Recursion relation for instanton counting for $SU(2)$ $\mathcal{N}=2$ SYM in NS limit of $\Omega$ background

Abstract

In this paper we investigate different ways of deriving the A-cycle period as a series in instanton counting parameter $q$ for $\mathcal{N}=2$ SYM with up to four antifundamental hypermultiplets in NS limit of $\Omega$ background. We propose a new method for calculating the period and demonstrate its efficiency by explicit calculations. The new way of doing instanton counting is more advantageous compared to known standard techniques and allows to reach substantially higher order terms with less effort. This approach is applied for the pure case as well as for the case with several hypermultiplets. We also investigate a numerical method for deriving the $A$-cycle period valid for arbitrary values of $q$. Analyzing large $q$ asymptotic we get convincing agreement with an analytic expression deduced from a conjecture by Alexei Zamolodchikov in a different context.

arXiv comment28 pages, 6 figures, some clarifications and citations added, published version

References in corpus (34)

• 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
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Instantons and recursion relations in N=2 Susy gauge theory
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• The ODE/IM Correspondence
• Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
• Multi-Instanton Calculus and Equivariant Cohomology
• An Algorithm for the Microscopic Evaluation of the Coefficients of the Seiberg-Witten Prepotential
• Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Recursion relations in CFT and N=2 SYM theory
• The Omega deformed B-model for rigid N=2 theories
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Classical Conformal Blocks and Painleve VI
• Matone's Relation in the Presence of Gravitational Couplings
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• On the Thermodynamic Bethe Ansatz Equation in Sinh-Gordon Model
• Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
• Integrability and cycles of deformed $\mathcal{N}=2$ gauge theory
• Recursion representation of the Neveu-Schwarz superconformal block
• Exact WKB Analysis of N = 2 Gauge Theories
• Elliptic recurrence representation of the N=1 superconformal blocks in the Ramond sector
• Bands and gaps in Nekrasov partition function
• 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
• Recurrence relations for the ${\mathcal{W}}_3$ conformal blocks and $\mathcal{N}=2$ SYM partition functions
• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
• Toward the Pole

Cited by in corpus (3)

• CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses
• Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions
• Kerr-Newman quasinormal modes and Seiberg-Witten theory