TY - JOUR

T1 - Some details on the gopakumar-vafa and ooguri-vafa formulas

AU - Dedushenko, Mykola

AU - Witten, Edward

N1 - Funding Information:
Research of EW was supported in part by NSF Grant PHY-1314311. We thank N. Berkovits, J. Bryan, E. Diaconescu, D. Kaplan, J. Maldacena, R. Meyer, V. Mikhaylov, R. Pandharipande, N. Seiberg, H. Ooguri, V. Pestun, C. Vafa, J. Walcher, I. Yaakov, and M. Yamazaki for discussions.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

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U2 - 10.4310/ATMP.2016.v20.n1.a1

DO - 10.4310/ATMP.2016.v20.n1.a1

M3 - Article

AN - SCOPUS:84982126261

SN - 1095-0761

VL - 20

SP - 1

EP - 132

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

IS - 1

ER -