Supersymmetric vacua and Bethe ansatz

Abstract

An announcement of some results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. The Heisenberg spin chain is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model are related to the four dimensional theory compactified on a torus. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains such as the Hubbard model. Compactifications of four dimensional N=2 theories on a two-sphere lead to the instanton-corrected Bethe equations. We propose a completely novel way for the Yangian, quantum affine, and elliptic algebras to act as a symmetry of a union of quantum field theories. This paper accompanies arXiv:0901.4748

35 pages, short version I, Cargese and Landau-100 conferences proceedings; v2. typos and refs corrected

References in corpus (3)

• Quantum integrability and supersymmetric vacua
• Higgs Bundles, Gauge Theories and Quantum Groups
• Algebraic representation of correlation functions in integrable spin chains

Cited by in corpus (254)

• Review of AdS/CFT Integrability: An Overview
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Quantum integrability and supersymmetric vacua
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• Y-system for Scattering Amplitudes
• Holomorphic Blocks in Three Dimensions
• Darboux coordinates, Yang-Yang functional, and gauge theory
• Comments on twisted indices in 3d supersymmetric gauge theories
• Quantum Geometry of Refined Topological Strings
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Defects and Quantum Seiberg-Witten Geometry
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• A & B model approaches to surface operators and Toda theories
• Gauge Theory and Integrability, II
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• On Three Dimensional Quiver Gauge Theories and Integrability
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Gauge Theory and Integrability, I
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Baxter's Relations and Spectra of Quantum Integrable Models
• Supersymmetric partition functions and the three-dimensional A-twist
• A direct proof of AGT conjecture at beta = 1
• The equivariant A-twist and gauged linear sigma models on the two-sphere
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Lectures on AdS Black Holes, Holography and Localization
• Surface Defects and Resolvents
• String theory of the Omega deformation
• Bethe/Gauge correspondence on curved spaces
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Topologically twisted indices in five dimensions and holography
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• 5d Partition Functions with A Twist
• Factorisation and holomorphic blocks in 4d
• Line operators on S^1xR^3 and quantization of the Hitchin moduli space
• On one-point functions for sinh-Gordon model at finite temperature
• 3-Manifolds and 3d Indices
• Quantization of Integrable Systems and a 2d/4d Duality
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Quivers, YBE and 3-manifolds
• Towards a proof of AGT conjecture by methods of matrix models
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Opers, surface defects, and Yang-Yang functional
• Relativistic Classical Integrable Tops and Quantum R-matrices
• Quantum Integrability and Generalised Quantum Schubert Calculus
• Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants
• Worldsheet Realization of the Refined Topological String
• Baxter Q-operator from quantum K-theory
• Gauge/Liouville Triality
• Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory
• On the L^2-metric of vortex moduli spaces
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• Relating Gauge Theories via Gauge/Bethe Correspondence
• Partition functions on 3d circle bundles and their gravity duals
• Gauge Theories Labelled by Three-Manifolds
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• A slow review of the AGT correspondence
• Magnetic expansion of Nekrasov theory: the SU(2) pure gauge theory
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• Blowup Equations for Refined Topological Strings
• N=2 Generalized Superconformal Quiver Gauge Theory
• 3d-3d Correspondence Revisited
• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Orientifolds and the Refined Topological String
• New Integrable Models from the Gauge/YBE Correspondence
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• From 3d duality to 2d duality
• Matrix models for 2* theories
• BPS States in Omega Background and Integrability
• ADE Little String Theory on a Riemann Surface (and Triality)
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Topological Holography: The Example of The D2-D4 Brane System
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Deformed supersymmetric gauge theories from the fluxtrap background
• A 5d/3d duality from relativistic integrable system
• Gauge/Bethe correspondence from quiver BPS algebras
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Splitting of surface defect partition functions and integrable systems
• Liouville theory, N=2 gauge theories and accessory parameters
• Quantum K theory of symplectic Grassmannians
• G/G gauged WZW model and Bethe Ansatz for the phase model
• Geometric Algebra and Algebraic Geometry of Loop and Potts Models
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Quiver gauge theories and integrable lattice models
• R-matrix-valued Lax pairs and long-range spin chains
• 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
• A search for AdS5 X S2 IIB supergravity solutions dual to N = 2 SCFTs
• Trisecting non-Lagrangian theories
• Integrability from 2d N=(2,2) Dualities
• Quantum toroidal gl(1) and Bethe ansatz
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• Quantum Spin Systems and Supersymmetric Gauge Theories, I
• Superspin chains from superstring theory
• Equivariant Verlinde formula from fivebranes and vortices
• BPS/CFT correspondence V: BPZ and KZ equations from qq-characters
• Superspin chains and supersymmetric gauge theories
• qKZ/tRS Duality via Quantum K-Theoretic Counts
• On spectrum of ILW hierarchy in conformal field theory II: coset CFT's
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• Quantum toroidal algebras and solvable structures in gauge/string theory
• XXZ scalar products and KP
• On Three-Dimensional Quiver Gauge Theories of Type B
• Large-N ground state of the Lieb-Liniger model and Yang-Mills theory on a two-sphere
• Network, Cluster coordinates and N=2 theory I
• G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra
• Mirror Symmetry in Three Dimensions via Gauged Linear Quivers
• TBA for non-perturbative moduli spaces
• $(SL(N),q)$-opers, the $q$-Langlands correspondence, and quantum/classical duality
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Bands and gaps in Nekrasov partition function
• Alpha- and Omega-Deformations from fluxes in M-Theory
• Holonomy Saddles and Supersymmetry
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• A-twisted correlators and Hori dualities
• The joy of factorization at large $N$: five-dimensional indices and AdS black holes
• Supersymmetric Partition Functions and a String Theory in 4 Dimensions
• Intersecting Defects and Supergroup Gauge Theory
• Exact results for boundaries and domain walls in 2d supersymmetric theories
• Quantum K-Theory of Calabi-Yau Manifolds
• Wilson loop algebras and quantum K-theory for Grassmannians
• Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• Classical limit of irregular blocks and Mathieu functions
• The Gauge-Bethe Correspondence and Geometric Representation Theory
• 't Hooft lines of ADE-type and Topological Quivers
• Topologically twisted index of $T[SU(N)]$ at large $N$
• Integrable lattice spin models from supersymmetric dualities
• Integrability and duality in spin chains
• BPS Indices, Modularity and Perturbations in Quantum K-theory
• Twisted indices, Bethe ideals and 3d $\mathcal{N}=2$ infrared dualities
• Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Exact results in N=2 gauge theories
• On a singular Fredholm-type integral equation arising in N=2 super Yang-Mills theories
• 3d Mirror Symmetry for Instanton Moduli Spaces
• A-type Quiver Varieties and ADHM Moduli Spaces
• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Elliptic modular double and 4d partition functions
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Seiberg-Witten geometry of four-dimensional N=2 SO-USp quiver gauge theories, I
• Correlators on the wall and ${\mathfrak{sl}}_n$ spin chain
• Supersymmetric quiver gauge theories on the lattice
• From multi-gravitons to Black holes: The role of complex saddles
• Twisted Masses and Enhanced Symmetries: the A&D Series
• On Phases of 3d $\mathcal{N}=2$ Chern-Simons-Matter Theories
• Toroidal q-Opers
• Residue mirror symmetry for Grassmannians
• Combinatorial approach to Mathieu and Lamé equations
• Equivariant quantum cohomology and Yang-Baxter algebras
• Characters of tangent spaces at torus fixed points and $3d$-mirror symmetry
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• 3d N=2 Chern-Simons-matter theory, Bethe ansatz, and quantum K-theory of Grassmannians
• Bethe-State Counting and the Witten Index
• Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains
• Advances in R-matrices and their applications (after Maulik-Okounkov, Kang-Kashiwara-Kim-Oh,...)
• Nested coordinate Bethe wavefunctions from the Bethe/gauge correspondence
• BPS states in the Omega-background and torus knots
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• More on Affine Dynkin Quiver Yangians
• A pedagogical introduction to quantum integrability, with a view towards theoretical high-energy physics
• Spin-$s$ Rational $Q$-system
• Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence
• Embedding Integrable Superspin Chain in String Theory
• RG limit cycles
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• di-Langlands correspondence and extended observables
• Faces of matrix models
• N=2 supersymmetric QCD and elliptic potentials
• Parallel surface defects, Hecke operators, and quantum Hitchin system
• Algorithms for representations of quiver Yangian algebras
• Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N}=2$ theories
• Composite Non-Abelian Strings with Grassmannian Models on the World Sheet
• New differential equations in the six-vertex model
• Givental J-functions, Quantum integrable systems, AGT relation with surface operator
• Gravity Dual of Two-Dimensional $\mathcal{N}=(2,2{)}^{\ast }$ Supersymmetric Yang-Mills Theory and Integrable Models
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
• Dynamics of Two-Dimensional $\mathcal{N}=(2,2)$ Supersymmetric Theories with Semichiral Superfields I
• Surface defects and instanton partition functions
• Bethe/Gauge Correspondence for linear quiver theories with ABCD gauge symmetry and spin chains
• Quantum K theory rings of partial flag manifolds
• Engineering 3D $\mathcal{N}=2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra
• Moduli Spaces of Abelian Vortices on Kahler Manifolds
• Spectra of elliptic potentials and supersymmetric gauge theories
• Towards the theory of Yangians
• Higher spin sl_2 R-matrix from equivariant (co)homology
• The Zoo of Opers and Dualities
• Differential approach to on-shell scalar products in six-vertex models
• Bethe/Gauge Correspondence for ABCDEFG-type 3d Gauge Theories
• A Family of Vertex Algebras from Argyres-Douglas Theory
• Gauge/Bethe correspondence on $S^1\times {\Sigma }_h$ and index over moduli space
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Defects and type D relativistic Toda lattice for some 5d gauge theories
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Decomposition squared
• General Composite Non-Abelian Strings and Flag Manifold Sigma Models
• Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles
• Solution of quantum integrable systems from quiver gauge theories
• Integrability As Duality: The Gauge/YBE Correspondence
• New dimer integrable systems and defects in five dimensional gauge theory
• Topologically Twisted SUSY Gauge Theory, Gauge-Bethe Correspondence and Quantum Cohomology
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows
• An Overview of Crystals and Double Quiver Yangians
• ${\text{AdS}}_4$ Holography and the Hilbert Scheme
• Generalized Calogero-Moser system and supergroup gauge origami
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals
• 3D-3D Correspondence from Seifert Fibering Operators
• On the planar limit of 3d $T_{\rho }^{\sigma }[SU(N)]$
• On a path integral representation of the Nekrasov instanton partition function and its Nekrasov--Shatashvili limit
• Poisson sigma model and semiclassical quantization of integrable systems
• Supersymmetric Localization in GLSMs for Supermanifolds
• Chiral rings for surface operators in 4d and 5d SQCD
• Counting Bethe States in Twisted Spin Chains
• Higher rank elliptic partition functions and multisymmetric elliptic functions
• A class of partition functions associated with $E_{\tau ,\eta }(g{l}_3)$ by Izergin-Korepin analysis
• Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials
• A stringy perspective on the quantum integrable model/gauge correspondence
• On Wronskians and $qq$-systems
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• A survey of recent developments in GLSMs
• Supersymmetric Grassmannian Sigma Models in Gross-Neveu Formalism
• Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence
• Difference Equations: from Berry Connections to the Coulomb Branch
• $\beta$-function of the level-zero Gross-Neveu model
• Quantum K-theory and Integrability
• Bethe/Gauge correspodence: a short review on an aspect of the integrability nature of supersymmetric gauge theories
• An update of quantum cohomology of homogeneous varieties
• Virtual Coulomb branch and vertex functions
• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials
• SUSY localization for Coulomb branch operators in omega-deformed 3d N=4 gauge theories
• Mass deformed world-sheet action of semi-local vortices
• Global variants of $\mathcal{N}=1^{\ast }$ theories and Calogero-Moser systems