Construction and Characterization of Representations of SU(7) for GUT Model Builders

• Main Authors: Daniel Jones, Jeffery A. Secrest
• Format: Article
• Language: English
• Published: MDPI AG 2021-06-01
• Series: Symmetry
• Subjects: GUT; grand unified theories; quarks; leptons; gauge symmetry breaking; lie algebra
• Online Access: https://www.mdpi.com/2073-8994/13/6/1044
• ISSN: 2073-8994

The natural extension to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SU</mi><mo>(</mo><mn>5</mn><mo>)</mo></mrow></semantics></math></inline-formula> Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SU</mi><mo>(</mo><mn>7</mn><mo>)</mo></mrow></semantics></math></inline-formula> symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SU</mi><mo>(</mo><mn>7</mn><mo>)</mo></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SU</mi><mo>(</mo><mn>7</mn><mo>)</mo></mrow></semantics></math></inline-formula> Lie group to supersymmetric grand unification as well as applications are discussed.