Review of AdS/CFT Integrability: An Overview

By N. Beisert, C. Ahn, L. Alday, Z. Bajnok, J. Drummond, L. Freyhult, N. Gromov, Romuald A. Janik, Vladimir Kazakov, T. Klose and 16 more. Letters in Mathematical Physics, 2010

1,583 citations recorded by the source corpus.

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection, we present an overview of the achievements and the status of this subject as of the year 2010.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bc80a41e800e58c4bbf965cf6fa89b3a6985cdfa

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Citations in the corpus

On the rotating and oscillating strings in (AdS3 × S3)ϰ (2014, background): “Integrability has played an important role in understanding the spectrum of the superstring theory on AdS5 × S5 [1].”
The full four-loop cusp anomalous dimension in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{do (2019, neutral): “the celebrated AdS/CFT correspondence, and is believed to be integrable, at least in the planar limit [28].”
Fermi gases in one dimension: From Bethe ansatz to experiments (2013, background): “T - systems and integrability in general also play a fundamental role in the gauge/string theories of high energy physics (Beisert et al., 2012; Kuniba et al., 2011).”
When does the gluon reggeize? (2013, background): “This is by now well established and for a review we refer to [104].”
Hexagonalization of correlation functions (2016, background): “2 This appears to be an inconvenient truth for integrability practitioners: owing to the remarkable progress in the last ten years, we now have powerful nonperturbative methods to study the spectrum [5] (see [6] for the current state of the art), and the structure constants [7] of planar N = 4 SYM.”
Jordanian deformations of the AdS5 × S5 superstring (2014, background): “It has been revealed that an integrable structure exists behind the duality and it plays a fundamental role in testing the correspondence of physical quantities (for a comprehensive review, see [5]).”
Integrability, spin-chains and the AdS3/CFT2 correspondence (2011, neutral): “2 A recent review of the developments in this ﬁeld can be found in [15].”
Summing up all genus free energy of ABJM matrix model (2011, background): “Through its connection to the spin chain systems, the large N integrability allowed us to successfully check the duality from weak to strong ’t Hooft coupling with remarkably high accuracy [2].”
A dynamic $ su{(1|1)^2} $ S-matrix for AdS3/CFT2 (2012, background): “A significant success in the investigation of the correspondence was obtained in the case of type IIB strings on AdS5 × S(5) and N = 4 Super-Yang-Mills (SYM) in the ’t Hooft limit, where it was found that integrability techniques could be applied to the computation of the string energy spectrum, or ”
Space-time S-matrix and flux tube S-matrix II. Extracting and matching data (2013, background): “It lays the ground for the application of the powerful integrability technology (see [18] for a recent review) and allows one to come up with an educated guess for the pentagon transitions at finite coupling.”
hep-th (2018, background): “review on the integrable structure of N = 4 super-Yang–Mills theory [45].”
The quark anti-quark potential and the cusp anomalous dimension from a TBA equation (2012, background): “theory is integrable [12], we expected to be able to derive an exact expression.”