Exact WKB Analysis of N = 2 Gauge Theories

Abstract

We study N = 2 supersymmetric gauge theories with gauge group SU(2) coupled to fundamental flavours, covering all asymptotically free and conformal cases. We re-derive, from the conformal field theory perspective, the differential equations satisfied by omega deformed instanton partition functions. We confirm their validity at leading order in one of the deformation parameters via a saddle-point analysis of the partition function. In the semi-classical limit we show that these differential equations take a form amenable to exact WKB analysis. We compute the monodromy group associated to the differential equations in terms of deformed and Borel resummed Seiberg-Witten data. For each case, we study pairs of Stokes graphs that are related by flips and pops, and show that the monodromy groups allow one to confirm the Stokes automorphisms that arise as the phase of the deformation parameter is varied. Finally, we relate the Borel resummed monodromies with the traditional Seiberg-Witten variables in the semi-classical limit.

arXiv comment53 pages, 19 figures

References in corpus (29)

• 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
• N=2 dualities
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Solutions Of Four-Dimensional Field Theories Via M Theory
• 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
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• Non-perturbative effects and the refined topological string
• Spectral networks
• Gauge Theory Loop Operators and Liouville Theory
• Irregular singularities in Liouville theory
• On AGT conjecture
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• The toroidal block and the genus expansion
• Transformations of Spherical Blocks
• Deformed Seiberg-Witten Curves for ADE Quivers
• Mathieu equation and Elliptic curve
• Quantum geometry from the toroidal block
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations
• Non-perturbative studies of N=2 conformal quiver gauge theories

Cited by in corpus (26)

• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Holomorphic Anomaly and Quantum Mechanics
• Resurgence in $\eta$-deformed Principal Chiral Models
• A slow review of the AGT correspondence
• On exact-WKB analysis, resurgent structure, and quantization conditions
• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Exact-WKB analysis for SUSY and quantum deformed potentials: Quantum mechanics with Grassmann fields and Wess-Zumino terms
• Accessory parameters in confluent Heun equations and classical irregular conformal blocks
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• Discrete Painleve system for the partition function of $N_f=2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
• Exact WKB analysis for $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics: Study of the Ai-Bender-Sarkar conjecture
• The Exact WKB analysis and the Stokes phenomena of the Unruh effect and Hawking radiation
• Resurgence, Painleve Equations and Conformal Blocks
• Recursion relation for instanton counting for $SU(2)$ $\mathcal{N}=2$ SYM in NS limit of $\Omega$ background
• Quantum Seiberg-Witten periods for $\mathcal{N}=2$ $SU(N_c)$ SQCD around the superconformal point
• On Chebyshev Wells: Periods, Deformations, and Resurgence
• Quantum Hamilton-Jacobi Theory, Spectral Path Integrals and Exact-WKB Analysis
• Non-perturbative particle production and differential geometry
• Exact WKB in all sectors I: Potentials with degenerate saddles
• Nonperturbative Formulation of Resonances in Quantum Mechanics Based on Exact WKB Method
• Exact-WKB Analysis of Two-level Floquet Systems
• A duality of the classical action yields a reflection symmetry of the quantum energy spectrum
• Exact WKB in all sectors II: Potentials with non-degenerate saddles