Instanton counting on blowup. I. 4-dimensional pure gauge theory

Abstract

We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on ${\mathbb{R}}^4$ gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY Yang-Mills theory. Through a study of moduli spaces on the blowup of ${\mathbb{R}}^4$, we derive a differential equation for the Nekrasov's partition function. It is a deformation of the equation for the Seiberg-Witten prepotential, found by Losev et al., and further studied by Gorsky et al.

Title is changed. Introduction is expanded. A section on Seiberg-Witten prepotential is added. Accepted for publication in Invent. Math

References in corpus (1)

• Multi-Instanton Calculus and Equivariant Cohomology

Cited by in corpus (150)

• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• M-Strings
• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• Refined Topological Vertex and Instanton Counting
• Affine SL(2) conformal blocks from 4d gauge theories
• The affine Yangian of ${\mathfrak{gl}}_1$ revisited
• The Quiver Matrix Model and 2d-4d Conformal Connection
• The elliptic Hall algebra and the equivariant K-theory of the Hilbert scheme of ${\mathbb{A}}^2$
• The Omega deformed B-model for rigid N=2 theories
• Quantum Algebraic Approach to Refined Topological Vertex
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• Five-dimensional AGT Relation and the Deformed beta-ensemble
• Non-Lagrangian Theories from Brane Junctions
• Coulomb Branch and The Moduli Space of Instantons
• Explicit examples of DIM constraints for network matrix models
• Instanton moduli spaces and bases in coset conformal field theory
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Instantons on ALE spaces and Super Liouville Conformal Field Theories
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Two-point Correlators in N=2 Gauge Theories
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Instantons and 2d Superconformal field theory
• Highest Weight Generating Functions for Hilbert Series
• Hilbert Series for Moduli Spaces of Two Instantons
• On AGT Conjecture for Pure Super Yang-Mills and W-algebra
• Counting Exceptional Instantons
• Bilinear equations on Painleve tau functions from CFT
• On Exceptional Instanton Strings
• Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• The Nekrasov Conjecture for Toric Surfaces
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Changing the preferred direction of the refined topological vertex
• Blowup Equations for 6d SCFTs. I
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• Bootstrapping BPS spectra of 5d/6d field theories
• Quiver Matrix Model and Topological Partition Function in Six Dimensions
• Blowup Equations for Refined Topological Strings
• Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
• Self-Duality and Self-Similarity of Little String Orbifolds
• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Virtual refinements of the Vafa-Witten formula
• Riemann-Hilbert correspondence and blown up surface defects
• A Combinatorial Study on Quiver Varieties
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• 4d $\mathcal{N}=3$ indices via discrete gauging
• Analyticity of Nekrasov Partition Functions
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Perverse coherent sheaves on blow-up. III. Blow-up formula from wall-crossing
• 2-parameter $\tau$-function for the first Painlevé equation -Topological recursion and direct monodromy problem via exact WKB analysis-
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
• Self-dual Strings and 2D SYM
• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Instantons from Blow-up
• Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces
• BPS relations from spectral problems and blowup equations
• Painleve equations from Nakajima-Yoshioka blowup relations
• Instanton on toric singularities and black hole countings
• $\mathcal{N}=2^{\ast }$ gauge theory, free fermions on the torus and Painlevé VI
• N=2 quiver gauge theories on A-type ALE spaces
• 5d/6d Wilson loops from blowups
• More on topological vertex formalism for 5-brane webs with O5-plane
• Numerical Analyses on Moduli Space of Vacua
• Fiber-base duality from the algebraic perspective
• Monads for framed torsion-free sheaves on multi-blow-ups of the projective plane
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Discrete Painleve system for the partition function of $N_f=2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
• Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations
• On the Jeffrey-Kirwan residue of BCD-instantons
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• Quantum spectral problems and isomonodromic deformations
• Construction and Deconstruction of Single Instanton Hilbert Series
• M5 branes and Theta Functions
• Partition functions of web diagrams with an O7${}^{-}$-plane
• Exact results in N=2 gauge theories
• Instantons to the people: the power of one-form symmetries
• A Macdonald refined topological vertex
• Tetrahedron instantons
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Playing with the index of M-theory
• Refined topological vertex with ON-planes
• Topological strings and Wilson loops
• Recursive Method for Nekrasov partition function for classical Lie groups
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Equivariant volumes of non-compact quotients and instanton counting
• Expansions for semiclassical conformal blocks
• A Nekrasov-Okounkov formula for Macdonald polynomials
• Gauge origami and quiver W-algebras
• Seiberg-Witten curves with O7${}^{\pm }$-planes
• Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case
• Irregular conformal blocks, Painlevé III and the blow-up equations
• Whittaker vectors for $\mathcal{W}$-algebras from topological recursion
• Blowup Equations for Little Strings
• $t{t}^{\ast }$ Toda equations for surface defects in $\mathcal{N}=2$ SYM and instanton counting for classical Lie groups
• Noncommutative Instantons in Diverse Dimensions
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• Thermodynamic limit of the Nekrasov-type formula for E-string theory
• Affine Laumon spaces and iterated W-algebras
• Combinatorial realizations of crystals via torus actions on quiver varieties
• Integrable structure of melting crystal model with two q-parameters
• Moduli space of logarithmic states in critical massive gravities
• Unitary matrix with a Penner-like potential also yields N_f=2
• Parallel surface defects, Hecke operators, and quantum Hitchin system
• An(1) Affine Quiver Matrix Model
• Superconformal Quantum Mechanics on Kähler Cones
• S-duality and supersymmetry on curved manifolds
• From topological strings to minimal models
• $DE$-type little strings from glued brane webs
• Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N}=2$ theories
• Symmetric Orbifold Theories from Little String Residues
• $E_8$ spectral curves
• Moduli spaces of framed sheaves and quiver varieties
• MacMahon KZ equation for Ding-Iohara-Miki algebra
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• A Klein TQFT: the local Real Gromov-Witten theory of curves
• Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
• Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties
• Quasi-Hopf twist and elliptic Nekrasov factor
• Five-dimensional gauge theories and the local B-model
• Aspects of the moduli space of instantons on $\mathbb{C}{P}^2$ and its orbifolds
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories
• Restriction theorems for $\mu$-(semi)stable framed sheaves
• Towards a gauge theory interpretation of the real topological string
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• Topological Field Theory Amplitudes for $A_{N-1}$ Fibration
• Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves
• Recurrence relation for instanton partition function in SU(N) gauge theory
• Wall-crossing for vortex partition function and handsaw quiver varierty
• On the fixed locus of framed instanton sheaves on ${\mathbb{P}}^3$
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• On a 5D UV completion of Argyres-Douglas theories
• On palindromic numerators of bigraded symmetric orbifold Hilbert series and Kostka-Foulkes polynomials
• Comments on the Nekrasov-type formula for E-string theory
• Effective Gravitational Couplings of Kaluza-Klein Gauge Theories
• $\mathrm{Sp}(1)$-symmetric hyperkähler quantisation
• On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations
• $K$-theoretic wall-crossing formulas and multiple basic hypergeometric series
• Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory
• Highest-weight vectors and three-point functions in GKO coset decomposition