Discrete Flavour Symmetries from the Heisenberg Group

Abstract

Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular in the $PS{L}_2(p)$ groups which contain the phenomenologically interesting cases.

16 pages

References in corpus (7)

• Neutrino Mass and Mixing with Discrete Symmetry
• Stringy origin of non-Abelian discrete flavor symmetries
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models
• On the origin of neutrino flavour symmetry
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• A new family symmetry for SO(10) GUTs

Cited by in corpus (2)

• The quantum cat map on the modular discretization of extremal black hole horizons
• PSL(2,7) Representations and their relevance to Neutrino Physics