Holomorphic Anomaly and Quantum Mechanics

Autor:	Codesido, Santiago, Marino, Marcos
Rok vydání:	2016
Předmět:	High Energy Physics - Theory Mathematical Physics
Zdroj:	Journal of Physics A: Mathematical and Theoretical, 51 (5) 055402, 2018
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8121/aa9e77
Popis:	We show that the all-orders WKB periods of one-dimensional quantum mechanical oscillators are governed by the refined holomorphic anomaly equations of topological string theory. We analyze in detail the double-well potential and the cubic and quartic oscillators, and we calculate the WKB expansion of their quantum free energies by using the direct integration of the anomaly equations. We reproduce in this way all known results about the quantum periods of these models, which we express in terms of modular forms on the WKB curve. As an application of our results, we study the large order behavior of the WKB expansion in the case of the double well, which displays the double factorial growth typical of string theory. Comment: 30 pages, 5 figures; comments and references added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1612.07687 Zobrazit plný text záznamu View this record from Arxiv