Defects and Quantum Seiberg-Witten Geometry

Abstract

We study the Nekrasov partition function of the five dimensional U(N) gauge theory with maximal supersymmetry on R^4 x S^1 in the presence of codimension two defects. The codimension two defects can be described either as monodromy defects, or by coupling to a certain class of three dimensional quiver gauge theories on R^2 x S^1. We explain how these computations are connected with both classical and quantum integrable systems. We check, as an expansion in the instanton number, that the aforementioned partition functions are eigenfunctions of an elliptic integrable many-body system, which quantizes the Seiberg-Witten geometry of the five-dimensional gauge theory.

89 pages, 8 figures, references added, typos corrected

References in corpus (67)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• Supersymmetric Yang-Mills Systems And Integrable Systems
• SUSY Gauge Theories on Squashed Three-Spheres
• Notes on SUSY Gauge Theories on Three-Sphere
• Supersymmetric vacua and Bethe ansatz
• Elliptic genera of 2d N=2 gauge theories
• The ODE/IM Correspondence
• Quantum integrability and supersymmetric vacua
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Mirror Symmetry in Three-Dimensional Gauge Theories, SL(2,Z) and D-Brane Moduli Spaces
• Bootstrapping the superconformal index with surface defects
• Issues in Topological Gauge Theory
• Holomorphic Blocks in Three Dimensions
• Five Dimensional Gauge Theories and Relativistic Integrable Systems
• Darboux coordinates, Yang-Yang functional, and gauge theory
• Witten Index and Wall Crossing
• 2d Index and Surface operators
• Integrability and Seiberg-Witten Theory: Curves and Periods
• Factorisation of N = 2 theories on the squashed 3-sphere
• Surface Operators in N=2 4d Gauge Theories
• On instantons as Kaluza-Klein modes of M5-branes
• Affine SL(2) conformal blocks from 4d gauge theories
• Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the modular double, and the multiparticle q-deformed Toda chains
• On Three Dimensional Quiver Gauge Theories and Integrability
• Quantum cohomology of flag manifolds and Toda lattices
• Non-Lagrangian Theories from Brane Junctions
• Prepotential and the Seiberg-Witten Theory
• Instanton counting with a surface operator and the chain-saw quiver
• Exact Results for 't Hooft Loops in Gauge Theories on S^4
• Topological strings and 5d T_N partition functions
• Surface Defects and Resolvents
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Algebraic Bethe Ansatz for XYZ Gaudin model
• The Abelian/Nonabelian Correspondence and Frobenius Manifolds
• On Double-Elliptic Integrable Systems. 1. A Duality Argument for the case of SU(2)
• Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories
• From Characters to Quantum (Super)Spin Chains via Fusion
• Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety
• The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory
• An Index Formula for Supersymmetric Quantum Mechanics
• Gauge/Liouville Triality
• The superconformal index and an elliptic algebra of surface defects
• On spectrum of ILW hierarchy in conformal field theory
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin Algebras
• Wilson loops in supersymmetric Chern-Simons-matter theories and duality
• The Curve of Compactified 6D Gauge Theories and Integrable Systems
• Finite difference quantum Toda lattice via equivariant K-theory
• 't Hooft Operators in Gauge Theory from Toda CFT
• Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems
• On spectrum of ILW hierarchy in conformal field theory II: coset CFT's
• Semi-infinite Schubert varieties and quantum K-theory of flag manifolds
• Localization for nonabelian group actions
• Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory
• More lectures on Hilbert schemes of points on surfaces
• Localization of a supersymmetric gauge theory in the presence of a surface defect
• Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda Hierarchy
• Givental J-functions, Quantum integrable systems, AGT relation with surface operator
• Quantum cohomology of flag manifolds G/B and quantum Toda lattices
• Elliptic analog of the Toda lattice
• On some special solutions to periodic Benjamin-Ono equation with discrete Laplacian

Cited by in corpus (94)

• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• The equivariant A-twist and gauged linear sigma models on the two-sphere
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Supersymmetric Casimir Energy and the Anomaly Polynomial
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Line defects and 5d instanton partition functions
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• Baxter Q-operator from quantum K-theory
• Duality walls and defects in 5d N=1 theories
• Hofstadter's Butterfly in Quantum Geometry
• Aspects of Defects in 3d-3d Correspondence
• Central Charges of 2d Superconformal Defects
• A slow review of the AGT correspondence
• Surface defects and instanton-vortex interaction
• A Solvable Deformation of Quantum Mechanics
• Quantization condition from exact WKB for difference equations
• An elliptic Virasoro symmetry in 6d
• Boundaries, Vermas, and Factorisation
• Supersymmetric localization in two dimensions
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• Splitting of surface defect partition functions and integrable systems
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Quantum K theory of symplectic Grassmannians
• Higgsed network calculus
• Wilson loops in 5d $\mathcal{N}=1$ theories and S-duality
• The Quantum DELL System
• $q$-Virasoro modular double and 3d partition functions
• Expanding the Bethe/Gauge Dictionary
• Surface operators, chiral rings, and localization in N=2 gauge theories
• Quantum K-theory of Quiver Varieties and Many-Body Systems
• 6d strings and exceptional instantons
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Mirror theories of 3d $\mathcal{N}=2$ SQCD
• qKZ/tRS Duality via Quantum K-Theoretic Counts
• Surface defects in gauge theory and KZ equation
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• 5d/6d Wilson loops from blowups
• Refined 3d-3d Correspondence
• Modular and duality properties of surface operators in N=2* gauge theories
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• Intersecting Defects and Supergroup Gauge Theory
• 3d Expansions of 5d Instanton Partition Functions
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• On the Quantization of Seiberg-Witten Geometry
• Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs
• Quantum spectral problems and isomonodromic deformations
• Factorisation of 3d $\mathcal{N}=4$ Twisted Indices and the Geometry of Vortex Moduli Space
• BPS Indices, Modularity and Perturbations in Quantum K-theory
• Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories
• Elliptic Quantum Curves of 6d SO(N) theories
• On complete solution of the quantum Dell system
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Orbifolds, Defects and Sphere Partition Function
• A-type Quiver Varieties and ADHM Moduli Spaces
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Surface operators in 5d gauge theories and duality relations
• Cardy Limits of 6d Superconformal Theories
• Blowup Equations for Little Strings
• Asymptotic M5-brane entropy from S-duality
• Dualities for adjoint SQCD in three dimensions and emergent symmetries
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• Gauging and Decoupling in 3d $\mathcal{N}=2$ dualities
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• Modular properties of full 5D SYM partition function
• Double Inozemtsev Limits of the Quantum DELL System
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Supersymmetric Wilson Loops, Instantons, and Deformed $\mathcal{W}$-Algebras
• Exact quantization conditions for the elliptic Ruijsenaars-Schneider model
• Non-stationary difference equation for q-Virasoro conformal blocks
• Quantum K theory rings of partial flag manifolds
• MacMahon KZ equation for Ding-Iohara-Miki algebra
• Spectra of elliptic potentials and supersymmetric gauge theories
• Bootstrapping ADE M-strings
• Decomposition squared
• Topologically Twisted SUSY Gauge Theory, Gauge-Bethe Correspondence and Quantum Cohomology
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Solution of quantum integrable systems from quiver gauge theories
• Branes and DAHA Representations
• Refined Topological Branes
• Self-duality in quantum K-theory
• Complex rational Ruijsenaars model. The two-particle case
• Quantum cohomology from mixed Higgs-Coulomb branches
• Non-Perturbative Schwinger-Dyson Equations for 3d $\mathcal{N}=4$ Gauge Theories
• q-Opers, QQ-systems, and Bethe Ansatz II: Generalized Minors
• A survey of recent developments in GLSMs
• Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• Chiral rings for surface operators in 4d and 5d SQCD
• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials
• Painlevé Kernels and Surface Defects at Strong Coupling