Some details on the gopakumar-vafa and ooguri-vafa formulas

Mykola Dedushenko, Edward Witten

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25 Scopus citations


The Gopakumar-Vafa (GV) formula expresses certain couplings that arise in Type IIA compactification to four dimensions on a Calabi-Yau manifold in terms of a counting of BPS states in Mtheory. The couplings in question have applications to topological strings and supersymmetric black holes. In this paper, we reconsider the GV formula, taking a close look at the Schwinger-like computation that was suggested in the original GV work. The goal is to understand the background that must be used in this computation, the role played by the extended supersymmetry of this background, and how the computation gives a holomorphic result though superficially depending only on particle masses. We also examine in a similar way the Ooguri-Vafa (OV) formula, which is an extension of the GV formula to include D4-branes.

Original languageEnglish (US)
Pages (from-to)1-132
Number of pages132
JournalAdvances in Theoretical and Mathematical Physics
Issue number1
StatePublished - 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy


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