Some details on the Gopakumar-Vafa and Ooguri-Vafa formulas. (English) Zbl 1355.81140
Thematically organized into five parts, this article covers topics in the following areas.
- 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.
- 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.
- 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.
- 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.
- 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.
Reviewer: Gert Roepstorff (Aachen)
MSC:
81T60 | Supersymmetric field theories in quantum mechanics |
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
83E50 | Supergravity |
83E30 | String and superstring theories in gravitational theory |
83E15 | Kaluza-Klein and other higher-dimensional theories |