More on Gopakumar-Vafa formula: coefficients $\mathcal{F}_0$ and $\mathcal{F}_1$

Mykola Dedushenko

More on Gopakumar-Vafa formula: coefficients $\mathcal{F}_0$ and $\mathcal{F}_1$

High Energy Physics - Theory 2015-01-30 v1

Authors: Mykola Dedushenko

Abstract

In Type IIA compactified on a Calabi-Yau threefold, the genus zero and one terms of the Gopakumar-Vafa (GV) formula describe F-terms that are related to genus zero and one topological amplitudes. While for higher-genus terms $\mathcal{F}_g, g\ge 2$ , the contribution of a light hypermultiplet can be computed via a sum over Kaluza-Klein harmonics, as has been shown in a recent paper, for $g \leq 1$ , the sum diverges and it is better to compute $\mathcal{F}_0$ and $\mathcal{F}_1$ directly in five-dimensional field theory. Such a computation is presented here.

Keywords

gopakumar-vafa formula topological amplitudes calabi-yau threefold type iia string theory f-terms hypermultiplets five-dimensional field theory

Cite

@article{arxiv.1501.07589,
  title  = {More on Gopakumar-Vafa formula: coefficients $\mathcal{F}_0$ and $\mathcal{F}_1$},
  author = {Mykola Dedushenko},
  journal= {arXiv preprint arXiv:1501.07589},
  year   = {2015}
}

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22 pages, 1 figure

More on Gopakumar-Vafa formula: coefficients $\mathcal{F}_0$ and $\mathcal{F}_1$

Abstract

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