Flavon alignments from orbifolding: SU(5) × SU(3) model with 𝕋6 /∆(54)
Francisco Anda (Tepatitlán’s Institute for Theoretical Studies, Jalisco, C.P. 47600, México); Stephen King (School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, U.K.); Elena Perdomo (School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, U.K.); Patrick Vaudrevange (Physik Department T75, Technische Universität München, James-Franck-Straße 1, Garching, 85748, Germany)
We systematically develop the formalism necessary for ensuring that boundary conditions of flavon fields in extra dimensions are consistent with heterotic string theory. Having developed a set of consistency conditions on the boundary conditions, we explore a series of examples of orbifolds in various dimensions to see which ones can satisfy them. In addition we impose the further phenomenological requirements of having non-trivial flavon vacuum alignments and also of having quarks and leptons located appropriately in extra dimensions. The minimal successful case seems to be a 10d theory with a SU(3)fl gauged flavour symmetry, where the six-dimensional torus is compactified on a 𝕋6 /∆(54) orbifold. We construct a realistic SU(5) grand unified theory along these lines, leading to tribimaximal-reactor lepton mixing, which we show to be consistent with current neutrino data.
