di-Langlands correspondence and extended observables

Abstract

We explore the $\text{difference Langlands correspondence}$ using the four dimensional $\mathcal{N}=2$ super-QCD. Surface defects and surface observables play the crucial role. As an application, we give the first construction of the full set of quantum integrals, i.e. commuting differential operators, such that the partition function of the so-called regular monodromy surface defect is their joint eigenvectors in an evaluation module over the Yangian $Y(\mathfrak{gl}(2))$, making it the wavefunction of a $N$-site $\mathfrak{gl}(2)$ spin chain with bi-infinite spin modules. We construct the $\mathbf{Q}$- and $\tilde{\mathbf{Q}}$-surface observables which are believed to be the $Q$-operators on the bi-infinite module over the Yangian $Y(\mathfrak{gl}(2))$, and compute their eigenvalues, the $Q$-functions, as vevs of the surface observables.

50+11 pages; v2. published version

References in corpus (40)

• N=2 dualities
• Supersymmetric vacua and Bethe ansatz
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Quantum integrability and supersymmetric vacua
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• Darboux coordinates, Yang-Yang functional, and gauge theory
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• A Shortcut to the Q-Operator
• On Three Dimensional Quiver Gauge Theories and Integrability
• Instanton counting with a surface operator and the chain-saw quiver
• Deforming SW curve
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• Nahm Transform For Periodic Monopoles And N=2 Super Yang-Mills Theory
• Quiver W-algebras
• Lectures on Yangian Symmetry
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Spectral Duality in Integrable Systems from AGT Conjecture
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• Quantization of Integrable Systems and a 2d/4d Duality
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Opers, surface defects, and Yang-Yang functional
• Bethe eigenvectors of higher transfer matrices
• Periodic Monopoles With Singularities And N=2 Super-QCD
• Riemann-Hilbert correspondence and blown up surface defects
• BPS States in Omega Background and Integrability
• Discrete Miura Opers and Solutions of the Bethe Ansatz Equations
• Splitting of surface defect partition functions and integrable systems
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• Expanding the Bethe/Gauge Dictionary
• Quantum Spin Systems and Supersymmetric Gauge Theories, I
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
• Quantum Elliptic Calogero-Moser Systems from Gauge Origami
• Center of the quantum affine vertex algebra in type A
• Manin matrices and Talalaev's formula
• Multiplicative Hitchin Systems and Supersymmetric Gauge Theory
• $(SL(N),q)$-opers, the $q$-Langlands correspondence, and quantum/classical duality
• q-Opers, QQ-Systems, and Bethe Ansatz
• Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories
• The Zoo of Opers and Dualities

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• Defects and type D relativistic Toda lattice for some 5d gauge theories
• Dimers for Type D Relativistic Toda Model
• New dimer integrable systems and defects in five dimensional gauge theory