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Symmetries of abelian orbifolds

  • Amihay Hanany
  • Rak-Kyeong Seong
Article

Abstract

Using the Polya Enumeration Theorem, we count with particular attention to \( {{{{\mathbb{C}^3}}} \left/ {\Gamma } \right.} \) up to \( {{{{\mathbb{C}^6}}} \left/ {\Gamma } \right.} \), abelian orbifolds in various dimensions which are invariant under cycles of the permutation group S D . This produces a collection of multiplicative sequences, one for each cycle in the Cycle Index of the permutation group. A multiplicative sequence is controlled by its values on prime numbers and their pure powers. Therefore, we pay particular attention to orbifolds of the form \( {{{{\mathbb{C}^D}}} \left/ {\Gamma } \right.} \) where the order of Γ is p α. We propose a generalization of these sequences for any D and any p.

Keywords

Differential and Algebraic Geometry Superstring Vacua D-branes Conformal Field Models in String Theory 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Theoretical Physics Group, The Blackett LaboratoryImperial College LondonLondonU.K.

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