Resummations and Non-Perturbative Corrections
Abstract
We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the resolved conifold, and find a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling gs, we find that it includes not only the M-theoretic resummation a la Gopakumar and Vafa, but also a non-perturbative correction in gs. Remarkably, the obtained non-perturbative correction is in perfect agreement with a proposal for membrane instanton corrections in arXiv:1306.1734. Various other examples are also presented.
Cite
@article{arxiv.1505.07460,
title = {Resummations and Non-Perturbative Corrections},
author = {Yasuyuki Hatsuda and Kazumi Okuyama},
journal= {arXiv preprint arXiv:1505.07460},
year = {2016}
}
Comments
25 pages, 8 figures, v2: published version