Eulerian digraphs and toric Calabi-Yau varieties
arXiv:1011.2963 · doi:10.1007/JHEP07(2011)051
Abstract
We investigate the structure of a simple class of affine toric Calabi-Yau varieties that are defined from quiver representations based on finite eulerian directed graphs (digraphs). The vanishing first Chern class of these varieties just follows from the characterisation of eulerian digraphs as being connected with all vertices balanced. Some structure theory is used to show how any eulerian digraph can be generated by iterating combinations of just a few canonical graph-theoretic moves. We describe the effect of each of these moves on the lattice polytopes which encode the toric Calabi-Yau varieties and illustrate the construction in several examples. We comment on physical applications of the construction in the context of moduli spaces for superconformal gauged linear sigma models.
arXiv comment27 pages, 8 figures
References in corpus (20)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Large N Field Theories, String Theory and Gravity
- Phases of Theories In Two Dimensions
- Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
- D-branes, Quivers, and ALE Instantons
- Gauge Theories from Toric Geometry and Brane Tilings
- Orbifold Resolution by D-Branes
- D-Brane Gauge Theories from Toric Singularities and Toric Duality
- Brane Dimers and Quiver Gauge Theories
- Dimer models and toric diagrams
- Toric Duality Is Seiberg Duality
- Varieties of vacua in classical supersymmetric gauge theories
- Phase Structure of D-brane Gauge Theories and Toric Duality
- The Master Space of N=1 Gauge Theories
- Quivers, Tilings, Branes and Rhombi
- D3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefolds
- Moduli Spaces of Gauge Theories from Dimer Models: Proof of the Correspondence
- On the Classification of Brane Tilings
- Master Space, Hilbert Series and Seiberg Duality
- Notes on GIT and symplectic reduction for bundles and varieties