Gauge Symmetry | ScienceGate

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

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A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem

Symmetry ◽

10.3390/sym13060956 ◽

2021 ◽

Vol 13 (6) ◽

pp. 956

Author(s):

Dafne Carolina Arias-Perdomo ◽

Adriano Cherchiglia ◽

Brigitte Hiller ◽

Marcos Sampaio

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Gauge Symmetry ◽

Particle Physics ◽

Analytic Extension ◽

Quantum Field ◽

Loop Order ◽

Time Dimension ◽

The Core ◽

Striking Success

Quantum Field Theory, as the keystone of particle physics, has offered great insights into deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculation, which encompasses the need for some regularization/renormalization prescription. As an alternative to traditional methods, based on the analytic extension of space–time dimension, frameworks that stay in the physical dimension have emerged; Implicit Regularization is one among them. We briefly review the method, aiming to illustrate how Implicit Regularization complies with the BPHZ theorem, which implies that it respects unitarity and locality to arbitrary loop order. We also pedagogically discuss how the method complies with gauge symmetry using one- and two-loop examples in QED and QCD.

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Electroweak-like baryogenesis with new chiral matter

Journal of High Energy Physics ◽

10.1007/jhep07(2021)224 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Kohei Fujikura ◽

Keisuke Harigaya ◽

Yuichiro Nakai ◽

Ruoquan Wang

Keyword(s):

Phase Transition ◽

Gauge Symmetry ◽

Cp Violation ◽

Standard Model ◽

Dipole Moments ◽

Dark Matter Candidate ◽

Lepton Asymmetry ◽

First Order ◽

The Standard Model ◽

Concrete Realization

Abstract We propose a framework where a phase transition associated with a gauge symmetry breaking that occurs (not far) above the electroweak scale sets a stage for baryogenesis similar to the electroweak baryogenesis in the Standard Model. A concrete realization utilizes the breaking of SU(2)R× U(1)X→ U(1)Y. New chiral fermions charged under the extended gauge symmetry have nonzero lepton numbers, which makes the B − L symmetry anomalous. The new lepton sector contains a large flavor-dependent CP violation, similar to the Cabibbo-Kobayashi-Maskawa phase, without inducing sizable electric dipole moments of the Standard Model particles. A bubble wall dynamics associated with the first-order phase transition and SU(2)R sphaleron processes generate a lepton asymmetry, which is transferred into a baryon asymmetry via the ordinary electroweak sphaleron process. Unlike the Standard Model electroweak baryogenesis, the new phase transition can be of the strong first order and the new CP violation is not significantly suppressed by Yukawa couplings, so that the observed asymmetry can be produced. The model can be probed by collider searches for new particles and the observation of gravitational waves. One of the new leptons becomes a dark matter candidate. The model can be also embedded into a left-right symmetric theory to solve the strong CP problem.

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ANOMALOUS U(1)A AND ELECTROWEAK SYMMETRY BREAKING

Modern Physics Letters A ◽

10.1142/s0217732301004005 ◽

2001 ◽

Vol 16 (13) ◽

pp. 835-844

Author(s):

ILIA GOGOLADZE ◽

MIRIAN TSULAIA

Keyword(s):

Gauge Symmetry ◽

Standard Model ◽

Symmetry Breaking ◽

Supersymmetric Standard Model ◽

Electroweak Symmetry Breaking ◽

Electroweak Symmetry ◽

Superstring Theory

We suggest a new mechanism for electroweak symmetry breaking in the supersymmetric Standard Model. Our suggestion is based on the presence of an anomalous U (1)A gauge symmetry, which naturally arises in the four-dimensional superstring theory, and heavily relies on the value of the corresponding Fayet–Illiopoulos ξ-term.

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DYNAMICAL SYMMETRY BREAKING IN A MINIMAL 3-3-1 MODEL

International Journal of Modern Physics A ◽

10.1142/s0217751x12501564 ◽

2012 ◽

Vol 27 (26) ◽

pp. 1250156 ◽

Cited By ~ 6

Author(s):

A. DOFF ◽

A. A. NATALE

Keyword(s):

Gauge Symmetry ◽

Symmetry Breaking ◽

Dynamical Symmetry ◽

Mass Scale ◽

Coupling Constant ◽

Walking Behavior ◽

Dynamical Symmetry Breaking ◽

Dynamical Generation ◽

Breaking Scale

The gauge symmetry breaking in some versions of 3-3-1 models can be implemented dynamically because at the scale of a few TeVs the U(1)X coupling constant becomes strong. In this work, we consider the dynamical symmetry breaking in a minimal SU(3) TC × SU(3)L × U(1)X model, where we propose a new scheme to cancel the chiral anomalies, including two-index symmetric (6) technifermions, which incorporates naturally the walking behavior in the Technicolor (TC) sector. The composite scalar content of the model is minimal and all the symmetry breaking is implemented by a multiplet of technifermions. The choice of TC representations not only provides the anomaly cancelation with a walking behavior, but is crucial to promote the model's full dynamical symmetry breaking. We consider the dynamical generation of technigluon masses and, depending on the 3-3-1 symmetry breaking scale (μ331), we verify that the technigluon mass is strongly linked to the Z′ mass scale, for instance, if μ331 = 1 TeV , we have MZ′ > 1 TeV only if M TG < 350 GeV .

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Gauge symmetry saved, mass endowed

Physics Today ◽

10.1063/pt.3.1700 ◽

2012 ◽

Vol 65 (9) ◽

pp. 14-14 ◽

Cited By ~ 1

Author(s):

Steven K. Blau

Keyword(s):

Gauge Symmetry

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