Non-Perturbative Quantum Geometry

Abstract

The beta-ensemble with cubic potential can be used to study a quantum particle in a double-well potential with symmetry breaking term. The quantum mechanical perturbative energy arises from the ensemble free energy in a novel large N limit. A relation between the generating functions of the exact non-perturbative energy, similar in spirit to the one of Dunne-Unsal, is found. The exact quantization condition of Zinn-Justin and Jentschura is equivalent to the Nekrasov-Shatashvili quantization condition on the level of the ensemble. Refined topological string theory in the Nekrasov-Shatashvili limit arises as a large N limit of quantum mechanics.

20 pages

References in corpus (3)

• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Shift versus Extension in Refined Partition Functions

Cited by in corpus (20)

• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
• Holomorphic Anomaly and Quantum Mechanics
• Non-Perturbative Quantum Geometry III
• Remark on the Dunne-Unsal relation in exact semi-classics
• Resurgence and Holomorphy: From Weak to Strong Coupling
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Non-Perturbative Quantum Geometry II
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Bootstrapping Calabi-Yau Quantum Mechanics
• Quantization of Harer-Zagier formulas
• Resurgence, Painleve Equations and Conformal Blocks
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• On Chebyshev Wells: Periods, Deformations, and Resurgence
• Resurgent transseries $\&$ Dyson-Schwinger equations
• Mellin-Barnes Representation of the Topological String
• Higher-Order Krylov State Complexity in Random Matrix Quenches