Exact multi-instantons in topological string theory

Gu, Jie; Mariño, Marcos

doi:10.21468/SciPostPhys.15.4.179

SciPost Physics

Exact multi-instantons in topological string theory

Jie Gu, Marcos Mariño

SciPost Phys. 15, 179 (2023) · published 26 October 2023

doi: 10.21468/SciPostPhys.15.4.179
pdf
Submissions/Reports

Abstract

Topological string theory has multi-instanton sectors which lead to non-perturbative effects in the string coupling constant and control the large order behavior of the perturbative genus expansion. As proposed by Couso, Edelstein, Schiappa and Vonk, these sectors can be described by a trans-series extension of the BCOV holomorphic anomaly equations. In this paper we find exact, closed form solutions for these multi-instanton trans-series in the case of local Calabi-Yau manifolds. The resulting multi-instanton amplitudes turn out to be very similar to the eigenvalue tunneling amplitudes of matrix models. Their form suggests that the flat coordinates of the Calabi-Yau manifold are naturally quantized in units of the string coupling constant, as postulated in large $N$ dualities. Based on our results we obtain a general picture for the resurgent structure of the topological string in the local case, which we illustrate with explicit calculations for local $\mathbb{P}^2$.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.4.179
TI  - Exact multi-instantons in topological string theory
PY  - 2023/10/26
UR  - https://scipost.org/SciPostPhys.15.4.179
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 4
SP  - 179
A1  - Gu, Jie
AU  - Mariño, Marcos
AB  - Topological string theory has multi-instanton sectors which lead to non-perturbative effects in the string coupling constant and control the large order behavior of the perturbative genus expansion. As proposed by Couso, Edelstein, Schiappa and Vonk, these sectors can be described by a trans-series extension of the BCOV holomorphic anomaly equations. In this paper we find exact, closed form solutions for these multi-instanton trans-series in the case of local Calabi-Yau manifolds. The resulting multi-instanton amplitudes turn out to be very similar to the eigenvalue tunneling amplitudes of matrix models. Their form suggests that the flat coordinates of the Calabi-Yau manifold are naturally quantized in units of the string coupling constant, as postulated in large $N$ dualities. Based on our results we obtain a general picture for the resurgent structure of the topological string in the local case, which we illustrate with explicit calculations for local $\mathbb{P}^2$.
ER  -

@Article{10.21468/SciPostPhys.15.4.179,
	title={{Exact multi-instantons in topological string theory}},
	author={Jie Gu and Marcos Mariño},
	journal={SciPost Phys.},
	volume={15},
	pages={179},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.4.179},
	url={https://scipost.org/10.21468/SciPostPhys.15.4.179},
}

Cited by 5

Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.

¹ Jie Gu,
² Marcos Mariño

Funders for the research work leading to this publication