Introduction to Seiberg-Witten Theory and its Stringy Origin

Abstract

We give an elementary introduction to the recent solution of $N=2$ supersymmetric Yang-Mills theory. In addition, we review how it can be re-derived from string duality.

Proceedings of 1996 Trieste Spring School on String Theory, 37p, 22 figs, espcrc2.sty

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• Geometric Engineering of Quantum Field Theories
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• New N=2 Superconformal Field Theories in Four Dimensions
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• The Vacuum Structure of N=2 SuperQCD with Classical Gauge Groups
• Study of $N=2$ Superconformal Field Theories in $4$ Dimensions
• The Strong-Coupling Spectrum of the Seiberg-Witten Theory
• Low-Energy Analysis of $M$ and $F$ Theories on Calabi-Yau Threefolds
• D-Strings on D-Manifolds
• On the Ubiquity of K3 Fibrations in String Duality
• Prepotentials of $N=2$ Supersymmetric Gauge Theories and Soliton Equations
• N=2 Heterotic Superstring and its Dual Theory in Five Dimensions
• On the Relation Between the Holomorphic Prepotential and the Quantum Moduli in SUSY Gauge Theories
• Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory
• On the Quantum Moduli Space of N=2 Supersymmetric Gauge Theories
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• Integrable Structures in Supersymmetric Gauge and String Theory
• New Principles for String/Membrane Unification
• Heterotic phase transitions and singularities of the gauge dyonic string
• Superspace Effective Actions for 4D Compactifications of Heterotic and Type II Superstrings
• Duality in N=2 SUSY SU(2) Yang-Mills Theory: A pedagogical introduction to the work of Seiberg and Witten
• The Effective Prepotential of N=2 Supersymmetric SO(N_c) and Sp(N_c) Gauge Theories
• Monopole and Dyon Bound States in N=2 Supersymmetric Yang-Mills Theories
• D-Brane Realization of N=2 Super Yang-Mills Theory in Four Dimensions
• One-Instanton Calculations in $N=2$ Supersymmetric $SU(N_c)$ Yang-Mills Theory
• An N=2 Dual Pair and a Phase Transition
• Nonperturbative Renormalization Group Equation and Beta Function in N=2 SUSY Yang-Mills
• Multi-Instanton Check of the Relation Between the Prepotential F and the Modulus u in N=2 SUSY Yang-Mills Theory
• Exceptional SW Geometry from ALE Fibrations
• Exact Monodromy Group of N=2 Heterotic Superstring
• More on softly broken N=2 QCD
• $N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$
• The Moduli Space and Monodromies of the $N=2$ Supersymmetric Yang-Mills Theory with any Lie Gauge Groups
• Exceptional Equivalences in N=2 Supersymmetric Yang-Mills Theory
• Topological Amplitudes in Heterotic Superstring Theory
• A New Derivation of the Picard-Fuchs Equations for Effective $N=2$ Super Yang-Mills Theories
• Heterotic-Heterotic String Duality and Multiple K3 Fibrations
• A Two-Instanton Test of the Exact Solution of N=2 Supersymmetric QCD
• String-dual $F_1$-Function in the Three Parameter Model
• The Moduli Space of the $N=2$ Supersymmetric $G_2$ Yang-Mills Theory
• Topological partition function and string-string duality
• Electric-Magnetic Duality and Effective Field Theories
• Periods, Coupling Constants and Modular Functions in N=2 SU(2) SYM with Massive Matter
• On the Seiberg-Witten Approach to electric-magnetic Duality
• Heterotic Gauge Structure of Type II K3 Fibrations
• Prepotentials in N=2 Supersymmetric SU(3) YM-Theory with Massless Hypermultiplets
• Calabi-Yau Varieties and Pencils of K3 Surfaces
• Counting Curves with Modular Forms
• Black Hole Condensation and Duality in String Theory
• (0,2) Noncritical Strings in Six Dimensions
• Simple Calculation of Instanton Corrections in Massive N=2 SU(3) SYM
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• On the Worldsheet Formulation of the Six-Dimensional Self-Dual String
• Peierls model and vacuum structure in N=2 supersymmetric gauge theories
• Exact Multiplets of Spontaneously Broken Discrete Global Symmetries: the Example of $N=2$ Susy QCD
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• From Nonperturbative SUSY Gauge Theories to Integrable Systems

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• Fractional Branes and Boundary States in Orbifold Theories
• Wall-Crossing in Coupled 2d-4d Systems
• N=2 Quantum Field Theories and Their BPS Quivers
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Little String Theory at a TeV
• Instanton sums and five-dimensional gauge theories
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• Quantum Wall Crossing in N=2 Gauge Theories
• M Theory And Seiberg-Witten Curves: Orthogonal and Symplectic Groups
• N=2 supersymmetric dynamics for pedestrians
• A holomorphic and background independent partition function for matrix models and topological strings
• Calogero-Moser Models: A New Formulation
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Fluxes in Heterotic and Type II String Compactifications
• Softly Broken N=2 QCD with Massive Quark Hypermultiplets, I
• Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models
• The BPS Spectrum of N=2 SU(N) SYM and Parton Branes
• Seiberg-Witten Geometries Revisited
• On a Boundary CFT Description of Nonperturbative N=2 Yang-Mills Theory
• Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras
• Logarithmic Conformal Field Theory and Seiberg-Witten Models
• Strings, Branes and Extra Dimensions
• Magnetic expansion of Nekrasov theory: the SU(2) pure gauge theory
• Exponential Networks and Representations of Quivers
• An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems
• Instanton corrections in N=2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets
• Semiclassical framed BPS states
• The rigid limit in Special Kahler geometry; From K3-fibrations to Special Riemann surfaces: a detailed case study
• On Moduli Spaces in $\mathbf{Ad}{\mathbf{S}}_4$ Supergravity
• M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
• Towards the classification of rank-$r$ $\mathcal{N}=2$ SCFTs. Part I: twisted partition function and central charge formulae
• Quantum Curves, Resurgence and Exact WKB
• Dual Description of Supergravity MacDowell-Mansouri Theory
• Solitons in Seiberg-Witten Theory and D-branes in the Derived Category
• Interacting fermions on noncommutative spaces: Exactly solvable quantum field theories in 2n+1 dimensions
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Investigating the BPS Spectrum of Non-Critical E_n Strings
• A geometric recipe for twisted superpotentials
• Lax Pairs and Spectral Curves for Calogero-Moser and Spin Calogero-Moser Systems
• Seiberg-Witten Theory and Integrable Systems
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• Monopole Dynamics in N=2 super Yang-Mills Theory From a Threebrane Probe
• Instanton Counting, Quantum Geometry and Algebra
• Special geometry of local Calabi-Yau manifolds and superpotentials from holomorphic matrix models
• Supersymmetric Field Theory in 2T-physics
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Seiberg-Witten Theory and Calogero-Moser Systems
• Three-form periods on Calabi-Yau fourfolds: Toric hypersurfaces and F-theory applications
• Supersymmetry and Duality in Field Theory and String Theory
• On the WDVV Equation and M-Theory
• N=2,4 Supersymmetric Gauge Field Theory in 2T-physics
• Integration Over The u-Plane In Donaldson Theory With Surface Operators
• Confinement and duality in supersymmetric gauge theories
• Heterotic-Type II duality in the hypermultiplet sector
• Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories
• Thermodynamics of SU(2) N=2 supersymmetric Yang-Mills theory
• Superconformal R-charges and dyon multiplicities in N=2 gauge theories
• Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups
• Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings
• WDVV equation and Triple-product Relation
• Exact Solutions of Exceptional Gauge Theories from Toric Geometry
• Special geometry of Calabi-Yau compactifications near a rigid limit
• Enhanced Gauge Symmetry in Three-Moduli Models of Type-II String and Hypergeometric Series
• Symplectic forms in the theory of solitons
• F-Theory, Seiberg-Witten Curves and N = 2 Dualities
• Disconnected gauge groups in the infrared
• Solving Four Dimensional Field Theories with the Dirichlet Fivebrane
• Order Parameters, Free Fermions, and Conservation Laws for Calogero-Moser Systems
• Gravitational corrections to N=2 supersymmetric lagrangians
• Matching Exact Results and One-Instanton Predictions in N=2 Supersymmetric SU(N) Theories
• Supersymmetric Gauge Theories from String Theory
• Dimensional Reduction of Seiberg-Witten Monopole Equations, N=2 Noncommutative Supersymmetric Field Theories and Young Diagrams
• Singularity Structure of N=2 Supersymmetric Yang-Mills Theories: A Review
• The rigid limit in Special Kähler geometry for SU(2) SYM with a massive quark hypermultiplet
• Threebranes in F-theory
• Pure Gauge SU(2) Seiberg-Witten Theory and Modular Forms
• Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape