Deforming SW curve

Abstract

A system of Bethe-Ansatz type equations, which specify a unique array of Young tableau responsible for the leading contribution to the Nekrasov partition function in the ${\epsilon }_2\to 0$ limit is derived. It is shown that the prepotential with generic ${\epsilon }_1$ is directly related to the (rescaled by ${\epsilon }_1$) number of total boxes of these Young tableau. Moreover, all the expectation values of the chiral fields $\langle \tr ϕ^J \rangle $ are simple symmetric functions of their column lengths. An entire function whose zeros are determined by the column lengths is introduced. It is shown that this function satisfies a functional equation, closely resembling Baxter's equation in 2d integrable models. This functional relation directly leads to a nice generalization of the equation defining Seiberg-Witten curve.

14 pages

References in corpus (10)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Instantons and recursion relations in N=2 Susy gauge theory
• Integrating Over Higgs Branches
• An Algorithm for the Microscopic Evaluation of the Coefficients of the Seiberg-Witten Prepotential
• Small Instantons, Little Strings and Free Fermions
• Matone's Relation in the Presence of Gravitational Couplings
• Testing Seiberg-Witten Solution

Cited by in corpus (71)

• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Vertices, Vortices & Interacting Surface Operators
• QNMs of branes, BHs and fuzzballs from Quantum SW geometries
• Topological Strings and Quantum Spectral Problems
• CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Quantization of Integrable Systems and a 2d/4d Duality
• Deformed N=2 theories, generalized recursion relations and S-duality
• A New 2d/4d Duality via Integrability
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• 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
• Instanton effects and quantum spectral curves
• On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit
• A slow review of the AGT correspondence
• RG-Whitham dynamics and complex Hamiltonian systems
• Wilson Loops and Chiral Correlators on Squashed Sphere
• A Solvable Deformation of Quantum Mechanics
• Deformed Seiberg-Witten Curves for ADE Quivers
• Exact WKB Analysis of N = 2 Gauge Theories
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Liouville theory, N=2 gauge theories and accessory parameters
• Generalized matrix models and AGT correspondence at all genera
• Refined geometric transition and $qq$-characters
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• BPS/CFT correspondence V: BPZ and KZ equations from qq-characters
• Quantum geometry from the toroidal block
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• On the monodromy problem for the four-punctured sphere
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Bands and gaps in Nekrasov partition function
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• Confinement and Mayer cluster expansions
• Classical limit of irregular blocks and Mathieu functions
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Wilson Loops and Chiral Correlators on Squashed Spheres
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• Exact results in N=2 gauge theories
• Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• On a singular Fredholm-type integral equation arising in N=2 super Yang-Mills theories
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• $T$, $Q$ and periods in $SU(3)$ $\mathcal{N}=2$ SYM
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Deformed BPS Monopole in Omega-background
• Quantum integrability from non-simply laced quiver gauge theory
• Recursion relation for instanton counting for $SU(2)$ $\mathcal{N}=2$ SYM in NS limit of $\Omega$ background
• Recurrence relations for the ${\mathcal{W}}_3$ conformal blocks and $\mathcal{N}=2$ SYM partition functions
• Notes on Mayer Expansions and Matrix Models
• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• BPS Monopole Equation in Omega-background
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Parallel surface defects, Hecke operators, and quantum Hitchin system
• di-Langlands correspondence and extended observables
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• More on the SW-QNM correspondence
• Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
• Seiberg-Witten period relations in Omega background
• Deformed planar topological open string amplitudes on Seiberg-Witten curve
• On a path integral representation of the Nekrasov instanton partition function and its Nekrasov--Shatashvili limit
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• Deformed SW curve and the null vector decoupling equation in Toda field theory
• VEV of $Q$-operator in $U(1)$ linear quiver 5d gauge theories
• On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain