Supersymmetric Yang-Mills Systems And Integrable Systems

Abstract

The Coulomb branch of $N=2$ supersymmetric gauge theories in four dimensions is described in general by an integrable Hamiltonian system in the holomorphic sense. A natural construction of such systems comes from two-dimensional gauge theory and spectral curves. Starting from this point of view, we propose an integrable system relevant to the $N=2$ $SU(n)$ gauge theory with a hypermultiplet in the adjoint representation, and offer much evidence that it is correct. The model has an $SL(2,\mathbf{Z})$ $S$-duality group (with the central element $-1$ of $SL(2,\mathbf{Z})$ acting as charge conjugation); $SL(2,\mathbf{Z})$ permutes the Higgs, confining, and oblique confining phases in the expected fashion. We also study more exotic phases.

50 pages, harvmac. added references

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Cited by in corpus (472)

• Large N Field Theories, String Theory and Gravity
• Bound States Of Strings And $p$-Branes
• Solutions Of Four-Dimensional Field Theories Via M Theory
• New N=2 Superconformal Field Theories in Four Dimensions
• Deep Inelastic Scattering and Gauge/String Duality
• Supersymmetric vacua and Bethe ansatz
• Self-Dual Strings and N=2 Supersymmetric Field Theory
• Integrating Over Higgs Branches
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Quantum integrability and supersymmetric vacua
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• On AGT relation in the case of U(3)
• Supersymmetric Three-Form Flux Perturbations on $Ad{S}_5$
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• Five Dimensional Gauge Theories and Relativistic Integrable Systems
• Darboux coordinates, Yang-Yang functional, and gauge theory
• Matrix Models, Geometric Engineering and Elliptic Genera
• Gauge Dual and Noncommutative Extension of an N=2 Supergravity Solution
• Integrability and Seiberg-Witten Theory: Curves and Periods
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
• Sound waves in strongly coupled non-conformal gauge theory plasma
• Defects and Quantum Seiberg-Witten Geometry
• Introduction to Seiberg-Witten Theory and its Stringy Origin
• Wild Quiver Gauge Theories
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Affine SL(2) conformal blocks from 4d gauge theories
• N=2 Supersymmetric Gauge Theories, Branes and Orientifolds
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Brane Constructions, Conifolds and M-Theory
• The Omega deformed B-model for rigid N=2 theories
• Duality in Integrable Systems and Gauge Theories
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• On Three Dimensional Quiver Gauge Theories and Integrability
• Transport properties of cascading gauge theories
• Integrable Structures in Supersymmetric Gauge and String Theory
• Hitchin systems, N=2 gauge theories and W-gravity
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• An N = 2 Supersymmetric Membrane Flow
• 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
• Instantons and Merons in Matrix Models
• Prepotential and the Seiberg-Witten Theory
• The Effective Prepotential of N=2 Supersymmetric SU(N_c) Gauge Theories
• N=1 Supersymmetric Renormalization Group Flows from IIB Supergravity
• A direct proof of AGT conjecture at beta = 1
• Ding-Iohara-Miki symmetry of network matrix models
• The Power of Nekrasov Functions
• Probing F-theory With Multiple Branes
• Explicit examples of DIM constraints for network matrix models
• M5-branes, toric diagrams and gauge theory duality
• Multiscale N=2 SUSY field theories, integrable systems and their stringy/brane origin -- I
• Giant Tachyons in the Landscape
• Rigorous Test of Non-conformal Holography: Wilson Loops in N=2* Theory
• D_n Quivers From Branes
• Extended Seiberg-Witten Theory and Integrable Hierarchy
• On Painlevé/gauge theory correspondence
• Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory
• N=2 supersymmetric dynamics for pedestrians
• Seiberg-Witten theory as a Fermi gas
• On Combinatorial Expansions of Conformal Blocks
• Special complex manifolds
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Ω-deformation and quantization
• Evidence for Large-N Phase Transitions in N=2* Theory
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• Complex Curve of the Two Matrix Model and its Tau-function
• New Curves from Branes
• Generalized Conifolds and 4d N=1 SCFT
• New N=1 Superconformal Field Theories and their Supergravity Description
• Holographic Aspects of Four Dimensional $\mathcal{N}=2$ SCFTs and their Marginal Deformations
• Calogero-Moser Models: A New Formulation
• Thermodynamics of the N=2^* strongly coupled plasma
• Line operators on S^1xR^3 and quantization of the Hitchin moduli space
• Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations
• Asymptotic growth of the 4d $\mathcal{N}=4$ index and partially deconfined phases
• Classification of 4d N=2 gauge theories
• Thermodynamics of the N=2* flow
• Twistor Approach to String Compactifications: a Review
• Field Theory Questions for String Theory Answers
• On Double-Elliptic Integrable Systems. 1. A Duality Argument for the case of SU(2)
• Quantization of Integrable Systems and a 2d/4d Duality
• Deconstruction of the Maldacena-Nunez Compactification
• Holographic, N=1 Supersymmetric RG Flows on M2 Branes
• Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d $(2,0)$ theories
• Nonperturbative Renormalization Group Equation and Beta Function in N=2 SUSY Yang-Mills
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Non-Abelian Vortices in N=1* Gauge Theory
• Exact Superpotentials from Matrix Models
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• An N=2 gauge theory and its supergravity dual
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Curvature Singularities: the Good, the Bad, and the Naked
• Towards a proof of AGT conjecture by methods of matrix models
• Bulk viscosity of N=2* plasma
• The N=2 gauge theory prepotential and periods from a perturbative matrix model calculation
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Nahm's equations, $N=1^{\ast }$ domain walls, and D-strings in $Ad{S}_{5}x{S}_5$
• Opers, surface defects, and Yang-Yang functional
• Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models
• Saddle point equations in Seiberg-Witten theory
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory
• Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory
• Instanton Expansions for Mass Deformed N=4 Super Yang-Mills Theories
• On certain aspects of string theory/gauge theory correspondence
• String Interactions from Matrix String Theory
• The Nekrasov Conjecture for Toric Surfaces
• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• $N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$
• New modular invariance in the N=1* theory, operator mixings and supergravity singularities
• Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated
• Holography for $\mathcal{N}=1^{\ast }$ on $S^4$
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Calogero-Moser Models II: Symmetries and Foldings
• Orientifold planes, affine algebras and magnetic monopoles
• Counter-examples to the correlated stability conjecture
• Anomaly in RTT relation for DIM algebra and network matrix models
• Topological Model for Domain Walls in (Super-)Yang-Mills Theories
• Solution of N=2 Gauge Theories via Compactification to Three Dimensions
• Space-Time Foam From Non-Commutative Instantons
• An Exact Elliptic Superpotential for N=1^* Deformations of Finite N=2 Gauge Theories
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• S-Duality, Deconstruction and Confinement for a Marginal Deformation of N=4 SUSY Yang-Mills
• Check of AGT Relation for Conformal Blocks on Sphere
• Seiberg-Witten Geometries Revisited
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Quiver elliptic W-algebras
• Relating Gauge Theories via Gauge/Bethe Correspondence
• Spectral dualities in XXZ spin chains and five dimensional gauge theories
• Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras
• Cosmic strings from pure Yang-Mills theory
• Decomposing Nekrasov Decomposition
• Hitchin Equation, Singularity, and N=2 Superconformal Field Theories
• Partial Breaking of N=2 Supersymmetry and of Gauge Symmetry in the U(N) Gauge Model
• A slow review of the AGT correspondence
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• Non-Abelian Vortex and Confinement
• Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills
• Magnetic expansion of Nekrasov theory: the SU(2) pure gauge theory
• Non-Abelian Vortices at Weak and Strong Coupling in Mass Deformed ABJM Theory
• Generalizing the N=2 supersymmetric RG flow solution of IIB supergravity
• Matrix String Theory and its Moduli Space
• Solving N=2 SYM by Reflection Symmetry of Quantum Vacua
• A Dielectric Flow Solution with Maximal Supersymmetry
• N=1 Superpotentials from Multi-Instanton Calculus
• Color superconductivity, Z_N flux tubes and monopole confinement in deformed N=2* super Yang-Mills theories
• Adding flavour to the Polchinski-Strassler background
• S-duality as a beta-deformed Fourier transform
• Exact results for $\mathcal{N}=2$ supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
• Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry
• Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case
• 5d and 6d Supersymmetric Gauge Theories: Prepotentials from Integrable Systems
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• Fractional quiver W-algebras
• Integrable structures and duality in high-energy QCD
• Towards Mass Deformed N=4 SO(n) and Sp(k) gauge configurations
• Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation
• Towards the solution to the giant graviton puzzle
• The Curve of Compactified 6D Gauge Theories and Integrable Systems
• On elementary proof of AGT relations from six dimensions
• New N=2 superconformal field theories from M/F theory orbifolds
• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• On the Coulomb Branch of a Marginal Deformation of N=4 SUSY Yang-Mills
• Integrability and Seiberg-Witten theory
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• Deformations of Holographic Duals to Non-Relativistic CFTs
• On the Moduli Space of N = 2 Supersymmetric G_2 Gauge Theory
• Supersymmetric U(N) Gauge Model and Partial Breaking of N=2 Supersymmetry
• Twisted M2 brane holography and sphere correlation functions
• Non-invertible symmetries along 4d RG flows
• Relaxation time of non-conformal plasma
• Generalized Hitchin system, Spectral curve and N=1 dynamics
• BPS States in Omega Background and Integrability
• Matrix models for 2* theories
• Affine Toda Solitons and Systems of Calogero-Moser Type
• Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• QCD, Supersymmetric QCD, Lattice QCD and String Theory: Synthesis on the Horizon?
• Insights and Puzzles from Branes: 4d SUSY Yang-Mills from 6d Models
• Supersymmetric U(N) Gauge Model and Partial Breaking of N=2 Supersymmetry
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Splitting of surface defect partition functions and integrable systems
• Les Houches Lectures on Fields, Strings and Duality
• Generalized matrix models and AGT correspondence at all genera
• Superconformal index of low-rank gauge theories via the Bethe Ansatz
• N=2 gauge theories and quantum phases
• Isomonodromic Properties of the Seiberg-Witten Solution
• Deep Inelastic Scattering from Holographic Spin-One Hadrons
• Universal magnetoresponse in QCD and $\mathcal{N}=4$ SYM
• R-matrix-valued Lax pairs and long-range spin chains
• The Quantum DELL System
• The periodic and open Toda lattice
• S-duality as Fourier transform for arbitrary ${\epsilon }_1,{\epsilon }_2$
• The 10d Uplift of the GPPZ Solution
• Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
• The Supergravity Dual of the BMN Matrix Model
• Quantum Spin Systems and Supersymmetric Gauge Theories, I
• BPS relations from spectral problems and blowup equations
• Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I
• The Vafa-Witten Theory for Gauge Group SU(N)
• T-Branes and $G_2$ Backgrounds
• Branes and integrability in the N=2 SUSY YM theory
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Seiberg-Witten curve via generalized matrix model
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Special Arithmetic of Flavor
• Three-particle Integrable Systems with Elliptic Dependence on Momenta and Theta Function Identities
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• A Small Cosmological Constant, Grand Unification and Warped Geometry
• One-Instanton Test of a Seiberg-Witten Curve from M-theory: the Antisymmetric Representation of SU(N)
• The moduli space of vacua of N=2 class S theories
• Supereigenvalue Model and Dijkgraaf-Vafa Proposal
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint
• Non-Abelian k-Vortex Dynamics in N=1^* theory and its Gravity Dual
• Quantum Elliptic Calogero-Moser Systems from Gauge Origami
• Towards holographic walking from N=4 super Yang-Mills
• Whitham Prepotential and Superpotential
• Quantum geometry from the toroidal block
• A note on the algebraic engineering of 4D $\mathcal{N}=2$ super Yang-Mills theories
• N = 2* Phase Transitions and Holography
• Quantum toroidal algebras and solvable structures in gauge/string theory
• AdS RG-Flow and the Super-Yang-Mills Cascade
• N=2 quiver gauge theories on A-type ALE spaces
• $\mathcal{N}=2^{\ast }$ gauge theory, free fermions on the torus and Painlevé VI
• Seiberg-Witten curves and double-elliptic integrable systems
• Duality in twisted N=4 supersymmetric gauge theories in four dimensions
• N=1* vacua, Fuzzy Spheres and Integrable Systems
• Screening in strongly coupled N=2* supersymmetric Yang-Mills plasma
• Elliptic models and M-theory
• de Sitter Vacua of Strongly Interacting QFT
• Large N, Z_N Strings and Bag Models
• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Maulik-Okounkov's R-matrix from Ding-Iohara-Miki algebra
• Bands and gaps in Nekrasov partition function
• Homological Classification of 4d $\mathcal{N}=2$ QFT. Part I: Rank-1 revisited
• Geometric construction of elliptic integrable systems and N=1^* superpotentials
• Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories
• Modular and duality properties of surface operators in N=2* gauge theories
• Fiber-base duality from the algebraic perspective
• Collapsing hyperkähler manifolds
• Holographic dual of hot Polchinski-Strassler quark-gluon plasma
• Compactifications of the N=2^* flow
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• A geometric recipe for twisted superpotentials
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• Non-Supersymmetric SO(3)-Invariant Deformations of N=1* Vacua and their Dual String Theory Description
• Spectral curves of the hyperelliptic Hitchin systems
• Status Report on the Instanton Counting
• E-string Quantum Curve
• Lax Pairs and Spectral Curves for Calogero-Moser and Spin Calogero-Moser Systems
• Geometric Endoscopy and Mirror Symmetry
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• The N=1* Theories on R^{1+2} X S^1 with Twisted Boundary Conditions
• Exact results for boundaries and domain walls in 2d supersymmetric theories
• String Theory Duals for Mass-deformed SO(N) and USp(2N) N=4 SYM Theories
• Solutions to the reflection equation and integrable systems for N=2 SQCD with classical groups
• Instanton Counting, Quantum Geometry and Algebra
• New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation
• Singular Phases of Seiberg-Witten Integrable Systems: Weak and Strong Coupling
• Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems
• Comment on integrability in Dijkgraaf-Vafa beta-ensembles
• Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces
• Vacuum states of N=1* mass deformations of N=4 and N=2 conformal gauge theories and their brane interpretations
• Integrability, Seiberg-Witten Models and Picard-Fuchs Equations
• Integrable structure in supersymmetric gauge theories with massive hypermultiplets
• Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems
• Rank 2 integrable systems of Prym varieties
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
• Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential
• On Equivalence of two Hurwitz Matrix Models
• The BPS Spectrum Generator In 2d-4d Systems
• Challenges of beta-deformation
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Super instanton counting and localization
• Quantum Integrable Systems from Supergroup Gauge Theories
• Matching branches of non-perturbative conformal block at its singularity divisor
• The Coulomb branch of the Leigh-Strassler deformation and matrix models
• Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories
• Irregular conformal block, spectral curve and flow equations
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Evidence for S-Duality in N=4 Supersymmetric Gauge Theory
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• N=2 gauge theories, instanton moduli spaces and geometric representation 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
• 3d Mirror Symmetry for Instanton Moduli Spaces
• Space-wave function duality and enhanced dKdV on a Riemann surface
• BPS Geodesics in N=2 Supersymmetric Yang-Mills Theory
• Chiral Green's Functions in Superconformal Field Theory
• q-Painleve equation from Virasoro constraints
• Duality in Topological Quantum Field Theories
• Counting the Massive Vacua of N=1* Super Yang-Mills Theory
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Instanton Correction, Wall Crossing And Mirror Symmetry Of Hitchin's Moduli Spaces
• ABCD of qq-characters
• Conformal S-dualities from O-planes
• Two antisymmetric hypermultiplets in N=2 SU(N) gauge theory: Seiberg-Witten curve and M-theory interpretation
• On the WDVV Equation and M-Theory
• Quantum integrability from non-simply laced quiver gauge theory
• G(2)-Calogero-Moser Lax operators from reduction
• On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega Background
• Hyper-symplectic structures on integrable systems
• Toward the Pole
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Combinatorial approach to Mathieu and Lamé equations
• Gauge origami and quiver W-algebras
• $K3$-Fibrations and Softly Broken $N=4$ Supersymmetric Gauge Theories
• The Glueball Superpotential
• Gaugino Condensation and Generation of Supersymmetric 3-Form Flux
• Self-duality of the SL_2 Hitchin integrable system at genus two
• Yang-Mills mass gap, Floer homology, glueball spectrum, and conformal window in large-N QCD
• Check-Operators and Quantum Spectral Curves
• Study of gapped phases of 4d gauge theories using temporal gauging of the ${\mathbb{Z}}_N$ 1-form symmetry
• Higher Toda Mechanics and Spectral Curves
• A Note on Domain Walls and the Parameter Space of N=1 Gauge Theories
• World-sheet Instantons via the Myers Effect and N=1^* Quiver Superpotentials
• A note on S-duality for the N=1* Sp(2n) and SO(2n+1) super-Yang-Mills theories
• A pedagogical introduction to quantum integrability, with a view towards theoretical high-energy physics
• Abelian Projections of the Mass-deformed ABJM theory and Weakly Curved Dual Geometry
• The geometry of the M5-branes and TQFTs
• Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories
• Inozemtsev System as Seiberg-Witten Integrable system
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• Dyon dynamics near marginal stability and non-BPS states
• Quantum Phases of a Vortex String
• Generalized Devil's staircase and RG flows
• A Holographic Kaleidoscope for $\mathcal{N}=1^{\ast }$
• New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
• Modular properties of 6d (DELL) systems
• Holographic Renormalization Group Flows: The View from Ten Dimensions
• Integrability in N=2 Gauge Theory: A Proof
• N=1 G_2 SYM theory and Compactification to Three Dimensions
• On the Geometry of Matrix Models for N=1*
• Intersecting branes, Higgs sector, and chirality from $\mathcal{N}=4$ SYM with soft SUSY breaking
• On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials
• An infrared bootstrap of the Schur index with surface defects
• Partition function of N=2* SYM on a large four-sphere
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• N=2 supersymmetric QCD and elliptic potentials
• WDVV equation and Triple-product Relation
• Special Kaehler manifolds: a survey
• Strings Inside Walls in N=1 Super Yang-Mills
• Dielectric-branes in Non-supersymmetric SO(3)-invariant Perturbation of Three-dimensional N=8 Yang-Mills Theory
• The Phase Structure of Mass-Deformed SU(2)xSU(2) Quiver Theory
• On Effective Superpotentials and Compactification to Three Dimensions
• Generalized Toda mechanics associated with classical Lie algebras and their reductions
• Localization on the D-brane, two-dimensional gauge theory and matrix models
• Brane Configurations of BPS Domain Walls for the N=1^* SU(N) Gauge Theory
• On the moduli spaces of 4d $\mathcal{N}=3$ SCFTs I: triple special Kähler structure
• Non-crystallographic reduction of generalized Calogero-Moser models
• Twisted reduction of quiver W-algebras
• On Confinement Index
• Double Inozemtsev Limits of the Quantum DELL System
• On Phases of Gauge Theories and the Role of Non-BPS Solitons in Field Theory
• Duality and Modularity in Elliptic Integrable Systems and Vacua of N=1* Gauge Theories
• c-map as c=1 string
• Duality Symmetry in Softly Broken N=2 Gauge Theories
• N=2 supersymmetric gauge theories and quantum integrable systems
• Seiberg-Witten Solution from Matrix Theory
• Black hole spectra in holography: consequences for equilibration of dual gauge theories
• Quantum spectral curve for (q,t)-matrix model
• On the N=1* Gauge Theory on a Circle and Elliptic Integrable Systems
• D-Bundles and Integrable Hierarchies
• Seiberg-Witten differential via primitive forms
• Lectures on Higgs moduli and abelianisation
• Masses, Sheets and Rigid SCFTs
• Aspects of Hecke Symmetry: Anomalies, Curves, and Chazy Equations
• Exact quantization conditions for the elliptic Ruijsenaars-Schneider model
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Permutations of Massive Vacua
• Orientifold 4-plane in brane configurations and N=4 USp(2Nc) and SO(Nc) theory
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Solving matrix models using holomorphy
• Effective Gravitational Couplings of Higher-Rank Supersymmetric Gauge Theories
• Tangles, Generalized Reidemeister Moves, and Three-Dimensional Mirror Symmetry
• The Arithmetic of Supersymmetric Vacua
• Seiberg-Witten Monopole Equations And Riemann Surfaces
• Symplectic forms in the theory of solitons
• The Dilaton Potential from N= 1*
• F-Theory, Seiberg-Witten Curves and N = 2 Dualities
• WKB analysis of the linear problem for modified affine Toda field equations
• Inhomogeneous Thermal Quenches
• Instanton Correction of Prepotential in Ruijsenaars Model Associated with N=2 SU(2) Seiberg-Witten Theory
• Seiberg-Witten period relations in Omega background
• Exact beta function from the holographic loop equation of large-N QCD_4
• Meromorphic Higgs bundles And Related Geometries
• Elliptic analog of the Toda lattice
• From solitons to many-body systems
• SQCD, Superconducting Gaps and Cyclic RG Flows
• Flavor symmetries and the topology of special Kähler structures at rank 1
• Holographic duals of the $\mathcal{N}=1$* gauge theory
• A Journey Between Two Curves
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• $A_n^{(1)}$ Toda solitons and the dressing symmetry
• Galois symmetries in Super Yang-Mills Theories
• Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
• Dimers for Type D Relativistic Toda Model
• Comments on fractional instantons in N=2 gauge theories
• Solution of quantum integrable systems from quiver gauge theories
• D-Brane Probes and Mirror Symmetry
• Central charges, S-duality and massive vacua of N=1* super Yang-Mills
• Branes and DAHA Representations
• Prepotential Recursion Relations in N=2 Super-Yang Mills with Adjoint Matter
• An integrable system on the moduli space of rational functions and its variants
• Solitons on Noncommutative Torus as Elliptic Calogero Gaudin Models, Branes and Laughlin Wave Functions
• Wall Crossing Structures and Application to SU(3) Seiberg-Witten Integrable system
• M-Theory Five-brane Wrapped on Curves for Exceptional Groups
• Deformed planar topological open string amplitudes on Seiberg-Witten curve
• Lens space index and global properties for 4d N = 2 models
• New dimer integrable systems and defects in five dimensional gauge theory
• The constraining power of Coulomb Branch Geometry: lectures on Seiberg-Witten theory
• Chiral rings, anomalies and loop equations in N=1* gauge theories
• Twisted Six Dimensional Gauge Theories on Tori, Matrix Models, and Integrable Systems
• Super Yang-Mills Theories with Inhomogeneous Mass Deformations
• Special Kähler geometry and holomorphic Lagrangian fibrations
• Seiberg-Witten Curve for E-String Theory Revisited
• Elliptic Sklyanin integrable systems for arbitrary reductive groups
• Quantum Analytic Langlands Correspondence
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Exact low-energy effective actions for hypermultiplets in four dimensions
• Duality in the Context of Topological Quantum Field Theory
• Superconformal Quantum Mechanics and the Discrete Light-Cone Quantisation of N=4 SUSY Yang-Mills
• Generalized Calogero-Moser system and supergroup gauge origami
• Conformal Affine Toda Soliton and Moduli of IIB Superstring on $Ad{S}_5\times S^5$
• On an integrable deformation of Kapustin-Witten systems
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• Novikov-Veselov Symmetries of the Two-Dimensional $O(N)$ Sigma Model
• Dualities in integrable systems and N=2 theories
• Mixed Hodge structure and $\mathcal{N}=2$ Coulomb branch solution
• Polynomilal Poisson algebras with regular structure of symplectic leaves
• Poisson-Nijenhuis structures on quiver path algebras
• Order Parameters, Free Fermions, and Conservation Laws for Calogero-Moser Systems
• Separation of Variables and Vacuum Structure of N=2 SUSY QCD
• Families of Hitchin systems and N=2 theories
• A stringy perspective on the quantum integrable model/gauge correspondence
• Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
• Representations of the elliptic affine Hecke algebras
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• Semiclassical Entropy of BPS States in 4d $\mathcal{N}=2$ Theories and Counts of Geodesics
• The elliptic Gaudin system with spin
• Hitchin systems on hyperelliptic curves
• On K3-Thurston 7-manifolds and their deformation space: A case study with remarks on general K3T and M-theory compactification
• Global variants of $\mathcal{N}=1^{\ast }$ theories and Calogero-Moser systems
• Bethe/Gauge correspodence: a short review on an aspect of the integrability nature of supersymmetric gauge theories
• Completely (iso-)split scale-invariant Coulomb branch geometries are isotrivial
• Unifying structures in quantum integrable systems
• Frobenius manifolds and algebraic integrability
• Singularity Structure of N=2 Supersymmetric Yang-Mills Theories: A Review
• Comments on BPS Bound State Decay
• Quasinormal Modes of Extremal Reissner-Nordstrom Black Holes via Seiberg-Witten Quantization
• Exact solutions for some sigma models in quantum field theory
• Spectral Networks and Non-abelianization
• The Hitchin Image in Type-D
• Novel wall-crossing behaviour in rank one $\mathcal{N}=2^{\ast }$ gauge theory
• Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case
• Aspects of 4d supersymmetric dynamics and geometry
• Some remarks on special Kähler geometry
• Nonperturbative Recursion Relations in N=2 Supersymmetric Gauge Theories
• Flows of Calogero-Moser Systems
• Testing S-duality conjecture and exceptional bundles