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

In this introductory review we discuss dynamical tests of the AdS(5) × S(5) string/[Formula: see text] 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 mo...

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Autor principal: Plefka, Jan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2005
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5253969/
https://www.ncbi.nlm.nih.gov/pubmed/28163650
http://dx.doi.org/10.12942/lrr-2005-9
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author Plefka, Jan
author_facet Plefka, Jan
author_sort Plefka, Jan
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description In this introductory review we discuss dynamical tests of the AdS(5) × S(5) string/[Formula: see text] 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 [Formula: see text] 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.
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spelling pubmed-52539692017-02-03 Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence Plefka, Jan Living Rev Relativ Review Article In this introductory review we discuss dynamical tests of the AdS(5) × S(5) string/[Formula: see text] 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 [Formula: see text] 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. Springer International Publishing 2005-11-30 2005 /pmc/articles/PMC5253969/ /pubmed/28163650 http://dx.doi.org/10.12942/lrr-2005-9 Text en © The Author(s) 2005
spellingShingle Review Article
Plefka, Jan
Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence
title Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence
title_full Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence
title_fullStr Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence
title_full_unstemmed Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence
title_short Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence
title_sort spinning strings and integrable spin chains in the ads/cft correspondence
topic Review Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5253969/
https://www.ncbi.nlm.nih.gov/pubmed/28163650
http://dx.doi.org/10.12942/lrr-2005-9
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