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Holomorphic Anomaly and Quantum Mechanics

Submitted to Journal of High Energy Physics. 2016
Description 29
Abstract 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.
arXiv: 1612.07687
Note 29 pages, 5 figures; corrections, comments and references added
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Projects FNS: 200021-156995, 200020-141329
Swiss-NSF NCCR 51NF40-141869
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CODESIDO SANCHEZ, Santiago, MARINO BEIRAS, Marcos. Holomorphic Anomaly and Quantum Mechanics. Submitted to: Journal of High Energy Physics, 2016. https://archive-ouverte.unige.ch/unige:92110

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Deposited on : 2017-02-27

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