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

Abstract

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 D4 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 DS, is uniquely specified by the Abelianization of the space group. For all Abelian orbifolds with \( \mathcal{N}=1 \) supersymmetry we compute DS and identify new cases, for example, where DS contains a 2 dark matter-parity with charges 0 and 1 for massless and massive strings, respectively.

A preprint version of the article is available at ArXiv.

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Correspondence to Saúl Ramos-Sánchez.

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Ramos-Sánchez, S., Vaudrevange, P.K.S. Note on the space group selection rule for closed strings on orbifolds. J. High Energ. Phys. 2019, 55 (2019). https://doi.org/10.1007/JHEP01(2019)055

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Keywords

  • Discrete Symmetries
  • Superstrings and Heterotic Strings