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Counting orbifolds

  • John Davey
  • Amihay Hanany
  • Rak-Kyeong Seong
Article

Abstract

We present several methods of counting the orbifolds \( {{{{\mathbb{C}^D}}} \left/ {\Gamma } \right.} \). A correspondence between counting orbifold actions on \( {\mathbb{C}^D} \), brane tilings, and toric diagrams in D - 1 dimensions is drawn. Barycentric coordinates and scaling mechanisms are introduced to characterize lattice simplices as toric diagrams. We count orbifolds of \( {\mathbb{C}^3} \), \( {\mathbb{C}^4} \), \( {\mathbb{C}^5} \), \( {\mathbb{C}^6} \) and \( {\mathbb{C}^7} \). Some remarks are made on closed form formulas for the partition function that counts distinct orbifold actions.

Keywords

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

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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.The Blackett LaboratoryImperial College LondonLondonU.K.

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