Non-Perturbative Quantum Geometry III

Abstract

The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stokes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stokes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.

34 pages; v2: Minor correction and refs added; v3: Table 2 modified, clarifying comment and footnote added

References in corpus (10)

• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Seiberg-Witten Theory and Random Partitions
• Extended Holomorphic Anomaly in Gauge Theory
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Topological Strings and Quantum Spectral Problems
• Non-Perturbative Quantum Geometry III
• Shift versus Extension in Refined Partition Functions
• Non-Perturbative Quantum Geometry II
• The Real Topological String on a local Calabi-Yau
• Lectures on Instanton Counting

Cited by in corpus (22)

• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Hofstadter's Butterfly in Quantum Geometry
• Non-Perturbative Quantum Geometry III
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Splitting of surface defect partition functions and integrable systems
• Calabi-Yau geometry and electrons on 2d lattices
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Bootstrapping Calabi-Yau Quantum Mechanics
• Quantum Seiberg-Witten curve and Universality in Argyres-Douglas theories
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• Exact WKB analysis and TBA equations for the Mathieu equation
• Quantization of Harer-Zagier formulas
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Pure N=2 Super Yang-Mills and Exact WKB
• Resurgence, Painleve Equations and Conformal Blocks
• Quantum Seiberg-Witten periods for $\mathcal{N}=2$ $SU(N_c)$ SQCD around the superconformal point
• On Chebyshev Wells: Periods, Deformations, and Resurgence
• On statistical models on super trees
• Resurgent transseries $\&$ Dyson-Schwinger equations
• Exact Chern-Simons / Topological String duality
• Recent Developments in Topological String Theory