nLab open/closed string duality

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

• the KLT relations

• the AdS/CFT correspondence

• the AdS/QCD correspondence

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).

Related concepts

• duality in physics

• duality in string theory

• classical double copy

• 't Hooft double line construction

• large N limit, small N limit

• KLT relations

• AdS/CFT correspondence

• AdS/QCD correspondence

• string theory results applied elsewhere

• effective QFT incarnations of open/closed string duality,

  relating (super-)gravity to (super-)Yang-Mills theory:

  • KLT relations

  • BCJ relations

  • classical double copy

References

Review:

• Leonardo Rastelli, Lectures on open/closed string duality, PiTP 2004 (pdf, pdf)

• Volker Schomerus, Strings for quantum chromodynamics, International journal of modern physics A 22:30 (2007) (doi:10.1142/S0217751X07038827)

• R. Peschanski, Gauge-gravity duality and high energy collisions, Nuclear Physics B - Proceedings Supplements, Volume 191, June 2009, Pages 320-330 (doi:10.1016/j.nuclphysbps.2009.03.138)

Original articles:

• Rajesh Gopakumar, Cumrun Vafa, On the Gauge Theory/Geometry Correspondence, Adv. Theor. Math. Phys. 3 (1999) 1415-1443 (arXiv:hep-th/9811131)

• Justin Khoury, Herman Verlinde, On Open/Closed String Duality (arXiv:hep-th/0001056)

• Andreas Karch, Lisa Randall, Open and Closed String Interpretation of SUSY CFT’s on Branes with Boundaries, JHEP 0106:063, 2001 (arXiv:hep-th/0105132)

• Davide Gaiotto, Leonardo Rastelli, A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model, JHEP 0507:053,2005 (hep-th/0312196)

• Rajesh Gopakumar, Free Field Theory as a String Theory?, Comptes Rendus Physique 5 (2004) 1111-1119 (hep-th/0409233)