String Junctions for Arbitrary Lie Algebra Representations

Abstract

We consider string junctions with endpoints on a set of branes of IIB string theory defining an ADE-type gauge Lie algebra. We show how to characterize uniquely equivalence classes of junctions related by string/brane crossing through invariant charges that count the effective number of prongs ending on each brane. Each equivalence class defines a point on a lattice of junctions. We define a metric on this lattice arising from the intersection pairing of junctions, and use self-intersection to identify junctions in the adjoint and fundamental representations of all ADE algebras. This information suffices to determine the relation between junction lattices and the Lie-algebra weight lattices. Arbitrary representations are built by allowing junctions with asymptotic (p,q) charges, on which the group of conjugacy classes of representations is represented additively. One can view the (p,q) asymptotic charges as Dynkin labels associated to two new fundamental weight vectors.

60 pages, 17 figures, BoxedEPS.tex

References in corpus (10)

• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• Stable Non-BPS States in String Theory
• String Network
• BPS Nature of 3-String Junctions
• Three-Pronged Strings and 1/4 BPS States in N=4 Super-Yang-Mills Theory
• Open string - string junction transitions
• BPS Dynamics of Triple (p,q) String Junction
• 3-String Junction and BPS Saturated Solutions in SU(3) Supersymmetric Yang-Mills Theory
• String Junctions and BPS States in Seiberg-Witten Theory
• Worldsheet Dynamics of String Junctions

Cited by in corpus (81)

• Atomic Classification of 6D SCFTs
• Lectures on F-theory compactifications and model building
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• Model Building with F-Theory
• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Non-Lagrangian Theories from Brane Junctions
• Mapping 6D N = 1 supergravities to F-theory
• Global F-theory Models: Instantons and Gauge Dynamics
• Ghost D-branes
• Fiber-Base Duality and Global Symmetry Enhancement
• Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality
• More on Dimension-4 Proton Decay Problem in F-theory -- Spectral Surface, Discriminant Locus and Monodromy
• IIB flux non-commutativity and the global structure of field theories
• Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations
• Constraints on the BPS Spectrum of N = 2, D = 4 Theories with A-D-E Flavor Symmetry
• Matter From Geometry Without Resolution
• Tao Probing the End of the World
• Baryon and Dark Matter Genesis from Strongly Coupled Strings
• Intersecting brane solutions in string and M-theory
• String Junctions and BPS States in Seiberg-Witten Theory
• F-theory and 2d (0,2) Theories
• Local models for intersecting brane worlds
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• Chiral 2d Theories from N=4 SYM with Varying Coupling
• Landscaping with fluxes and the E8 Yukawa Point in F-theory
• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations
• Three Looks at Instantons in F-theory -- New Insights from Anomaly Inflow, String Junctions and Heterotic Duality
• T-Branes, String Junctions, and 6D SCFTs
• Mordell-Weil Lattice via String Junctions
• One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
• Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions
• Physics of Infinite Complex Structure Limits in eight Dimensions
• Affine Lie Algebras, String Junctions and 7-Branes
• Calabi-Yau Duals of Torus Orientifolds
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• N=2 Superconformal Field Theory with ADE Global Symmetry on a D3-brane Probe
• Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows
• Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds
• Strong Coupling in F-theory and Geometrically Non-Higgsable Seven-branes
• Affine 7-brane Backgrounds and Five-Dimensional $E_N$ Theories on $S^1$
• The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds
• Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-theory
• The Conformal Sector of F-theory GUTs
• Supersymmetry breaking deformations and phase transitions in five dimensions
• F-theory Family Unification
• Charged Tachyons and Gauge Symmetry Breaking
• F-Theory, GUTs and Chiral Matter
• The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory Compactifications
• Self-Intersection Number of BPS Junctions in Backgrounds of Three and Seven-Branes
• Non-simply-laced Lie algebras via F theory strings
• Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions
• Monopole Dynamics in N=2 super Yang-Mills Theory From a Threebrane Probe
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• Duality and Weyl Symmetry of 7-brane Configurations
• Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces
• On the BPS Spectrum of the Rank-1 Minahan-Nemeschansky Theories
• ${}^1{S}_0$ pairing correlation in symmetric nuclear matter with Debye screening effects
• More on a dessin on the base: Kodaira exceptional fibers and mutually (non-)local branes
• Equivalent String Networks and Uniqueness of BPS States
• $6$D Anomaly-Free Matter Spectrum in F-theory on Singular Spaces
• Abelian Fibrations, String Junctions, and Flux/Geometry Duality
• Map of Heterotic and Type IIB Moduli in 8 Dimensions
• On finiteness of Type IIB compactifications: Magnetized branes on elliptic Calabi-Yau threefolds
• From F/M-theory to K-theory and back
• Affine Algebras at Infinite Distance Limits in the Heterotic String
• Counting Associatives in Compact $G_2$ Orbifolds
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Atomic Higgsings of 6D SCFTs II: Induced Flows
• String junctions on backgrounds with a positively charged orientifold plane
• Dualities of Deformed $\mathcal{N}=2$ SCFTs from Link Monodromy on D3-brane States
• Exotic Brane Junctions from F-theory
• Flavor symmetries and the topology of special Kähler structures at rank 1
• Knots, Braids and BPS States in M-Theory
• Non-Perturbative Structure in Heterotic Strings from Dual F-Theory Models
• A dessin on the base: a description of mutually non-local 7-branes without using branch cuts
• A plethora of K3 metrics
• Monodromies of rational elliptic surfaces and extremal elliptic $K3$ surfaces
• Lie symmetries and 2D Material Physics
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Threebranes in F-theory