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We systematically develop the formalism necessary for ensuring that boundaryconditions of flavon fields in extra dimensions are consistent with heteroticstring theory. Having developed a set of consistency conditions on the boundaryconditions, we explore a series of examples of orbifolds in various dimensionsto see which ones can satisfy them. In addition we impose the furtherphenomenological requirements of having non-trivial flavon vacuum alignmentsand also of having quarks and leptons located appropriately in extradimensions. The minimal successful case seems to be a 10d theory with a$SU(3)_{fl}$ gauged flavour symmetry, where the six-dimensional torus iscompactified on a $\mathbb{T}^6/\Delta(54)$ orbifold. We construct a realistic$SU(5)$ grand unified theory along these lines, leading to tribimaximal-reactorlepton mixing, which we show to be consistent with current neutrino data.

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