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 (12)

• Notes on SUSY Gauge Theories on Three-Sphere
• The ODE/IM Correspondence
• Witten Index and Wall Crossing
• Instanton counting with a surface operator and the chain-saw quiver
• 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
• An Index Formula for Supersymmetric Quantum Mechanics
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• Wilson loops in supersymmetric Chern-Simons-matter theories and duality
• On spectrum of ILW hierarchy in conformal field theory II: coset CFT's
• Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory
• Localization of a supersymmetric gauge theory in the presence of a surface defect

Cited by in corpus (40)

• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• Duality walls and defects in 5d N=1 theories
• Hofstadter's Butterfly in Quantum Geometry
• Boundaries, Vermas, and Factorisation
• Surface operators, chiral rings, and localization in N=2 gauge theories
• Expanding the Bethe/Gauge Dictionary
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• 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
• Intersecting Defects and Supergroup Gauge Theory
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs
• Quantum spectral problems and isomonodromic deformations
• Elliptic Quantum Curves of 6d SO(N) theories
• BPS Indices, Modularity and Perturbations in Quantum K-theory
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Blowup Equations for Little Strings
• Dualities for adjoint SQCD in three dimensions and emergent symmetries
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• Double Inozemtsev Limits of the Quantum DELL System
• MacMahon KZ equation for Ding-Iohara-Miki algebra
• Non-stationary difference equation for q-Virasoro conformal blocks
• Quantum K theory rings of partial flag manifolds
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Bootstrapping ADE M-strings
• Self-duality in quantum K-theory
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Decomposition squared
• Branes and DAHA Representations
• Quantum cohomology from mixed Higgs-Coulomb branches
• Complex rational Ruijsenaars model. The two-particle case
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials
• q-Opers, QQ-systems, and Bethe Ansatz II: Generalized Minors
• A survey of recent developments in GLSMs
• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials
• Painlevé Kernels and Surface Defects at Strong Coupling