RECORD
On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
High Energy Physics - Theory · Submitted 17 Jun 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in two-dimensional sigma-models and in the AdS/CFT context. The first part is focused on the AdS_5/CFT_4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS_5 x S^5 are discussed in both pure spinor and Green-Schwarz formulations. The second part is dedicated to the AdS_4/CFT_3 duality with particular attention to the type IIA superstring on AdS_4 x CP^3 and its integrability. This review is based on a shortened and revised version of the author's PhD thesis, discussed at Uppsala University in September 2009.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | One of the main topics in the modern String Theory are the AdS/CFT dualities. | background 1.00 | 0.03 | 0.03 | asserted 1.00 |
| s1 | Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. | background 0.95 | 0.04 | 0.03 | asserted 1.00 |
| s2 | In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. | background 0.97 | 0.08 | 0.41 | asserted 1.00 |
| s3 | We review the fundamental concepts and properties of integrability in two-dimensional sigma-models and in the AdS/CFT context. | contribution 0.96 | 0.27 | 0.05 | asserted 0.82 |
| s4 | The first part is focused on the AdS_5/CFT_4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS_5 x S^5 are discussed in both pure spinor and Green-Schwarz formulations. | contribution 0.93 | 0.15 | 0.04 | asserted 0.97 |
| s5 | The second part is dedicated to the AdS_4/CFT_3 duality with particular attention to the type IIA superstring on AdS_4 x CP^3 and its integrability. | contribution 0.95 | 0.24 | 0.04 | asserted 0.93 |
| s6 | This review is based on a shortened and revised version of the author's PhD thesis, discussed at Uppsala University in September 2009. | background 0.66 | 0.48 | 0.02 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in two-dimensional sigma-models and in the AdS/CFT context. The first part is focused on the AdS_5/CFT_4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS_5 x S^5 are discussed in both pure spinor and Green-Schwarz formulations. The second part is dedicated to the AdS_4/CFT_3 duality with particular attention to the type IIA superstring on AdS_4 x CP^3 and its integrability. This review is based on a shortened and revised version of the author's PhD thesis, discussed at Uppsala University in September 2009.
Human review
References
How the literature uses it
9 arXiv papers cite this in 10 sentences
Papers citing it
Cites it as background 9 papers
-
One of the greatest achievements in string theory is the discovery of the integrability of the classical string sigma model on $AdS_5×S^5$ background [ref] [For recent review of integrability in the context of string theory, see [ref] ].
Integrability of D1-brane on Group Manifold · Introduction and Summary · 0.98
-
Famous example is the duality between $𝒩=4$ super-Yang-Mills theory in four dimensions and Type IIB theory on $AdS_5×S^5$ with the Ramond-Ramond (RR) flux, where the exact string spectrum and the spectrum of anomalous dimensions in the SYM theory can be described by Bethe-ansatz equations [For review, see [ref] .].
Integrability of D1-brane on Group Manifold with Mixed Three Form Flux · Introduction and Summary · 1.00
-
(For a recent review see [ref] .) The pure spinor approach avoids the presence of the kappa-symmetry.
Pure spinor superstring in AdS_4 x CP^3 with unconstrained ghosts · Introduction · 0.99
What it cites · 232 sentences without a confident label
Contests 7 papers
-
However, at three loops the proposed equality [ref] breaks down: The explicit three-loop computation of the near-BMN strings [ref] , i.e. $a_3^(1)$, and of the spinning strings [ref] showed a mismatch with the gauge theory predictions coming from the Bethe ansatz [ref] , (“three loop discrepancy”).
Planar N=4 gauge theory and the Inozemtsev long range spin chain · The BMN limit · contest 0.74
-
However, at three loops the proposed equality [ref] breaks down: The explicit three-loop computation of the near-BMN strings [ref] , i.e. $a_3^(1)$, and of the spinning strings [ref] showed a mismatch with the gauge theory predictions coming from the Bethe ansatz [ref] , (“three loop discrepancy”).
Two-loop commuting charges and the string/gauge duality · The BMN limit · contest 0.74
-
However, at three loops the proposed equality [ref] breaks down: The explicit three-loop computation of the near-BMN strings [ref] , i.e. $a_3^(1)$, and of the spinning strings [ref] showed a mismatch with the gauge theory predictions coming from the Bethe ansatz [ref] , (“three loop discrepancy”).
Holography Beyond the Penrose Limit · The BMN limit · contest 0.74
Uses the method or tool of 14 papers
-
Hence the super-coset approach á la GSMT, cf. section [ref], can be employed in this case for the formulation of the type IIA string action [ref] .
Superstrings on AdS_4 x CP^3 as a Coset Sigma-model · Integrability on the string theory side · 0.93
-
Hence the super-coset approach á la GSMT, cf. section [ref], can be employed in this case for the formulation of the type IIA string action [ref] .
Green-Schwarz action for Type IIA strings on $AdS_4\times CP^3$ · Integrability on the string theory side · 0.93
-
The strategy adopted in [ref] is to verify the presence (or the absence) of the dynamical constraints which define an integrable two-dimensional field theory: absence of particle production, elastic scatterings, S-matrix factorization.
Factorized world-sheet scattering in near-flat AdS_5 x S^5 · The world-sheet S-matrix factorization · 0.91
Compares with 2 papers
-
The energies up to order $1R^2$ obtained with the above finite-size procedure are compared with the strong coupling limit of the Bethe equations proposed in [ref] .
The all loop AdS4/CFT3 Bethe ansatz · The near-BMN corrections · 1.00
-
A very similar problem was faced in [ref] by using a Hamiltonian approach.
Current Algebra of the Pure Spinor Superstring in AdS(5) x S(5) · The operator algebra · 0.80
Cites as support 5 papers
-
However such currents are not present [ref] , implying that Q remains nilpotent at quantum level.]
Quantum Consistency of the Superstring in AdS_5 x S^5 Background · Type IIB superstring on $_5×^5$: PS action · 0.98
-
However, it has been shown in [ref] that integrability forces the coefficient in front of the WZW term to be fixed to the same values which are allowed by the $κ$-symmetry ($κ=±1$).
Foundations of the AdS_5 x S^5 Superstring. Part I · Classical integrability for the GSMT superstring action · 0.96
-
Other important tests which confirm the BES result have been given in the works [ref] .
Complete 1-loop test of AdS/CFT · The dressing phase · 0.97
Cites as background 64 papers
-
The Maldacena correspondence [ref] conjectures an exact duality between the type IIB superstring theory on the curved space $_5×^5$ and $=4$ super Yang-Mills (SYM) theory on the flat four-dimensional space $^3,1$ with gauge group $(N)$.
Anti De Sitter Space And Holography · Introduction · 0.92
-
The Maldacena correspondence [ref] conjectures an exact duality between the type IIB superstring theory on the curved space $_5×^5$ and $=4$ super Yang-Mills (SYM) theory on the flat four-dimensional space $^3,1$ with gauge group $(N)$.
Gauge Theory Correlators from Non-Critical String Theory · Introduction · 0.92
-
For the second part I will mainly refer to the work by Metsaev and Tseytlin [ref] for the super-coset construction of the action, to the paper by Bena, Polchinski and Roiban [ref] for the classical integrability of the GSMT action and finally to the reviews written by Zarembo [ref] and by Arutyunov and Frolov [ref] .
Hidden Symmetries of the AdS_5 x S^5 Superstring · Green-Schwarz-Metsaev-Tseytlin superstring · 0.89
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.