Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics

Abstract

We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence.

arXiv comment1 + 34 pages; v2: typos corrected

References in corpus (30)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Supersymmetric Yang-Mills Systems And Integrable Systems
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Integrability and Seiberg-Witten Exact Solution
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Supersymmetric vacua and Bethe ansatz
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• Quantum integrability and supersymmetric vacua
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Quantum Groups and Quantum Cohomology
• Small Instantons, Little Strings and Free Fermions
• Exact Kahler Potential from Gauge Theory and Mirror Symmetry
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• Integrable Structures in Supersymmetric Gauge and String Theory
• Hitchin systems, N=2 gauge theories and W-gravity
• Matone's Relation in the Presence of Gravitational Couplings
• Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory
• On spectrum of ILW hierarchy in conformal field theory
• Open topological strings and integrable hierarchies: Remodeling the A-model
• Instantons and affine algebras I: The Hilbert scheme and vertex operators
• Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories
• The Stringy Instanton Partition Function
• Dubrovin-Zhang hierarchy for the Hodge integrals
• The quantum differential equation of the Hilbert scheme of points in the plane

Cited by in corpus (28)

• Defects and Quantum Seiberg-Witten Geometry
• Ding-Iohara-Miki symmetry of network matrix models
• Explicit examples of DIM constraints for network matrix models
• Relativistic Classical Integrable Tops and Quantum R-matrices
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Anomaly in RTT relation for DIM algebra and network matrix models
• A slow review of the AGT correspondence
• Wilson Loops and Chiral Correlators on Squashed Sphere
• Exact results for $\mathcal{N}=2$ supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
• Elliptic solutions to integrable nonlinear equations and many-body systems
• Supersymmetric localization in two dimensions
• Non-chiral Intermediate Long Wave equation and inter-edge effects in narrow quantum Hall systems
• On spectrum of ILW hierarchy in conformal field theory II: coset CFT's
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• Wilson Loops and Chiral Correlators on Squashed Spheres
• Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Elliptic non-Abelian Donaldson-Thomas invariants of ${\mathbb{C}}^3$
• Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian
• The Condensate from Torus Knots
• The non-chiral intermediate Heisenberg ferromagnet equation
• Givental J-functions, Quantum integrable systems, AGT relation with surface operator
• Note on Nonlinear Schrödinger Equation, KdV Equation and 2D Topological Yang-Mills-Higgs Theory
• Solution of quantum integrable systems from quiver gauge theories
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• On the spectral problem of the quantum KdV hierarchy