On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)

Abstract

We find a relation between the spectrum of solitons of massive $N=2$ quantum field theories in $d=2$ and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetric $N=2$ conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A--D--E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.

116 pages, HUTP-92/A064 and SISSA-203/92/EP

References in corpus (5)

• A New Supersymmetric Index
• Geometry and Integrability of Topological-Antitopological Fusion
• Topological Orbifold Models and Quantum Cohomology Rings
• Scattering and Thermodynamics of Fractionally-Charged Supersymmetric Solitons
• Exact Results for Supersymmetric Sigma Models

Cited by in corpus (250)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• CFT's From Calabi-Yau Four-folds
• Superstrings and Topological Strings at Large N
• Four-dimensional wall-crossing via three-dimensional field theory
• D-Branes And Mirror Symmetry
• Self-Dual Strings and N=2 Supersymmetric Field Theory
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• Integrable systems and supersymmetric gauge theory
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Branes And The Dynamics Of QCD
• Non-Abelian String Junctions as Confined Monopoles
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Analytic Continuation Of Chern-Simons Theory
• Dynamics of $SU(N)$ Supersymmetric Gauge Theory
• A Geometric Unification of Dualities
• An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
• The Verlinde Algebra And The Cohomology Of The Grassmannian
• R-Twisting and 4d/2d Correspondences
• Holomorphic Blocks in Three Dimensions
• Branes and N=2 Theories in Two Dimensions
• Spectral networks
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• The Strong-Coupling Spectrum of the Seiberg-Witten Theory
• Wall-Crossing from Boltzmann Black Hole Halos
• TASI Lectures on Solitons
• Non-Abelian Meissner Effect in Yang--Mills Theories at Weak Coupling
• Wall-Crossing in Coupled 2d-4d Systems
• Surface Operators in N=2 4d Gauge Theories
• N=2 Quantum Field Theories and Their BPS Quivers
• Topological Orbifold Models and Quantum Cohomology Rings
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• On Three Dimensional Quiver Gauge Theories and Integrability
• Geometry and analytic theory of Frobenius manifolds
• Integrable Structures in Supersymmetric Gauge and String Theory
• Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• BPS Structure of Argyres-Douglas Superconformal Theories
• Localization of Non-Abelian Gauge Fields on Domain Walls at Weak Coupling (D-brane Prototypes)
• Degenerate Domain Wall Solutions in Supersymmetric Theories
• Curves of Marginal Stability and Weak and Strong-Coupling BPS Spectra in $N=2$ Supersymmetric QCD
• More on the N=2 superconformal systems of type $D_p(G)$
• The Witten equation and its virtual fundamental cycle
• Stability conditions on a non-compact Calabi-Yau threefold
• BPS Degeneracies and Superconformal Index in Diverse Dimensions
• Surface Defects and Chiral Algebras
• Infrared Computations of Defect Schur Indices
• Infinitely many N=2 SCFT with ADE flavor symmetry
• Dibaryons from Exceptional Collections
• BPS states and algebras from quivers
• Exploring Pure Spinor String Theory on AdS_4 x CP^3
• Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples
• RG Fixed Points and Flows in SQCD with Adjoints
• TBA equations and resurgent Quantum Mechanics
• Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces
• Seiberg-Witten theory and matrix models
• Quiver theories, soliton spectra and Picard-Lefschetz transformations
• Complex BPS domain walls and phase transition in mass in supersymmetric QCD
• Higher Form Symmetries of Argyres-Douglas Theories
• BPS Domain Walls in Large N Supersymmetric QCD
• BPS Wall Crossing and Topological Strings
• tt* Geometry in 3 and 4 Dimensions
• Resurgence in complex Chern-Simons theory
• A New 2d/4d Duality via Integrability
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• Geometric Realizations of BPS States in N=2 Theories
• Ends of the moduli space of Higgs bundles
• On Arnold's 14 `exceptional' N=2 superconformal gauge theories
• Categorical Tinkertoys for N=2 Gauge Theories
• From CFT's to Graphs
• Duality Walls, Duality Trees and Fractional Branes
• Nahm's equations, $N=1^{\ast }$ domain walls, and D-strings in $Ad{S}_{5}x{S}_5$
• Towards a Worldsheet Derivation of the Maldacena Conjecture
• Crossing the Wall: Branes vs. Bundles
• Marginal Stability and the Metamorphosis of BPS States
• Maruyoshi-Song Flows and Defect Groups of $D_p^b(G)$ Theories
• Introduction to Cluster Algebras. Chapters 1-3
• A Stringy Test of the Fate of the Conifold
• Mirror symmetry in two steps: A-I-B
• Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD
• Bound state transformation walls
• Complete Graphs, Hilbert Series, and the Higgs branch of the 4d N=2 $(A_n,A_m)$ SCFT's
• Peacock patterns and new integer invariants in topological string theory
• Open BPS Wall Crossing and M-theory
• Framed BPS States, Moduli Dynamics, and Wall-Crossing
• Counting Domain Walls in N=1 Super Yang-Mills Theory
• On a Boundary CFT Description of Nonperturbative N=2 Yang-Mills Theory
• Large N Domain Walls as D-branes for $\mathcal{N}=1$ QCD String
• Examples of non-commutative Hodge structures
• Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painleve' Equation: II
• Domain Wall Junction in N=2 Supersymmetric QED in four dimensions
• Domain Walls Zoo in Supersymmetric QCD
• Towards effective topological gauge theories on spectral curves
• Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians
• Counting RG flows
• Special Geometry and the Swampland
• R-charges, Chiral Rings and RG Flows in Supersymmetric Chern-Simons-Matter Theories
• String Webs from Field Theory
• Surface Defect Indices and 2d-4d BPS States
• Exact WKB methods in $SU(2)$ $N_f=1$
• Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on Confining Strings
• Relating 't Hooft Anomalies of 4d Pure Yang-Mills and 2d ${\mathbb{CP}}^{N-1}$ Model
• Exploring 5d BPS Spectra with Exponential Networks
• Integrable hierarchies and the mirror model of local CP1
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• ADE Spectral Networks
• Living on the walls of super-QCD
• More Arnold's N = 2 superconformal gauge theories
• Geometric realizations of quiver algebras
• Solitons and Helices: The Search for a Math-Physics Bridge
• $R^3$ index for four-dimensional $N=2$ field theories
• Orbifold equivalent potentials
• N=2 Supersymmetric Kinks and real algebraic curves
• The Exact Mass-Gap of the Supersymmetric CP^{n-1} Sigam Model
• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
• Crystal Melting and Wall Crossing Phenomena
• Domain Wall Junctions in Supersymmetric Field Theories in D=4
• Gauge/Bethe correspondence from quiver BPS algebras
• Single State Supermultiplet in 1+1 Dimensions
• Exact Electric-Magnetic Duality in N=2 Supersymmetric QCD Theories
• Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlevé Equation. I
• BPS Saturated Solitons in N=2 Two-Dimensional Theories on RxS (Domain Walls in Theories with Compactified Dimensions)
• N=2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons
• Graphs and Reflection Groups
• Quantum Dynamics of Low-Energy Theory on Semilocal Non-Abelian Strings
• Half--Hypers and Quivers
• Complete factorization of equations of motion in Wess-Zumino theory
• Complete factorization of equations of motion in supersymmetric field theories
• On the complete classification of the unitary N=2 minimal superconformal field theories
• 2d Wall-Crossing, R-twisting, and a Supersymmetric Index
• Non-Abelian String of a Finite Length
• The Stranger Things of Symmetric Product Orbifold CFTs
• Discontinuous BPS spectra in $N=2$ gauge theory
• BPS Domain Walls in Supersymmetric QCD: Higher Unitary Groups
• On a hyperholomorphic line bundle over the Coulomb branch
• Intersoliton forces in the Wess-Zumino model
• A new kind of McKay correspondence from non-Abelian gauge theories
• Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist
• Helix Structures in Quantum Cohomology of Fano Varieties
• Bands and gaps in Nekrasov partition function
• Long Range Forces and Supersymmetric Bound States
• Boundary Rings and N=2 Coset Models
• Homological Classification of 4d $\mathcal{N}=2$ QFT. Part I: Rank-1 revisited
• Moduli spaces of Calabi-Yau $d$-folds as gravitational-chiral instantons
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• Harmonic bundles and Toda lattices with opposite sign
• Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers
• On Duality Walls in String Theory
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• Wilson loop algebras and quantum K-theory for Grassmannians
• Kink scattering in a generalized Wess-Zumino model
• Construction of topological defect networks with complex scalar fields
• On gauge/string correspondence and mirror symmetry
• D-brane central charge and Landau-Ginzburg orbifolds
• Large-N Solution of the Heterotic CP(N-1) Model with Twisted Masses
• Conceptual Analysis of Black Hole Entropy in String Theory
• More on Homological Supersymmetric Quantum Mechanics
• The BPS Spectrum Generator In 2d-4d Systems
• Topological Strings with Scaling Violation and Toda Lattice Hierarchy
• Moduli Space Potentials for Heterotic non-Abelian Flux Tubes: Weak Deformation
• Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
• String "Baryon'' in Four-Dimensional $\mathcal{N}=2$ Supersymmetric QCD from 2D-4D Correspondence
• BPS Indices, Modularity and Perturbations in Quantum K-theory
• Kink manifolds in a three-component scalar field theory
• Borcherds Algebras and N=4 Topological Amplitudes
• On Integrable Structure behind the Generalized WDVV Equations
• The nonlinear Dirac equation in Bose-Einstein condensates: II. Relativistic soliton stability analysis
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Curvature of classifying spaces for Brieskorn lattices
• On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
• Swampland geometry and the gauge couplings
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• A Lie-theoretic description of the solution space of the tt*-Toda equations
• On the BPS Spectrum of the Rank-1 Minahan-Nemeschansky Theories
• ADE Spectral Networks and Decoupling Limits of Surface Defects
• Confinement and duality in supersymmetric gauge theories
• A Note on Domain Walls and the Parameter Space of N=1 Gauge Theories
• Geometry of moduli spaces of meromorphic connections on curves, Stokes data, wild nonabelian Hodge theory, hyperkahler manifolds, isomonodromic deformations, Painleve equations, and relations to Lie theory
• Comments on D-branes in Kazama-Suzuki models and Landau-Ginzburg theories
• Accelerating Solitons
• 6 + 1 Vacua in Supersymmetric QCD with G_2 Gauge Group
• Realizing IR theories by projections in the UV
• Why Is Landau-Ginzburg Link Cohomology Equivalent To Khovanov Homology?
• Landau-Ginzburg Description of Boundary Critical Phenomena in Two Dimensions
• BPS Spectrum, Indices and Wall Crossing in N=4 Supersymmetric Yang-Mills Theories
• Curves of Marginal Stability in Two-Dimensional CP(N-1) Models with Z_N-Symmetric Twisted Masses
• Superconformal R-charges and dyon multiplicities in N=2 gauge theories
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• A Study of Wall-Crossing: Flavored Kinks in D=2 QED
• Superconformal Block Quivers, Duality Trees and Diophantine Equations
• An infrared bootstrap of the Schur index with surface defects
• BPS Spectrum of Supersymmetric CP(N-1) Theory with Z_N Twisted Masses
• Vacuum polarization energy of the Shifman-Voloshin soliton
• Emergence and Correspondence for String Theory Black Holes
• Domain walls in a non-linear ${\mathbb{S}}^2$-sigma model with homogeneous quartic polynomial potential
• Grassmannian Sigma Models and Topological-Antitopological Fusion
• Large-N Solution of the Heterotic Weighted Non-Linear Sigma-Model
• FQHE and $t{t}^{\ast }$ geometry
• $S^1$-fixed-points in hyper-Quot-schemes and an exact mirror formula for flag manifolds from the extended mirror principle diagram
• Flux Compactification for the Critical Non-Abelian Vortex and Quark Masses
• Serre dimension and stability conditions
• A Fock Sheaf For Givental Quantization
• On the Classification of Duality Webs for Graded Quivers
• K3 metrics from little string theory
• Dynkin Diagrams of ${CP}^1$ Orbifolds
• Four-dimensional N=2 Field Theory and Physical Mathematics
• Quantum Deformation of the Effective Theory on Non-Abelian string and 2D-4D correspondence
• Reconstructing GKZ via topological recursion
• 2D BPS Rings from Sphere Partition Functions
• Domain wall moduli in softly-broken SQCD at $\bar{\theta }=\pi$
• Mildly Flavoring domain walls in SU(N) SQCD: baryons and monopole superpotentials
• Joyce-Song wall-crossing as an asymptotic expansion
• Matrix factorizations and the Landau-Ginzburg/conformal field theory correspondence
• RG flows on the phase spaces and the $\tau$ functions for the generic Hamiltonian systems
• Discontinuous BPS Spectra in N=2 Susy QCD
• 2D-4D Correspondence: Towers of Kinks versus Towers of Monopoles in N=2 Theories
• BPS solutions for generalised Wess-Zumino models and their applications
• Nonabelian mirrors and Gromov-Witten invariants
• Twisted-Mass Potential on the Non-Abelian String World Sheet Induced by Bulk Masses
• On the BPS Spectrum at the Root of the Higgs Branch
• Exponential Networks for Linear Partitions
• Categorical Wall-Crossing in Landau-Ginzburg Models
• Seiberg Duality, Quiver Gauge Theories, and Ihara Zeta Function
• 2d Sigma Models on Non-compact Calabi-Yau and $\mathcal{N}=2$ Liouville Theory
• Domain walls in super Yang-Mills: worldvolume TQFTs and deconfinement from semiclassics on ${\mathbb{R}}^3\times {\mathbb{S}}^1$
• Strings on type IIB pp-wave backgrounds with interacting massive theories on the worldsheet
• Topological charges in 2d N=(2,2) theories and massive BPS states
• Mildly Flavoring Domain Walls in Sp(N) SQCD
• The Statistics of Vacuum Geometry
• Hermitian metrics on F-manifolds
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• Dualities in integrable systems and N=2 theories
• Complete factorization of equations of motion for generalized scalar field theories
• Flat meromorphic connections of Frobenius manifolds with tt*-structure
• BPS and semi-BPS kink families in two-component scalar field theories with fourth-degree polynomial potentials
• Scalar Moduli, Wall Crossing and Phenomenological Predictions
• BPS and non-BPS states in a supersymmetric Landau-Ginzburg theory
• Non Scale-Invariant Topological Landau-Ginzburg Models
• Quantizing a solitonic string
• Smooth Solutions of the tt* Equation: A Numerical Aided Case Study
• Mixed moduli in 3d N=4 higher-genus quivers
• On the signature of certain intersection forms
• Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants
• Polytopes, supersymmetry, and integrable systems
• Dynamics of non-Abelian strings in supersymmetric gauge theories
• The extended tropical vertex group
• Ecalle's paralogarithmic resurgence monomials and effective synthesis
• Supersymmetric Sigma Models on Toric Varieties: A Test Case
• The Painlevé III equation of type (0,0,4,-4), its associated vector bundles with isomonodromic connections, and the geometry of the movable poles
• Topological $\sigma$-Models and Large-$N$ Matrix Integral