Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings

Abstract

Bethe/Gauge correspondence as it is usually stated is ill-defined in five dimensions and needs a "non-perturbative" completion; a related problem also appears in three dimensions. It has been suggested that this problem, probably due to incompleteness of Omega background regularization in odd dimension, may be solved if we consider gauge theory on compact $S^5$ and $S^3$ geometries. We will develop this idea further by giving a full Bethe/Gauge correspondence dictionary on $S^5$ and $S^3$ focussing mainly on the eigenfunctions of (open and closed) relativistic 2-particle Toda chain and its quantized spectral curve: these are most properly written in terms of non-perturbatively completed NS open topological strings. A key ingredient is Faddeev's modular double structure which is naturally implemented by the $S^5$ and $S^3$ geometries.

arXiv comment53 pages, 7 tables, 7 figures; ver.2: references added

References in corpus (61)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• N=2 dualities
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Topological Strings and Integrable Hierarchies
• SUSY Gauge Theories on Squashed Three-Spheres
• Integrability and Seiberg-Witten Exact Solution
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Discrete Heisenberg-Weyl Group and Modular Group
• Integrable systems and supersymmetric gauge theory
• The complete superconformal index for N=6 Chern-Simons theory
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Holographic Wilson Loops
• Index for three dimensional superconformal field theories with general R-charge assignments
• Disk Instantons, Mirror Symmetry and the Duality Web
• R-Twisting and 4d/2d Correspondences
• Holomorphic Blocks in Three Dimensions
• Five Dimensional Gauge Theories and Relativistic Integrable Systems
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• M5-branes from gauge theories on the 5-sphere
• Gauge Theory Loop Operators and Liouville Theory
• Supersymmetric Gauge Theories on the Five-Sphere
• Quantum Geometry of Refined Topological Strings
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Factorisation of N = 2 theories on the squashed 3-sphere
• Defects and Quantum Seiberg-Witten Geometry
• Twisted supersymmetric 5D Yang-Mills theory and contact geometry
• Generalized Superconformal Index for Three Dimensional Field Theories
• Affine SL(2) conformal blocks from 4d gauge theories
• Painleve III and 2D Polymers
• 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
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Instanton counting with a surface operator and the chain-saw quiver
• Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
• Instantons on the 5-sphere and M5-branes
• Perturbative partition function for a squashed S^5
• New Exact Quantization Condition for Toric Calabi-Yau Geometries
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• Operators from mirror curves and the quantum dilogarithm
• Ising Model and $N=2$ Supersymmetric Theories
• ABJM Wilson Loops in Arbitrary Representations
• Line defects and 5d instanton partition functions
• Exact quantization conditions for the relativistic Toda lattice
• Supersymmetric theories on squashed five-sphere
• The Superconformal Index of the (2,0) Theory with Defects
• Non-Perturbative Quantum Geometry III
• 5d $E_n$ Seiberg-Witten curve via toric-like diagram
• The Ruijsenaars-Schneider Model
• Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• ADHM Revisited: Instantons and Wilson Lines
• Quantization condition from exact WKB for difference equations
• Superconformal Index with Duality Domain Wall
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Exact eigenfunctions and the open topological string
• Non-Perturbative Quantum Geometry II
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• Comments on Exact Quantization Conditions and Non-Perturbative Topological Strings
• Classical limit of irregular blocks and Mathieu functions

Cited by in corpus (11)

• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Operators and higher genus mirror curves
• Resurgence Matches Quantization
• A Solvable Deformation of Quantum Mechanics
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Exact eigenfunctions and the open topological string
• Calabi-Yau geometry and electrons on 2d lattices
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves
• Exact quantization conditions for the elliptic Ruijsenaars-Schneider model
• Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries