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

TL;DR

This paper develops a formalism for flavon boundary conditions in string-inspired models, constructing a realistic $SU(5)$ GUT with tribimaximal-reactor neutrino mixing on a specific orbifold.

Contribution

It introduces a set of consistency conditions for flavon boundary conditions in extra dimensions and constructs a realistic GUT model satisfying these conditions.

Findings

Successful model with $SU(3)_{fl}$ symmetry on $ ext{T}^6/ ext{Δ}(54)$ orbifold

Achieves tribimaximal-reactor lepton mixing consistent with data

Provides a framework linking string theory, orbifolds, and flavor physics

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.