2021/05/06 by Joao Baptista, Baptista, Joao
Mathematics · Physics and Astronomy · #53Z05 #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2105.02901
openalex publication_date 2021/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the old spirit of Kaluza-Klein, we consider a spacetime of the form P = M4 × K, where K is the Lie group SU(3) equipped with a left-invariant metric that is not fully right-invariant. We observe that a complete generation of fermionic fields can be encoded in the 64 components of a single spinor over the 12-dimensional spacetime. The behaviour of the spinorial function along the internal space K can be chosen so that, after pairing and fibre-integration over K, the resulting Dirac kinetic terms in four dimensions couple to the \mathfraku(1) ⊕ \mathfraksu(2) ⊕ \mathfraksu(3) gauge fields in the exact chiral representations present in the Standard Model. Although we describe the action of the internal Dirac operator on the 12-dimensional spinor, the full calculation of the fermionic mass terms produced by the model is longer and is not carried out here. We calculate instead the action of the internal Laplace operator on the spinor components.