# nLab open/closed string duality

Contents

### Context

#### Duality in string theory

duality in string theory

general mechanisms

string-fivebrane duality

string-string dualities

M-theory

F-theory

string-QFT duality

QFT-QFT duality:

# Contents

## Idea

In string theory a given worldsheet with boundaries (Riemann surface with punctures) may typically be read in at least two different ways as describing either a closed string or an open string scattering-process.

graphics grabbed from Schomerus 07, Figure 4

But since the corresponding string scattering amplitude is the same no matter which perspective is taken, this exhibits an equivalence (“duality”) between these open- and closed string amplitudes.

For example, a cylinder worldsheet stretching between two D-brane worldvolumes manifestly represents equivalently the following two rather different-seeming string scattering-processes:

1. a closed string emitted from one of the branes and absorbed by the other;

2. an open string with ends on both branes going around a 1-loop vacuum diagram.

graphics grabbed from Schomerus 07, Figure 4, see also e.g. Peschanski 09, Figure 1

Since

1. closed string excitations include gravitons inducing gravity

(in the above example: the gravitational attraction between the two branes)

2. open string excitations include gluons inducing the force described by Yang-Mills gauge fields –e.g. the strong nuclear force in quantum chromodynamics

(in the above example: the worldvolume gauge field on coincident branes)

open/closed string duality implies gauge/gravity duality between these different effective field theories. This is exhibited by phenomena such as

## Applications

### In large $N$ limit and holography

Open/closed string duality plays a subtle role when interpreting the 't Hooft double line notation of gauge theory Feynman diagrams in the large N limit alternatively as open string or as closed string worldsheets (Gopakumar-Vafa 98, Gaiotto-Rastelli 03, Gopakumar 04).

## References

Review:

Original articles:

Last revised on August 30, 2020 at 11:30:09. See the history of this page for a list of all contributions to it.