Symmetries of Abelian Orbifolds
arXiv:1009.3017 · doi:10.1007/JHEP01(2011)027
Abstract
Using the Polya Enumeration Theorem, we count with particular attention to C^3/Gamma up to C^6/Gamma, 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 C^D/Gamma where the order of Gamma is p^alpha. We propose a generalization of these sequences for any D and any p.
75 pages, 13 figures, 30 tables
References in corpus (13)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- Gauge Symmetry and Supersymmetry of Multiple M2-Branes
- Algebraic structures on parallel M2-branes
- Modeling Multiple M2's
- Dimer models and toric diagrams
- Brane Tilings
- Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
- Brane Tilings and M2 Branes
- Brane Tilings and Their Applications
- Phases of M2-brane Theories
- M2-Branes and Quiver Chern-Simons: A Taxonomic Study
- Brane Tilings, M2-branes and Chern-Simons Theories
- M2-branes Theories without 3+1 Dimensional Parents via Un-Higgsing