Flavon alignments from orbifolding: $SU(5)\times SU(3)$ model with ${\mathbb{T}}^6/\Delta (54)$

Abstract

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 ${\mathbb{T}}^6/\Delta (54)$ 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.

Comments: 37 pages, 3 figures. v2: references added, matches published version