Vol. 8 (2005) > lrr-2005-9

doi: 10.12942/lrr-2005-9
Living Rev. Relativity 8 (2005), 9

Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence

1 Humboldt Universität zu Berlin, Institut für Physik, Newtonstrasse 15, D-12489 Berlin, Germany

Full text: HTML | PDF (568.8 Kb)

Article Abstract

In this introductory review we discuss dynamical tests of the AdS_5 × S^5 string/N = 4 Super Yang-Mills duality. After a brief introduction to AdS/CFT, we argue that semiclassical string energies yield information on the quantum spectrum of the string in the limit of large angular momenta on the S^5. The energies of the folded and circular spinning string solutions rotating on a S^3 within the S^5 are derived, which yield all-loop predictions for the dual gauge theory scaling dimensions. These follow from the eigenvalues of the dilatation operator of N = 4 Super Yang-Mills in a minimal SU(2) subsector, and we display its reformulation in terms of a Heisenberg s = 1/2 spin chain along with the coordinate Bethe ansatz for its explicit diagonalization. In order to make contact to the spinning string energies, we then study the thermodynamic limit of the one-loop gauge theory Bethe equations and demonstrate the matching with the folded and closed string result at this loop order. Finally, the known gauge theory results at higher-loop orders are reviewed and the associated long-range spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop conjecture for the gauge theory Bethe equations. This uncovers discrepancies at the three-loop order between gauge theory scaling dimensions and string theory energies, and the implications of this are discussed. Along the way, we comment on further developments and generalizations of the subject and point to the relevant literature.

Keywords: String Theory, Supersymmetric Yang-Mills, AdS/CFT Correspondence

Article Downloads

Article Format Size (Kb)
RIS UTF-8 Latin-1
EndNote UTF-8 Latin-1

Article Citation

Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

Jan Plefka,
"Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence",
Living Rev. Relativity 8,  (2005),  9. URL (cited on <date>):

Article History

ORIGINAL http://www.livingreviews.org/lrr-2005-9
Title Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence
Author Jan Plefka
Date accepted 20 October 2005, published 30 November 2005
  • Bookmark this article:
  • bibsonomy
  • citeulike
  • delicious
  • digg
  • mendeley
Comment(s) on this article



Impact Factor 2014