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Gauge origin of discrete flavor symmetries in heterotic orbifolds. (English) Zbl 1317.81215
Summary: We show that non-abelian discrete symmetries in orbifold string models have a gauge origin. This can be understood when looking at the vicinity of a symmetry enhanced point in moduli space. At such an enhanced point, orbifold fixed points are characterized by an enhanced gauge symmetry. This gauge symmetry can be broken to a discrete subgroup by a nontrivial vacuum expectation value of the Kähler modulus \(T\). Using this mechanism it is shown that the \(\operatorname{\Delta}(54)\) non-Abelian discrete symmetry group originates from a \(\mathrm{SU}(3)\) gauge symmetry, whereas the \(D_4\) symmetry group is obtained from a \(\mathrm{SU}(2)\) gauge symmetry.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T13 Yang-Mills and other gauge theories in quantum field theory
81R40 Symmetry breaking in quantum theory
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
57R18 Topology and geometry of orbifolds
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