An Introduction to Counting Orbifolds
John Davey, Amihay Hanany, Rak-Kyeong Seong
TL;DR
This paper reviews three combinatorial methods for counting abelian orbifolds of C^3/Gamma, providing a formula for their enumeration and discussing extensions to higher dimensions.
Contribution
It introduces and compares three counting techniques for abelian orbifolds of C^3, including a partition function formula, and discusses potential higher-dimensional generalizations.
Findings
Three counting methods for orbifolds are summarized.
A partition function formula for counting orbifolds is provided.
Extensions to higher dimensions are briefly discussed.
Abstract
We review three methods of counting abelian orbifolds of the form C^3/Gamma which are toric Calabi-Yau (CY). The methods include the use of 3-tuples to define the action of Gamma on C^3, the counting of triangular toric diagrams and the construction of hexagonal brane tilings. A formula for the partition function that counts these orbifolds is given. Extensions to higher dimensional orbifolds are briefly discussed.
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