Eulerian digraphs and toric Calabi-Yau varieties. (English) Zbl 1298.81266
Summary: 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.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 81T18 | Feynman diagrams |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 16G20 | Representations of quivers and partially ordered sets |
| 19L10 | Riemann-Roch theorems, Chern characters |
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