On relation between Nekrasov functions and BS periods in pure SU(N) case

Abstract

We investigate the duality between the Nekrasov function and the quantized Seiberg-Witten prepotential, first guessed in [1] and further elaborated in [2] and [3]. We concentrate on providing more thorough checks than the ones presented in [3] and do not discuss the motivation and historical context of this duality. The check of the conjecture up to $o({\hslash }^6,\ln (\Lambda ))$ is done by hands for arbitrary $N$ (explicit formulas are presented). Moreover, details of the calculation that are essential for the computerization of the check are worked out. This allows us to test the conjecture up to ${\hslash }^6$ and up to higher powers of $\Lambda$ for $N=2,3,4$. Only the case of pure SU(N) gauge theory is considered.

12 pages

References in corpus (33)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• S-duality and 2d Topological QFT
• On AGT relation in the case of U(3)
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On non-conformal limit of the AGT relations
• Asymptotically free N=2 theories and irregular conformal blocks
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Para-Liouville/Toda central charges from M5-branes
• Recursion relations in CFT and N=2 SYM theory
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Recursive representation of the torus 1-point conformal block
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Hitchin systems, N=2 gauge theories and W-gravity
• The Power of Nekrasov Functions
• BGWM as Second Constituent of Complex Matrix Model
• On Combinatorial Expansions of Conformal Blocks
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Proving AGT relations in the large-c limit
• Seiberg-Witten theory and matrix models
• Symplectic invariants, Virasoro constraints and Givental decomposition
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• N=2 gauge theories and degenerate fields of Toda theory
• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
• Coulomb integrals and conformal blocks in the AdS3-WZNW model
• On Crossing Symmmetry and Modular Invariance in Conformal Field Theory and S Duality in Gauge Theory
• On Microscopic Origin of Integrability in Seiberg-Witten Theory
• Matrix models for 2* theories
• From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality
• N=2 Quiver Gauge Model and Partial Supersymmetry Breaking

Cited by in corpus (31)

• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Proving AGT conjecture as HS duality: extension to five dimensions
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Towards a proof of AGT conjecture by methods of matrix models
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Nekrasov prepotential with fundamental matter from the quantum spin chain
• On 3d extensions of AGT relation
• Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble
• A slow review of the AGT correspondence
• RG-Whitham dynamics and complex Hamiltonian systems
• S-duality as a beta-deformed Fourier transform
• N=2 Generalized Superconformal Quiver Gauge Theory
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Quantum Seiberg-Witten curve and Universality in Argyres-Douglas theories
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• Challenges of beta-deformation
• Quantum periods for $\mathcal{N}=2$ $SU(2)$ SQCD around the superconformal point
• Deformed BPS Monopole in Omega-background
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• BPS Monopole Equation in Omega-background
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• Faces of matrix models
• Geometric transitions, double scaling limits and gauge theories