Brane Tilings and Their Applications
arXiv:0803.4474 · doi:10.1002/prop.200810536
Abstract
We review recent developments in the theory of brane tilings and four-dimensional N=1 supersymmetric quiver gauge theories. This review consists of two parts. In part I, we describe foundations of brane tilings, emphasizing the physical interpretation of brane tilings as fivebrane systems. In part II, we discuss application of brane tilings to AdS/CFT correspondence and homological mirror symmetry. More topics, such as orientifold of brane tilings, phenomenological model building, similarities with BPS solitons in supersymmetric gauge theories, are also briefly discussed. This paper is a revised version of the author's master's thesis submitted to Department of Physics, Faculty of Science, the University of Tokyo on January 2008, and is based on his several papers: math.AG/0605780, math.AG/0606548, hep-th/0702049, math.AG/0703267, arXiv:0801.3528 and some works in progress.
208 pages, 92 figures, based on master's thesis; v2: minor corrections, to appear in Fortschr. Phys
References in corpus (168)
- Gauge Theory Correlators from Non-Critical String Theory
- Large N Field Theories, String Theory and Gravity
- The Holographic Weyl anomaly
- Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
- Phases of Theories In Two Dimensions
- Supergravity and a Confining Gauge Theory: Duality Cascades and SB-Resolution of Naked Singularities
- Low energy hadron physics in holographic QCD
- Towards Inflation in String Theory
- Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
- Mirror Symmetry is T-Duality
- D-Branes And K-Theory
- An Index for 4 dimensional Super Conformal Theories
- (De)Constructing Dimensions
- More on a holographic dual of QCD
- 4d Conformal Field Theories and Strings on Orbifolds
- Deforming field theories with global symmetry and their gravity duals
- Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
- Geometric Engineering of Quantum Field Theories
- Rotation and the AdS/CFT correspondence
- The Exact Superconformal R-Symmetry Maximizes a
- Dynamical SUSY Breaking in Meta-Stable Vacua
- Counting chiral primaries in N=1 d=4 superconformal field theories
- The Topological Vertex
- Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
- On Conformal Theories in Four Dimensions
- Brane Dynamics and Gauge Theory
- Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
- Gauge Theories from Toric Geometry and Brane Tilings
- The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
- Intersecting Brane Worlds
- Self-Dual Strings and N=2 Supersymmetric Field Theory
- Solitons in the Higgs phase -- the moduli matrix approach --
- Two Dimensional QCD is a String Theory
- D-Brane Gauge Theories from Toric Singularities and Toric Duality
- Branes And The Dynamics Of QCD
- An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
- Entropy of Near-Extremal Black p-branes
- Brane Dimers and Quiver Gauge Theories
- Branes and N=1 Duality in String Theory
- Counting Gauge Invariants: the Plethystic Program
- Supersymmetric AdS_5 solutions of M-theory
- Neutrino Majorana Masses from String Theory Instanton Effects
- Yukawa couplings in intersecting D-brane models
- Einstein manifolds and conformal field theories
- The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds
- New Einstein-Sasaki Spaces in Five and Higher Dimensions
- World Volume Approach to Absorption by Non-dilatonic Branes
- Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
- Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
- A Geometric Unification of Dualities
- Khovanov-Rozansky Homology and Topological Strings
- Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
- Stringy Instantons and Quiver Gauge Theories
- Aspects of Type IIB Theory on ALE Spaces
- Toric Duality as Seiberg Duality and Brane Diamonds
- Holomorphy, Rescaling Anomalies and Exact beta Functions in Supersymmetric Gauge Theories
- D-branes, Categories and N=1 Supersymmetry
- Toric Duality Is Seiberg Duality
- Oriented Open-Closed String Theory Revisited
- Tensor Constructions of Open String Theories I: Foundations
- Toric Sasaki-Einstein metrics on S^2 x S^3
- Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves
- Supersymmetry on a Spatial Lattice
- Non-abelian Tensor-multiplet Anomalies
- Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges
- Phase Structure of D-brane Gauge Theories and Toric Duality
- Brane Tilings
- Instanton Induced Neutrino Majorana Masses in CFT Orientifolds with MSSM-like spectra
- Building the Standard Model on a D3-brane
- From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
- New checks and subtleties for AdS/CFT and a-maximization
- On the Moduli Space of the Cascading SU(M+p)xSU(p) Gauge Theory
- D-branes at Singularities, Compactification, and Hypercharge
- The dual superconformal theory for Lpqr manifolds
- Supersymmetry on a Euclidean Spacetime Lattice II: Theories with Eight Supercharges
- Gauge Mediation Simplified
- Discrete Riemann Surfaces and the Ising model
- Stringy Instantons at Orbifold Singularities
- R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
- Geometric Engineering of N=1 Quantum Field Theories
- Fractional Branes and Dynamical Supersymmetry Breaking
- On Orientifolds, Discrete Torsion, Branes and M Theory
- D-Branes, Derived Categories, and Grothendieck Groups
- Supersymmetry Breaking from a Calabi-Yau Singularity
- 3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3
- Derived Categories and Zero-Brane Stability
- D-brane Instantons on the T^6/Z_3 orientifold
- The Laplacian and operators on critical planar graphs
- D-Brane Stability and Monodromy
- Brane Configurations for Branes at Conifolds
- sl(3) link homology
- Orientifolds, Branes, and Duality of 4D Gauge Theories
- Non-Abelian Finite Gauge Theories
- Baryon Spectra and AdS/CFT Correspondence
- Supersymmetry breaking at the end of a cascade of Seiberg dualities
- Geometry of N=1 Dualities in Four Dimensions
- Landscape of Supersymmetry Breaking Vacua in Geometrically Realized Gauge Theories
- Stability and BPS branes
- Stability conditions on a non-compact Calabi-Yau threefold
- Counting Chiral Operators in Quiver Gauge Theories
- Dynamical SUSY Breaking at Meta-Stable Minima from D-branes at Obstructed Geometries
- Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
- Quiver Theories from D6-branes via Mirror Symmetry
- Non-supersymmetric Meta-stable Vacua from Brane Configurations
- Dibaryons from Exceptional Collections
- Simple Scheme for Gauge Mediation
- D-brane Construction for Non-Abelian Walls
- Counting 1/8-BPS Dual-Giants
- Overview Of K-Theory Applied To Strings
- Numerical Ricci-flat metrics on K3
- The Toric Phases of the Y^{p,q} Quivers
- Enhanced D-Brane Categories from String Field Theory
- Conformal Manifolds for the Conifold and other Toric Field Theories
- Surface Operators and Knot Homologies
- Orientifolds, RR Torsion, and K-theory
- Index for Orbifold Quiver Gauge Theories
- From Toric Geometry to Quiver Gauge Theory: the Equivalence of a-maximization and Z-minimization
- Marginal Deformations of Field Theories with AdS_4 Duals
- Brane Tilings and Exceptional Collections
- Moduli Spaces of Gauge Theories from Dimer Models: Proof of the Correspondence
- Seiberg Duality is an Exceptional Mutation
- Rings of short N=3 superfields in three dimensions and M-theory on AdS_4 x N^{0,1,0}
- Exceptional Collections and del Pezzo Gauge Theories
- Toric Sasaki-Einstein manifolds and Heun equations
- The structure of N=3 multiplets in AdS_4 and the complete Osp(3|4) X SU(3) spectrum of M-theory on AdS_4 X N^{010}
- The Minimal Quiver Standard Model
- D-Branes on Vanishing del Pezzo Surfaces
- Rank Two Quiver Gauge Theory, Graded Connections and Noncommutative Vortices
- D-brane categories
- Gauge Mediation in String Theory
- Dibaryon Spectroscopy
- Comments on the non-conformal gauge theories dual to Ypq manifolds
- Orientifold Planes, Type I Wilson Lines and Non-BPS D-branes
- Deformations of conformal theories and non-toric quiver gauge theories
- Deformations of Toric Singularities and Fractional Branes
- Explicit Toric Metric on Resolved Calabi-Yau Cone
- A Note on Einstein Sasaki Metrics in D \ge 7
- Baryon Charges in 4d Superconformal Field Theories and Their AdS Duals
- Kinky D-Strings
- Three Dimensional SCFT from M2 Branes at Conifold Singularities
- Classical Open-String Field Theory ; -Algebra, Renormalization Group and Boundary States
- Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge Theory
- Comments on Anomalies and Charges of Toric-Quiver Duals
- On Stable Non-Supersymmetric Vacua at the Bottom of Cascading Theories
- Multi-spin strings on AdS(5)xT(1,1) and operators of N=1 superconformal theory
- Spinning and rotating strings for N=1 SYM theory and brane constructions
- Exceptional collections and D-branes probing toric singularities
- Unitarity, D-brane dynamics and D-brane categories
- New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes
- Exactly marginal deformations of quiver gauge theories as seen from brane tilings
- AdS/CFT with Tri-Sasakian Manifolds
- Crystal Melting and Black Holes
- T-duality, Fiber Bundles and Matrices
- On Berenstein-Douglas-Seiberg Duality
- Lattice Formulation of Two Dimensional Topological Field Theory
- Global symmetries and 't Hooft anomalies in brane tilings
- Amoebas and Instantons
- Seiberg duality as derived equivalence for some quiver gauge theories
- Supersymmetry breaking metastable vacua in runaway quiver gauge theories
- N=2 SCFT and M Theory on AdS_4 x Q^{1,1,1}
- Cascading Quivers from Decaying D-branes
- Finite N Index and Angular Momentum Bound from Gravity
- Marginal Deformations from Branes
- New Geometries with in M Theory
- Anomaly Cancellations in Brane Tilings
- G_2 Quivers
- Near-flat space limit and Einstein manifolds
- On Dimer Models and Closed String Theories
Cited by in corpus (89)
- D-Branes at del Pezzo Singularities: Global Embedding and Moduli Stabilisation
- Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter
- Chiral flavors and M2-branes at toric CY4 singularities
- Fivebranes and 3-manifold homology
- Crystal Melting and Toric Calabi-Yau Manifolds
- On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
- Brane Tilings and Reflexive Polygons
- 2d (0,2) Quiver Gauge Theories and D-Branes
- D3/D7 Branes at Singularities: Constraints from Global Embedding and Moduli Stabilisation
- N=4 Chern-Simons theories and wrapped M-branes in their gravity duals
- Quiver Yangian from Crystal Melting
- Quivers, YBE and 3-manifolds
- Axion Monodromy Inflation on Warped Throats
- D-branes at Toric Singularities: Model Building, Yukawa Couplings and Flavour Physics
- The Standard Model Quiver in de Sitter String Compactifications
- Brane Tilings and Specular Duality
- Shifted Quiver Yangians and Representations from BPS Crystals
- Intersecting Solitons, Amoeba and Tropical Geometry
- Emergent 3-manifolds from 4d Superconformal Indices
- Symmetry-breaking vacua and baryon condensates in AdS/CFT
- Toroidal and Elliptic Quiver BPS Algebras and Beyond
- Network and Seiberg Duality
- The star-triangle relation, lens partition function, and hypergeometric sum/integrals
- Counting Orbifolds
- Towards a Systematic Construction of Realistic D-brane Models on a del Pezzo Singularity
- On the Classification of Brane Tilings
- New Integrable Models from the Gauge/YBE Correspondence
- Higgsing M2-brane Theories
- Toric CFTs, Permutation Triples, and Belyi Pairs
- Symmetries of Abelian Orbifolds
- Crystal Melting and Wall Crossing Phenomena
- On the computation of non-perturbative effective potentials in the string theory landscape -- IIB/F-theory perspective
- Gauge/Bethe correspondence from quiver BPS algebras
- Quiver gauge theories and integrable lattice models
- A Comprehensive Survey of Brane Tilings
- Integrability from 2d N=(2,2) Dualities
- String Theory Origin of Bipartite SCFTs
- Superconformal index for large N quiver Chern-Simons theories
- S-duality in orientifold SCFTs
- Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
- Quantum toroidal algebras and solvable structures in gauge/string theory
- E3-brane instantons and baryonic operators for D3-branes on toric singularities
- Invariants of Toric Seiberg Duality
- Neurons on Amoebae
- The Beta Ansatz: A Tale of Two Complex Structures
- Supersymmetry Breaking Warped Throats and the Weak Gravity Conjecture
- De Sitter Uplift with Dynamical Susy Breaking
- On the refined counting of graphs on surfaces
- Branes and instantons intersecting at angles
- BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations
- Orientifolds of Warped Throats from Toric Calabi-Yau Singularities
- (Un)Higgsing the M2-brane
- Surface operators in the Klebanov-Witten theory
- Quiver Yangians and Crystal Melting: A Concise Summary
- Mass Deformations of Unoriented Quiver Theories
- Integrable lattice spin models from supersymmetric dualities
- Toric Lego: A method for modular model building
- Graded Quivers, Generalized Dimer Models and Toric Geometry
- D-brane Instantons as Gauge Instantons in Orientifolds of Chiral Quiver Theories
- Dynamical Spin Chains in 4D SCFTs
- Brane Geometry and Dimer Models
- The Origin of Calabi-Yau Crystals in BPS States Counting
- Calabi-Yau Geometries: Algorithms, Databases, and Physics
- Gauge origami and quiver W-algebras
- Consistency and Derangements in Brane Tilings
- An Introduction to Counting Orbifolds
- Branes and integrable lattice models
- Radiative Fermion Masses in Local D-Brane Models
- Crystal Melting, BPS Quivers and Plethystics
- Brane Tilings and Non-Commutative Geometry
- Dimers, Orientifolds and Anomalies
- 5D N=1 super QFT: symplectic quivers
- BPS States Meet Generalized Cohomology
- Gauging and Decoupling in 3d dualities
- Algorithms for representations of quiver Yangian algebras
- conformal dualities from unoriented chiral quivers
- Graph Zeta Function and Gauge Theories
- D-branes Wrapped on Fuzzy del Pezzo Surfaces
- Probing the Space of Toric Quiver Theories
- Mahler Measure for a Quiver Symphony
- Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
- Quiver Gauge Theories: Beyond Reflexivity
- An Overview of Crystals and Double Quiver Yangians
- Implications of the weak gravity conjecture in anomalous quiver gauge theories
- New Gauged Linear Sigma Models for 8D HyperKahler Manifolds and Calabi-Yau Crystals
- Algebro-geometrical orientifolds and IR dualities
- On the structure of quadrilateral brane tilings
- Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations
- Metaheuristic Generation of Brane Tilings