Brane Tilings and Exceptional Collections
arXiv:hep-th/0602041 · doi:10.1088/1126-6708/2006/07/001
Abstract
Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3-branes probing a Calabi-Yau singularity. We provide a dictionary that translates between these two heretofore unconnected languages. Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of the non-compact Calabi-Yau threefold. Given an exceptional collection, we derive the periodic quiver of the gauge theory which is the graph theoretic dual of the brane tiling. Our results give new insight to the construction of quiver theories and their relation to geometry.
46 pages, 37 figures, JHEP3; v2: reference added, figure 13 corrected
References in corpus (33)
- Gauge Theories from Toric Geometry and Brane Tilings
- D-Brane Gauge Theories from Toric Singularities and Toric Duality
- Brane Dimers and Quiver Gauge Theories
- New Einstein-Sasaki Spaces in Five and Higher Dimensions
- Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
- A Geometric Unification of Dualities
- The spectrum of BPS branes on a noncompact Calabi-Yau
- Toric Duality as Seiberg Duality and Brane Diamonds
- Phase Structure of D-brane Gauge Theories and Toric Duality
- From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
- Symmetries of Toric Duality
- The dual superconformal theory for Lpqr manifolds
- R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
- On the realization of chiral four-dimensional gauge theories using branes
- Phases of Supersymmetric D-branes on Kaehler Manifolds and the McKay correspondence
- Computation of Superpotentials for D-Branes
- Brane Boxes and Branes on Singularities
- Dibaryons from Exceptional Collections
- Mirror Symmetries for Brane Configurations and Branes at Singularities
- D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay
- The Toric Phases of the Y^{p,q} Quivers
- Quiver theories, soliton spectra and Picard-Lefschetz transformations
- From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization
- Seiberg Duality is an Exceptional Mutation
- Exceptional Collections and del Pezzo Gauge Theories
- Scalar Laplacian on Sasaki-Einstein Manifolds Y^{p,q}
- Toric Sasaki-Einstein manifolds and Heun equations
- D-branes on Calabi-Yau manifolds and helices
- D-Branes on Vanishing del Pezzo Surfaces
- Solitons and Helices: The Search for a Math-Physics Bridge
- Exceptional collections and D-branes probing toric singularities
- A Trio of Dualities: Walls, Trees and Cascades
- Moduli Spaces for D-branes at the Tip of a Cone
Cited by in corpus (39)
- Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
- Sasaki-Einstein Manifolds and Volume Minimisation
- Brane Tilings and Their Applications
- Counting Chiral Operators in Quiver Gauge Theories
- Brane Tilings and Reflexive Polygons
- Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
- Dimers and Orientifolds
- The Standard Model Quiver in de Sitter String Compactifications
- Brane Tilings and Specular Duality
- Toric AdS4/CFT3 duals and M-theory Crystals
- Exceptional Sequences of Invertible Sheaves on Rational Surfaces
- Baryonic Generating Functions
- Wall Crossing, Quivers and Crystals
- Deformations of conformal theories and non-toric quiver gauge theories
- Deformations of Toric Singularities and Fractional Branes
- Colored BPS Pyramid Partition Functions, Quivers and Cluster Transformations
- On the computation of non-perturbative effective potentials in the string theory landscape -- IIB/F-theory perspective
- Quivers from Matrix Factorizations
- New N=1 dualities from orientifold transitions - Part II: String Theory
- Bipartite Field Theories from D-Branes
- Crystal Melting and Black Holes
- Toric Fano varieties and Chern-Simons quivers
- Non-perturbative effects and wall-crossing from topological strings
- B-branes and supersymmetric quivers in 2d
- S-duality in orientifold SCFTs
- Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
- 5D BPS Quivers and KK Towers
- Global embeddings for branes at toric singularities
- Branes and instantons intersecting at angles
- New Example of Infinite Family of Quiver Gauge Theories
- Toric Lego: A method for modular model building
- Seiberg duality for Chern-Simons quivers and D-brane mutations
- Gauge theories from D7-branes over vanishing 4-cycles
- Metastable vacua and geometric deformations
- Remarks on quiver gauge theories from open topological string theory
- Brane Tilings and Non-Commutative Geometry
- D-branes Wrapped on Fuzzy del Pezzo Surfaces
- conformal dualities from unoriented chiral quivers
- Attractor invariants, brane tilings and crystals