Note on the space group selection rule for closed strings on orbifolds

• Published in: The journal of high energy physics 2019-01, Vol.2019 (1), p.1-30, Article 55
• Main Authors: Ramos-Sánchez, Saúl, Vaudrevange, Patrick K. S.
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Dark matter; Discrete Symmetries; Elementary Particles; Flavor (particle physics); Group theory; High energy physics; Permutations; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Strings; Superstrings and Heterotic Strings; Supersymmetry; Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2019)055

A bstract It is well-known that the space group selection rule constrains the interactions of closed strings on orbifolds. For some examples, this rule has been described by an effective Abelian symmetry that combines with a permutation symmetry to a non-Abelian flavor symmetry like D 4 or Δ(54). However, the general case of the effective Abelian symmetries was not yet fully understood. In this work, we formalize the computation of the Abelian symmetry that results from the space group selection rule by imposing two conditions only: (i) well-defined discrete charges and (ii) their conservation. The resulting symmetry, which we call the space group flavor symmetry D S , is uniquely specified by the Abelianization of the space group. For all Abelian orbifolds with N = 1 supersymmetry we compute D S and identify new cases, for example, where D S contains a ℤ 2 dark matter-parity with charges 0 and 1 for massless and massive strings, respectively.