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SO(10) GUTs with large tensor representations on Noncommutative Space-time
High Energy Physics - Theory · Submitted 12 Nov 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The existence of these interactions helps to clearly distinguish noncommutative Minkowski space-time from ordinary Minkowski space-time.
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The abstract, sentence by sentence
We construct a noncommutative version of a general renormalizable SO(10) GUT with Higgses in the 210, $\overline{126}, 45, 10$ and 120 irreps of SO(10) and a Peccei-Quinn symmetry. Thus, we formulate the noncommutative counterpart of a non-supersymmetric SO(10) GUT which has recently been shown to be consistent with all the physics below $M_{GUT}$. The simplicity of our construction --the simplicity of the Yukawa terms, in particular-- stems from the fact that the Higgses of our GUT can be viewed as elements of the Clifford algebra $\mathbb{C}\rm{l}_{10}(\mathbb{C})$; elements on which the SO(10) gauge transformations act by conjugation. The noncommutative GUT we build contains tree-level interactions among different Higgs species that are absent in their ordinary counterpart as they are forbidden by SO(10) and Lorentz invariance. The existence of these interactions helps to clearly distinguish noncommutative Minkowski space-time from ordinary Minkowski space-time.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We construct a noncommutative version of a general renormalizable SO(10) GUT with Higgses in the 210, $\overline{126}, 45, 10$ and 120 irreps of SO(10) and a Peccei-Quinn symmetry. | contribution 1.00 | 0.95 | 0.19 | asserted 1.00 |
| s1 | Thus, we formulate the noncommutative counterpart of a non-supersymmetric SO(10) GUT which has recently been shown to be consistent with all the physics below $M_{GUT}$. | contribution 0.63 | 0.64 | 0.16 | asserted 0.94 |
| s2 | The simplicity of our construction --the simplicity of the Yukawa terms, in particular-- stems from the fact that the Higgses of our GUT can be viewed as elements of the Clifford algebra $\mathbb{C}\rm{l}_{10}(\mathbb{C})$; elements on which the SO(10) gauge transformations act by conjugation. | method 0.73 | 0.75 | 0.11 | asserted 1.00 |
| s3 | The noncommutative GUT we build contains tree-level interactions among different Higgs species that are absent in their ordinary counterpart as they are forbidden by SO(10) and Lorentz invariance. | result 0.94 | 0.86 | 0.29 | asserted 1.00 |
| s4 | The existence of these interactions helps to clearly distinguish noncommutative Minkowski space-time from ordinary Minkowski space-time. | interpretation 0.96 | 0.70 | 0.29 | asserted 0.91 |
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The paper
Original abstract
We construct a noncommutative version of a general renormalizable SO(10) GUT with Higgses in the 210, $\overline{126}, 45, 10$ and 120 irreps of SO(10) and a Peccei-Quinn symmetry. Thus, we formulate the noncommutative counterpart of a non-supersymmetric SO(10) GUT which has recently been shown to be consistent with all the physics below $M_{GUT}$. The simplicity of our construction --the simplicity of the Yukawa terms, in particular-- stems from the fact that the Higgses of our GUT can be viewed as elements of the Clifford algebra $\mathbb{C}\rm{l}_{10}(\mathbb{C})$; elements on which the SO(10) gauge transformations act by conjugation. The noncommutative GUT we build contains tree-level interactions among different Higgs species that are absent in their ordinary counterpart as they are forbidden by SO(10) and Lorentz invariance. The existence of these interactions helps to clearly distinguish noncommutative Minkowski space-time from ordinary Minkowski space-time.
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How the literature uses it
3 arXiv papers cite this in 3 sentences
Papers citing it · 1 sentence without a confident label
Cites it as background 2 papers
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The noncommutative extensions of particle physics models like the covariant noncommutative SM (NCSM) and the NC GUT models [ref] were constructed.
Forbidden and invisible Z boson decays in covariant theta-exact noncommutative standard model · Introduction · 0.98
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[ref] and concrete examples were given in Refs. [ref] .
The hybrid Seiberg-Witten map, its $\theta$-exact expansion and the antifield formalism · Introduction · 0.96
What it cites · 21 sentences without a confident label
Builds on 2 papers
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As we said at the beginning of this introduction, the purpose of this paper is to show that there is indeed a noncommutative counterpart of the SO(10) GUT of Ref. [ref] .
A non Supersymmetric SO(10) Grand Unified Model for All the Physics below $M_{GUT}$ · Introduction · 0.84
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The analysis of the UV/IR mixing effects was later extended [ref] to fermions in the fundamental representation coupled to $U(1)$ gauge fields.
On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED · Introduction · 0.80
Uses the method or tool of 6 papers
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Within the enveloping-algebra framework of Refs. [ref] , one introduces at least a noncommutative field for each ordinary field.
Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces · Introducing the noncommutative fields of the noncommutative SO(10) GUT. · 0.91
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Within the enveloping-algebra framework of Refs. [ref] , one introduces at least a noncommutative field for each ordinary field.
Gauge Theory on Noncommutative Spaces · Introducing the noncommutative fields of the noncommutative SO(10) GUT. · 0.91
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Within the enveloping-algebra framework of Refs. [ref] , one introduces at least a noncommutative field for each ordinary field.
Construction of non-Abelian gauge theories on noncommutative spaces · Introducing the noncommutative fields of the noncommutative SO(10) GUT. · 0.91
Cites as support 1 paper
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We should like to point out that there is no reason to set to zero from the beginning any of the $κ$'s in ([ref]), for one-loop Higgs radiative corrections generate contributions –see Ref. [ref] – to the effective action of gauge field that are of the type: [equation]
Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism · The noncommutative Yang-Mills action · 0.99
Cites as background 31 papers
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The nontrivial issue of constructing noncommutative Yukawa terms with the help of the enveloping-algebra formalism was addressed in Ref. [ref] .
Yukawa terms in noncommutative SO(10) and E6 GUTs · Introduction · 0.84
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The formulation of the gauge and fermionic sectors of noncommutative GUTs with SU(5) and SO(10) as gauge groups was tackled, within the enveloping-algebra framework, in Ref. [ref] .
Non-Commutative GUTs, Standard Model and C,P,T · Introduction · 0.87
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The UV/IR mixing in the one-loop propagator of adjoint fermions coupled to U(1) fields and its very relevant implications on neutrino physics have been studied in Refs. [ref] –see Ref. [ref] for a review.
Yukawa couplings and seesaw neutrino masses in noncommutative gauge theory · Introduction · 0.91
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