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 \( {\mathrm{\mathcal{F}}}_{\mathrm{g}},\mathrm{g}\ge 2 \), 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 \( \mathrm{g}\ \le 1 \), the sum diverges and it is better to compute ℱ0 and ℱ1 directly in five-dimensional field theory. Such a computation is presented here.
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Dedushenko, M. More on Gopakumar-Vafa formula: coefficients ℱ0 and ℱ1 . J. High Energ. Phys. 2015, 89 (2015). https://doi.org/10.1007/JHEP05(2015)089
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DOI: https://doi.org/10.1007/JHEP05(2015)089