Non-Perturbative Quantum Geometry II

Abstract

The Nekrasov-Shatashvili limit of beta-ensembles with polynomial potential and N=2 supersymmetric gauge theories in the Omega-background is intimately related to complex one-dimensional quantum mechanics. Multi-instanton corrections in quantum mechanics, inferable from exact quantization conditions, imply additional non-perturbative corrections to the Nekrasov-Shatashvili free energies. Besides filling some of the gaps in previous derivations, we present analytic expressions for such additional non-perturbative corrections in the case of SU(2) gauge theory expanded at strong coupling. In contrast, at weak coupling these additional non-perturbative corrections appear to be negligible.

41 pages. v2: minor corrections, refs and remark added

References in corpus (27)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• Topological Strings and Integrable Hierarchies
• Integrability and Seiberg-Witten Exact Solution
• On Geometry and Matrix Models
• Instantons and recursion relations in N=2 Susy gauge theory
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Nonperturbative Effective Actions of N=2 Supersymmetric Gauge Theories
• Gravitational corrections in supersymmetric gauge theory and matrix models
• Quantum Geometry of Refined Topological Strings
• Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
• Non-Perturbative Effects in Matrix Models and Vacua of Two Dimensional Gravity
• On the Relation Between the Holomorphic Prepotential and the Quantum Moduli in SUSY Gauge Theories
• Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations
• Extended Holomorphic Anomaly in Gauge Theory
• Matone's Relation in the Presence of Gravitational Couplings
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Holomorphic matrix models
• Loops versus Matrices - The nonperturbative aspects of noncritical string
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Refined Chern-Simons versus Vogel universality
• Non-Perturbative Quantum Geometry
• Quantum geometry from the toroidal block
• Large N techniques for Nekrasov partition functions and AGT conjecture
• ABCD of Beta Ensembles and Topological Strings
• Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain

Cited by in corpus (20)

• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Matrix models from operators and topological strings, 2
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Exact quantization conditions for the relativistic Toda lattice
• Holomorphic Anomaly and Quantum Mechanics
• Non-Perturbative Quantum Geometry III
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Splitting of surface defect partition functions and integrable systems
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• Quantization of Harer-Zagier formulas
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Resurgence, Painleve Equations and Conformal Blocks
• Quantum Seiberg-Witten periods for $\mathcal{N}=2$ $SU(N_c)$ SQCD around the superconformal point
• On statistical models on super trees
• On Chebyshev Wells: Periods, Deformations, and Resurgence
• Resurgent transseries $\&$ Dyson-Schwinger equations
• Mellin-Barnes Representation of the Topological String