More on Gopakumar-Vafa formula: coefficients \(\mathcal F_0\) and \(\mathcal F_1\). (English) Zbl 1388.83787
Summary: 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 \(\mathcal F_g\), \(g \geq 2\), 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.
MSC:
| 83E50 | Supergravity |
References:
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