H α β} 1 0_{i}^{β γ} {\overline{10}}_{H γ δ} 1 0_{j}^{δ α} \end{matrix}$

These couplings do break the R-symmetry.

References

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↑ Stenger, Victor J., Quantum Gods: Creation, Chaos and the Search for Cosmic Consciousness, Prometheus Books, 2009, 61. Template:ISBN
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↑ Freedman, D. H. "The new theory of everything", Discover, 1991, 54–61.
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↑ Barcow, Timothy et al., Electroweak symmetry breaking and new physics at the TeV scale World Scientific, 1996, 194. Template: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

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[1] Script error: No such module "Citation/CS1".

[2] Script error: No such module "Citation/CS1".

[3] Stenger, Victor J., Quantum Gods: Creation, Chaos and the Search for Cosmic Consciousness, Prometheus Books, 2009, 61. Template:ISBN

[4] Script error: No such module "Citation/CS1".

[5] Freedman, D. H. "The new theory of everything", Discover, 1991, 54–61.

[6] Script error: No such module "Citation/CS1".

[7] Barcow, Timothy et al., Electroweak symmetry breaking and new physics at the TeV scale World Scientific, 1996, 194. Template:ISBN

[8] L.~F.~Li, Group Theory of the Spontaneously Broken Gauge Symmetries, Phys. Rev. D 9, 1723-1739 (1974) doi:10.1103/PhysRevD.9.1723

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Flipped SU(5)

Contents

The model

Comparison with the standard SU(5)

Minimal supersymmetric flipped SU(5)

Spacetime

Spatial symmetry

Gauge symmetry group

Global internal symmetry

Vector superfields

Chiral superfields

Superpotential

See also

References

Navigation menu

Flipped SU(5)

The model

Comparison with the standard SU(5)

Minimal supersymmetric flipped SU(5)

Spacetime

Spatial symmetry

Gauge symmetry group

Global internal symmetry

Vector superfields

Chiral superfields

Superpotential

See also

References

Navigation menu

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