Bootstrapping Calabi-Yau Quantum Mechanics

Abstract

Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau geometries, where the exact quantization conditions have been conjecturally related to topological string theory. We find that the bootstrap method provides a promising alternative for the precision numerical calculations of the energy eigenvalues. An improvement in our approach is to use a larger set of two-dimensional operators instead of one-dimensional ones. We also apply our improved bootstrap methods to some non-relativistic models in the recent literature and demonstrate better numerical accuracies.

21 pages, 21 figures

References in corpus (9)

• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Topological Strings and Quantum Spectral Problems
• Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model
• Numerical Bootstrap in Quantum Mechanics
• Bootstrapping More QM Systems
• Bootstrapping Simple QM Systems
• Introduction to Monte Carlo for Matrix Models
• Large N Optimization for multi-matrix systems
• Exact quantization and analytic continuation

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• ${\varphi }^n$ trajectory bootstrap
• Analytic trajectory bootstrap for matrix models
• Bootstrapping entanglement in quantum spin systems
• Bootstrapping periodic quantum systems
• Bootstrap Method in Theoretical Physics