Some details on the Gopakumar-Vafa and Ooguri-Vafa formulas
type: Item
instance of: scholarly article
title: Some details on the Gopakumar-Vafa and Ooguri-Vafa formulas
zbMATH Open document ID: 1355.81140
author: Mykola Dedushenko
author: Edward Witten
published in: Advances in Theoretical and Mathematical Physics
publication date: 2016-11-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1411.7108
reviewed by: Gert Roepstorff
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 83E50
Mathematics Subject Classification ID: 83E30
Mathematics Subject Classification ID: 83E15
zbMATH DE Number: 6655268
zbMATH Keywords: superstring theory
zbMATH Keywords: supersymmetry
zbMATH Keywords: superspace
zbMATH Keywords: BPS states
zbMATH Keywords: Schwinger calculation
zbMATH Keywords: gauge fields
zbMATH Keywords: graviphoton
zbMATH Keywords: supergravity
zbMATH Keywords: Gopakumar-Vafa formula
zbMATH Keywords: Ooguri-Vafa formula
MaRDI profile type: Publication
arXiv ID: 1411.7108
OpenAlex ID: W2133488496
DOI: 10.4310/ATMP.2016.V20.N1.A1
review text: Thematically organized into five parts, this article covers topics in the following areas. {\parindent=6mm \begin{itemize}\item[1.] An introduction to the Gopakumar-Vafa approach to superstring theory. Supersymmetric terms in the effective potential that are supersymmetric cannot be written as integrals over all of superspace. Gopakumar and Vafa proposed that the interaction terms could be understood by considering a supersymmetric background obtained by turning on an anti-selfdual graviphoton field. \item[2.] The background in five dimensions and its supersymmetry. Minimal supergravity is described by bosonic fields forming the metric tensor and a \(U(1)\) gauge field \(V\). Its field strength \(dV\) describes the graviphoton. \item[3.] A Schwinger-like calculation for massive BPS states in five dimensions. Only the leading order approximations to the particle action are considered and couplings of higher dimension are ignored. \item[4.] The Schwinger calculation with fields. One aim here is to compute the one-loop effective action for a 4-dimensional BPS hypermultiplet in a background given by the graviton field. \item[5.] D4-branes and the Ooguri-Vafa formula as an opern-string analog of the Gopakumar-Vafa formula. It is pointed out that one should worry about infrared effects. NEWLINENEWLINE\end{itemize}} Three Appendices describe the supergravity conventions in dimensions 11, 5, and 4, the derivation of the 5-dimensional BPS superparticle action, and address the question whether short-range interactions will affect the Ooguri-Vafa formula. There are fifty-six published papers that address topics close to the abstract mathematical modeling used in the present article which now provides a very useful reference for everyone interested in modern field theory.
description: scientific article; zbMATH DE number 6655268