TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.6.155
TI  - Large N instantons from topological strings
PY  - 2024/06/19
UR  - https://scipost.org/SciPostPhys.16.6.155
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 6
SP  - 155
A1  - Mariño, Marcos
AU  - Miravitllas, Ramon
AB  - The $1/N$ expansion of matrix models is asymptotic, and it requires non-perturbative corrections due to large $N$ instantons. Explicit expressions for large $N$ instanton amplitudes are known in the case of Hermitian matrix models with one cut, but not in the multi-cut case. We show that the recent exact results on topological string instanton amplitudes provide the non-perturbative contributions of large $N$ instantons in generic multi-cut, Hermitian matrix models. We present a detailed test in the case of the cubic matrix model by considering the asymptotics of its $1/N$ expansion, which we obtain at relatively high genus for a generic two-cut background. These results can be extended to certain non-conventional matrix models which admit a topological string theory description. As an application, we determine the large $N$ instanton corrections for the free energy of ABJM theory on the three-sphere, which correspond to D-brane instanton corrections in superstring theory. We also illustrate the applications of topological string instantons in a more mathematical setting by considering orbifold Gromov-Witten invariants. By focusing on the example of ${\mathbb C}^3/{\mathbb Z}_3$, we show that they grow doubly-factorially with the genus and we obtain and test explicit asymptotic formulae for them.
ER  -

@Article{10.21468/SciPostPhys.16.6.155,
	title={{Large N instantons from topological strings}},
	author={Marcos Mariño and Ramon Miravitllas},
	journal={SciPost Phys.},
	volume={16},
	pages={155},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.6.155},
	url={https://scipost.org/10.21468/SciPostPhys.16.6.155},
}