On the resurgent structure of quantum periods

Gu, Jie; Mariño, Marcos

doi:10.21468/SciPostPhys.15.1.035

SciPost Physics

On the resurgent structure of quantum periods

Jie Gu, Marcos Mariño

SciPost Phys. 15, 035 (2023) · published 28 July 2023

doi: 10.21468/SciPostPhys.15.1.035
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Abstract

Quantum periods appear in many contexts, from quantum mechanics to local mirror symmetry. They can be described in terms of topological string free energies and Wilson loops, in the so-called Nekrasov-Shatashvili limit. We consider the trans-series extension of the holomorphic anomaly equations satisfied by these quantities, and we obtain exact multi-instanton solutions for these trans-series. Building on this result, we propose a unified perspective on the resurgent structure of quantum periods. We show for example that the Delabaere-Pham formula, which was originally obtained in quantum mechanical examples, is a generic feature of quantum periods. We illustrate our general results with explicit calculations for the double-well in quantum mechanics, and for the quantum mirror curve of local $\mathbb{P}^2$.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.1.035
TI  - On the resurgent structure of quantum periods
PY  - 2023/07/28
UR  - https://www.scipost.org/SciPostPhys.15.1.035
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 1
SP  - 035
A1  - Gu, Jie
AU  - Mariño, Marcos
AB  - Quantum periods appear in many contexts, from quantum mechanics to local mirror symmetry. They can be described in terms of topological string free energies and Wilson loops, in the so-called Nekrasov-Shatashvili limit. We consider the trans-series extension of the holomorphic anomaly equations satisfied by these quantities, and we obtain exact multi-instanton solutions for these trans-series. Building on this result, we propose a unified perspective on the resurgent structure of quantum periods. We show for example that the Delabaere-Pham formula, which was originally obtained in quantum mechanical examples, is a generic feature of quantum periods. We illustrate our general results with explicit calculations for the double-well in quantum mechanics, and for the quantum mirror curve of local $\mathbb{P}^2$.
ER  -

@Article{10.21468/SciPostPhys.15.1.035,
	title={{On the resurgent structure of quantum periods}},
	author={Jie Gu and Marcos Mariño},
	journal={SciPost Phys.},
	volume={15},
	pages={035},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.1.035},
	url={https://scipost.org/10.21468/SciPostPhys.15.1.035},
}

Cited by 7

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¹ Jie Gu,
² Marcos Mariño

Funders for the research work leading to this publication