Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory

Abstract

The exact solution of $N=2$ supersymmetric $SU(N)$ Yang-Mills theory is studied in the framework of the Whitham hierarchies. The solution is identified with a homogeneous solution of a Whitham hierarchy. This integrable hierarchy (Whitham-Toda hierarchy) describes modulation of a quasi-periodic solution of the (generalized) Toda lattice hierarchy associated with the hyperelliptic curves over the quantum moduli space. The relation between the holomorphic pre-potential of the low energy effective action and the $\tau$ function of the (generalized) Toda lattice hierarchy is also clarified.

13 pages, LaTeX

Cited by in corpus (84)

• Solutions Of Four-Dimensional Field Theories Via M Theory
• The Vacuum Structure of N=2 SuperQCD with Classical Gauge Groups
• Integrability and Seiberg-Witten Theory: Curves and Periods
• Prepotentials of $N=2$ Supersymmetric Gauge Theories and Soliton Equations
• Introduction to Seiberg-Witten Theory and its Stringy Origin
• N=2 Supersymmetric Gauge Theories, Branes and Orientifolds
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• On the Quantum Moduli Space of N=2 Supersymmetric Gauge Theories
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Integrable Structures in Supersymmetric Gauge and String Theory
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• RG Equations from Whitham Hierarchy
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• The Effective Prepotential of N=2 Supersymmetric SU(N_c) Gauge Theories
• Prepotential and the Seiberg-Witten Theory
• A direct proof of AGT conjecture at beta = 1
• Extended Seiberg-Witten Theory and Integrable Hierarchy
• On Painlevé/gauge theory correspondence
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• On Double-Elliptic Integrable Systems. 1. A Duality Argument for the case of SU(2)
• Nonperturbative Renormalization Group Equation and Beta Function in N=2 SUSY Yang-Mills
• The Renormalization Group Equation in N=2 Supersymmetric Gauge Theories
• Whitham Hierarchies, Instanton Corrections and Soft Supersymmetry Breaking in N=2 SU(N) Super Yang-Mills Theory
• Towards a proof of AGT conjecture by methods of matrix models
• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• $N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$
• Calogero-Moser Models II: Symmetries and Foldings
• N=2 supersymmetric gauge theories with massive hypermultiplets and the Whitham hierarchy
• Partial Breaking of N=2 Supersymmetry and of Gauge Symmetry in the U(N) Gauge Model
• Solving N=2 SYM by Reflection Symmetry of Quantum Vacua
• 5d and 6d Supersymmetric Gauge Theories: Prepotentials from Integrable Systems
• Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case
• Towards Mass Deformed N=4 SO(n) and Sp(k) gauge configurations
• Integrable structures and duality in high-energy QCD
• Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation
• Integrability and Seiberg-Witten theory
• Exact results for topological strings on resolved Y(p,q) singularities
• Supersymmetric U(N) Gauge Model and Partial Breaking of N=2 Supersymmetry
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Insights and Puzzles from Branes: 4d SUSY Yang-Mills from 6d Models
• Supersymmetric U(N) Gauge Model and Partial Breaking of N=2 Supersymmetry
• Free Fermion and Seiberg-Witten Differential in Random Plane Partitions
• Tau-Functions generating the Conservation Laws for Generalized Integrable Hierarchies of KdV and Affine-Toda type
• Branes and integrability in the N=2 SUSY YM theory
• Strong coupling expansion and Seiberg-Witten-Whitham equations
• Supereigenvalue Model and Dijkgraaf-Vafa Proposal
• Whitham Prepotential and Superpotential
• Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions
• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Maulik-Okounkov's R-matrix from Ding-Iohara-Miki algebra
• Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• The N=1* Theories on R^{1+2} X S^1 with Twisted Boundary Conditions
• Flat Coordinates, Topological Landau-Ginzburg Models and the Seiberg-Witten Period Integrals
• Solutions to the reflection equation and integrable systems for N=2 SQCD with classical groups
• Picard-Fuchs Equation and Prepotential of Five Dimensional SUSY Gauge Theory Compactified on a Circle
• Integrable structure in supersymmetric gauge theories with massive hypermultiplets
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II
• The Whitham Deformation of the Dijkgraaf-Vafa Theory
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups
• Space-wave function duality and enhanced dKdV on a Riemann surface
• BPS Geodesics in N=2 Supersymmetric Yang-Mills Theory
• On the WDVV Equation and M-Theory
• $K3$-Fibrations and Softly Broken $N=4$ Supersymmetric Gauge Theories
• Picard-Fuchs Equations and Whitham Hierarchy in N=2 Supersymmetric SU(r+1) Yang-Mills Theory
• New results in $\mathcal{N}=2$ theories from non-perturbative string
• Topological Field Theory and Second-Quantized Five-Branes
• N=1 G_2 SYM theory and Compactification to Three Dimensions
• WDVV equation and Triple-product Relation
• On supersymmetry breaking and the Dijkgraaf-Vafa conjecture
• Integrability in N=2 Gauge Theory: A Proof
• On Effective Superpotentials and Compactification to Three Dimensions
• N=2 supersymmetric gauge theories and quantum integrable systems
• Symplectic forms in the theory of solitons
• Differential Equations for Scaling Relation in N=2 Supersymmetric SU(2) Yang-Mills Theory Coupled with Massive Hypermultiplet
• Instanton Correction of Prepotential in Ruijsenaars Model Associated with N=2 SU(2) Seiberg-Witten Theory
• Elliptic analog of the Toda lattice
• Toda chain from the kink-antikink lattice
• Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
• Seiberg-Witten Theory of Rank Two Gauge Groups and Hypergeometric Series
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• Integrable hierarchies in Donaldson-Witten and Seiberg-Witten theories
• Direct Derivation of Scaling Relation of Prepotential in N=2 Supersymmetric G_2 Yang-Mills Theory