Whitham Hierarchies, Instanton Corrections and Soft Supersymmetry Breaking in N=2 SU(N) Super Yang-Mills Theory

Abstract

We study N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy. We develop a new recursive method to compute the whole instanton expansion of the prepotential using the theta function associated to the root lattice of the group. Explicit results for the one and two-instanton corrections in SU(N) are presented. Interpreting the slow times of the hierarchy as additional couplings, we show how they can be promoted to spurion superfields that softly break N=2 supersymmetry down to N=0. This provides a family of nonsupersymmetric deformations of the theory, associated to higher Casimir operators of the gauge group. The SU(3) theory is analyzed in some detail.

29 pages, LaTeX, no figures. Minor corrections and improvements on the instanton contributions formulae, one reference added. Final version to be published in Nuclear Physics B

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• Multi-Instanton Calculus and Equivariant Cohomology
• Matone's Relation in the Presence of Gravitational Couplings
• Extended Seiberg-Witten Theory and Integrable Hierarchy
• A note on instanton counting for N=2 gauge theories with classical gauge groups
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• Proving AGT relations in the large-c limit
• Counting Exceptional Instantons
• The N=2 gauge theory prepotential and periods from a perturbative matrix model calculation
• Commuting Hamiltonians from Seiberg-Witten Theta-Functions
• Can Renormalization Group Flow End in a Big Mess?
• N=2 supersymmetric gauge theories with massive hypermultiplets and the Whitham hierarchy
• RG-Whitham dynamics and complex Hamiltonian systems
• Calculating the Prepotential by Localization on the Moduli Space of Instantons
• Instanton corrections in N=2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets
• Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Instanton Recursion Relations for the Effective Prepotential in N=2 Super Yang-Mills
• Gauge/String Duality in Confining Theories
• Seiberg--Witten Duality in Dijkgraaf--Vafa Theory
• Multi-Instantons, Supersymmetry and Topological Field Theories
• Strong coupling expansion and Seiberg-Witten-Whitham equations
• Instantons from Blow-up
• Supereigenvalue Model and Dijkgraaf-Vafa Proposal
• Whitham Prepotential and Superpotential
• Cubic curves from instanton counting
• Singular Phases of Seiberg-Witten Integrable Systems: Weak and Strong Coupling
• The Liouville Geometry of N=2 Instantons and the Moduli of Punctured Spheres
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II
• Instantons to the people: the power of one-form symmetries
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Two antisymmetric hypermultiplets in N=2 SU(N) gauge theory: Seiberg-Witten curve and M-theory interpretation
• Field Theory Interpretation of N=2 Stringy Instantons
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• Improved matrix-model calculation of the N=2 prepotential
• WDVV equation and Triple-product Relation
• On supersymmetry breaking and the Dijkgraaf-Vafa conjecture
• Vacuum structure of spontaneously broken N=2 supersymmetric gauge theory
• Prepotential and Instanton Corrections in N=2 Supersymmetric SU(N_1)xSU(N_2) Yang Mills Theories
• The Instanton Universal Moduli Space of N=2 Supersymmetric Yang-Mills Theory
• RG flows on the phase spaces and the $\tau$ functions for the generic Hamiltonian systems
• Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• Low Energy Effective Action in N=2 Yang-Mills as an Integrated Anomaly