scholarly journals TOWARDS THE STANDARD MODEL SPECTRUM FROM ELLIPTIC CALABI–YAU MANIFOLDS

2004 ◽  
Vol 19 (12) ◽  
pp. 1987-2014 ◽  
Author(s):  
BJÖRN ANDREAS ◽  
GOTTFRIED CURIO ◽  
ALBRECHT KLEMM
Keyword(s):  
Standard Model ◽  
Global Section ◽  
Elliptic Surfaces ◽  
Spectral Cover ◽  
Elliptic Fiber ◽  
The Standard Model ◽  
Free Involution ◽  
Simply Connected ◽  
Rational Elliptic Surfaces ◽  
Standard Model Gauge Group

We show that it is possible to construct supersymmetric three-generation models with the Standard Model gauge group in the framework of non-simply-connected elliptically fibered Calabi–Yau threefolds, without section but with a bi-section. The fibrations on a cover Calabi–Yau threefold, where the model has six generations of SU(5) and the bundle is given via the spectral cover description, use a different description of the elliptic fiber which leads to more than one global section. We present two examples of a possible cover Calabi–Yau threefold with a free involution: one is a fiber product of rational elliptic surfaces dP9; another example is an elliptic fibration over a Hirzebruch surface. We compute the necessary amount of chiral matter by "turning on" a further parameter which is related to singularities of the fibration and the branching of the spectral cover.

scholarly journals STANDARD MODEL BUNDLES OF THE HETEROTIC STRING

2006 ◽  
Vol 21 (06) ◽  
pp. 1261-1281 ◽  
Author(s):  
GOTTFRIED CURIO
Keyword(s):  
Standard Model ◽  
Spectral Data ◽  
Gauge Group ◽  
Matter Content ◽  
Heterotic String ◽  
Spectral Cover ◽  
The Standard Model ◽  
Free Involution ◽  
Simply Connected ◽  
Calabi Yau Manifolds

We show how to construct supersymmetric three-generation models with gauge group and matter content of the Standard Model in the framework of non-simply-connected elliptically fibered Calabi–Yau manifolds Z. The elliptic fibration on a cover Calabi–Yau, where the model has six generations of SU(5) and the bundle is given via the spectral cover description, has a second section leading to the needed free involution. The relevant involution on the defining spectral data of the bundle is identified for a general Calabi–Yau of this type and invariant bundles are generally constructible.

Complexification of the Exceptional Jordan Algebra and Its Application to Particle Physics

2021 ◽  
Vol 61 ◽  
pp. 1-16
Author(s):  
Daniele Corradetti ◽  
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Jordan Algebra ◽  
Particle Physics ◽  
Compact Form ◽  
Symmetric Extension ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Standard Model Gauge Group

Recent papers contributed revitalizing the study of the exceptional Jordan algebra $\mathfrak{h}_{3}(\mathbb{O})$ in its relations with the true Standard Model gauge group $\mathrm{G}_{SM}$. The absence of complex representations of $\mathrm{F}_{4}$ does not allow $\Aut\left(\mathfrak{h}_{3}(\mathbb{O})\right)$ to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., $\mathfrak{h}_{3}^{\mathbb{C}}(\mathbb{O})$, are isomorphic to the compact form of $\mathrm{E}_{6}$ and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.

scholarly journals PROBING SO(10) SYMMETRY BREAKING PATTERNS THROUGH SFERMION MASS RELATIONS

2005 ◽  
Vol 20 (18) ◽  
pp. 4241-4257 ◽  
Author(s):  
B. ANANTHANARAYAN ◽  
P. N. PANDITA
Keyword(s):  
Standard Model ◽  
Supersymmetry Breaking ◽  
Gauge Group ◽  
Low Energy ◽  
Grand Unification ◽  
The Standard Model ◽  
Scalar Mass ◽  
Mass Terms ◽  
Standard Model Gauge Group ◽  
Slepton Mass

We consider supersymmetric SO(10) grand unification where the unified gauge group can break to the Standard Model gauge group through different chains. The breaking of SO(10) necessarily involves the reduction of the rank, and consequent generation of nonuniversal supersymmetry breaking scalar mass terms. We derive squark and slepton mass relations, taking into account these nonuniversal contributions to the sfermion masses, which can help distinguish between the different chains through which the SO(10) gauge group breaks to the Standard Model gauge group. We then study some implications of these nonuniversal supersymmetry breaking scalar masses for the low energy phenomenology.

scholarly journals Dark matter and baryogenesis from non-Abelian gauged lepton number

2017 ◽  
Vol 32 (19) ◽  
pp. 1730018 ◽  
Author(s):  
Bartosz Fornal
Keyword(s):  
Dark Matter ◽  
Gauge Symmetry ◽  
Simple Model ◽  
Standard Model ◽  
Gauge Group ◽  
Lepton Number ◽  
Dark Matter Candidate ◽  
The Standard Model ◽  
The Right ◽  
Standard Model Gauge Group

A simple model is constructed based on the gauge symmetry [Formula: see text], with only the leptons transforming nontrivially under [Formula: see text]. The extended symmetry is broken down to the Standard Model gauge group at TeV-scale energies. We show that this model provides a mechanism for baryogenesis via leptogenesis in which the lepton number asymmetry is generated by [Formula: see text] instantons. The theory also contains a dark matter candidate — the [Formula: see text] partner of the right-handed neutrino.

A GEOMETRIC BASIS FOR THE STANDARD-MODEL GAUGE GROUP

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 909-912 ◽  
Author(s):  
GREG TRAYLING ◽  
W. E. BAYLIS
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Clifford Algebra ◽  
Geometric Model ◽  
Geometric Approach ◽  
Natural Basis ◽  
Extra Space ◽  
Gauge Symmetries ◽  
The Standard Model ◽  
Standard Model Gauge Group

A geometric approach to the standard model in terms of the Clifford algebra Cℓ7 is advanced. The gauge symmetries and charge assignments of the fundamental fermions and the higgs boson arise uniquely from a geometric model involving only four extra space-like dimensions. A key feature of the model is its use of double-sided operations on the algebraic spinors. The four added dimensions form a natural basis for the Higgs isodoublet field.

scholarly journals the complexification of the exceptional Jordan algebra and applications to particle physics

2021 ◽  
Author(s):  
Daniele Corradetti
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Jordan Algebra ◽  
Particle Physics ◽  
Proper Subgroup ◽  
Group Of Automorphisms ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Standard Model Gauge Group

Abstract Recent papers of Todorov and Dubois-Violette[4] and Krasnov[7] contributed revitalizing the study of the exceptional Jordan algebra h3(O) in its relations with the true Standard Model gauge group GSM. The absence of complex representations of F4 does not allow Aut (h3 (O)) to be a candidate for any Grand Unified Theories, but the group of automorphisms of the complexification of this algebra isisomorphic to the compact form of E6. Following Boyle in [12], it is then easy to show that the gauge group of the minimal left-right symmetric extension of the Standard Model is isomorphic to a proper subgroup of Aut(C⊗h3(O))

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