2021/02/25 by Anthony Britto, Britto, Anthony
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2102.13465
openalex publication_date 2021/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Of the five exceptional groups, E6 is considered the most attractive for unification due to the following reasons: (i) it contains both Spin (10) × U(1) and SU (3) × SU(3) × SU(3) as maximal subgroups, each of which admit embeddings of the Standard Model; (ii) uniquely among the exceptional groups, it admits complex representations; in particular, its 27 dimensional fundamental representation accommodates one generation of left-handed fermions under the usual charge assignments; (iii) all of its representations are anomaly-free. In this master's thesis, written in the spirit of Baez and Huerta's "The Algebra of Grand Unified Theories", we rigorously show how an E6 grand unified theory is mathematically constructed. Our modest contribution to the literature includes an explicit check that that ℤ4 kernel of the homomorphism Spin (10) × U(1) → E6 acts trivially on every fermion; we also formulate symmetry breaking, in particular the symmetry breaking of the exotic E6 fermions under Spin (10) → SU(5), using a different approach than the usual Dynkin diagrams: we explicitly embedded \mathfraksu(5) \hookrightarrow \mathfrakso(10) ≅ \mathfrakspin (10) and solve the related eigenvalue problem. Phenomenological aspects of grand unified theories are also discussed.