Bethe Ansatz for Quantum Strings

Gleb Arutyunov; Matthias Staudacher; Sergey Frolov

REVIEW

Bethe Ansatz for Quantum Strings

Gleb Arutyunov, Sergey Frolov, Matthias Staudacher

High Energy Physics - Theory · Submitted 28 Jun 2004 · 29 references

Pith's verdict: The dressing-phase paper: a bold but honestly framed conjecture, with the near-BMN match against Callan et al. as its real teeth.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 5 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-th/0406256 (version 3)

Pith IDFYUI2AQ3, Pith's permanent record of this paper and its review

CitationGleb Arutyunov, Matthias Staudacher, Sergey Frolov. "Bethe Ansatz for Quantum Strings." arXiv:hep-th/0406256 (2004). https://pith.science/paper/FYUI2AQ3

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

This is the Arutyunov-Frolov-Staudacher proposal that adds an extra exponential term to the Beisert-Dippel-Staudacher S-matrix and calls the result the quantum-string Bethe ansatz in the su(2) sector. The genuinely new object is that term in (2.2); everything else — the phase function phi(p), the charge densities q_r(p), the energy formula (2.7) — is imported verbatim from [11]. The paper is upfront about this in §2.1, and that honesty matters for how you read the rest of it. The real content is: does the modified S-matrix reproduce known string data, and does it produce the right strong-coupling scaling? The answer to both is yes, with caveats worth naming. The near-BMN check is the strongest evidence in the paper. Formula (3.8) matches Callan et al. at M=2 and M=3, including the confluent case (3.18)-(3.19), and it does so at three loops where the gauge formula (3.9) does not. That is a discriminating external check, not a consistency exercise. The confluent-mode treatment via Hermite-polynomial roots (3.13)-(3.16) is clean and, as far as I can tell, correct. The strong-coupling section is more delicate than the abstract lets on. The 2(n^2 lambda)^{1/4} result does come out of the new term, which is the striking point, but it comes from a formal resummation of a divergent series with an assumed p ~ p_0/sqrt(g) scaling (footnote 4 is doing real work there). It shows compatibility with the known asymptotics; it does not derive the coefficient from the sigma model. The stress-test's complaint about 'everything currently known' is fair but slightly overpitched: the authors themselves say 'by construction' for the classical limit, and they flag in §6 that the general-M formula is a prediction awaiting an M=4 direct quantization. So the abstract is a bit generous, not misleading. The interpolating ansatz in §5 is pure speculation with undetermined functions c_r(g,L); treat it as a signpost, not a result. Who should read it: anyone working on AdS/CFT integrability, and anyone interested in how a dressing phase gets motivated before it is derived. The paper earns referee time.

Referee report

Major objections (3)

[Abstract [abstract:s2]; §2.2; §6] The abstract's claim that the ansatz 'quantitatively reproduces everything that is currently known' is stronger than the evidence assembled. The recovery of the classical integral equations in §2.2 is, as the authors themselves state, by construction: the exponential term in (2.2) was engineered to reproduce the last term of (2.14), so this is a consistency check on the discretization rather than independent evidence for the quantum structure. The genuinely independent check is the near-BMN comparison, and it is carried out only for M=2,3; the general-M formula (3.8) and the confluent formula (3.18) are predictions, not verifications, and §6 acknowledges that an M=4 direct quantization 'would be interesting' as a test. I recommend either softening the abstract sentence or adding the M=4 comparison, so that the headline claim matches the evidential base.
[§2.1, Eq. (2.2); §4 and footnote 4] The infinite series in the exponent of (2.2) is central to the proposal, but its convergence and the manipulation of the strong-coupling limit are not discussed. For finite g the terms behave as g(ratio²/2)^r with ratio < √2, so the series converges, but at g→∞ it is borderline and footnote 4 simply prescribes that 'one should first perform the sum and only then take the limit.' The paper should state the domain of convergence and justify the interchange of the g→∞ limit with the resummation used to obtain (4.2), or present the closed-form sum. Relatedly, the assumed scaling p ~ p_0/√g in (4.3) should be motivated from the leading g-dependence of the exponent rather than asserted.
[§2.1, Eq. (2.2); §2.2] The paper repeatedly invokes 'factorized scattering' and asserts that the charge-dependent exponential term preserves it, but it does not verify the Yang–Bragg equation for the full S-matrix (2.2). Unitarity is manifest (the difference-form factor and the antisymmetric charge factor each square to one under k↔j), but the factorization property that justifies the Bethe ansatz should be stated explicitly. The natural argument is that the exponential is built from the conserved charges q_r, which commute with the S-matrix; spelling this out, or verifying the YBE directly, would close a gap in the consistency of the central object.

Minor objections (5)

[§4] The sign prescription √(sin²(½p))/sin(½p) = sign Re p is stated without justification; a sentence explaining the branch choice would help the reader follow the grouping of roots into p⁺ and p⁻.
[§3.1, Eqs. (3.8)–(3.9)] The grouping of factors in the double sums of (3.8) and (3.9) is ambiguous in the typeset form; the intended numerator/denominator structure of the √(1+λ′n_j²)/√(1+λ′n_k²) factor should be made explicit.
[§2.2, Eq. (2.16)] The rescaling ϕ → ϕ/L and the resulting form (2.16) are quoted without intermediate steps; a short derivation would make the thermodynamic-limit comparison easier to check.
[§5, footnote 6] The two illustrative forms for c_r(g,L) should be checked against all four stated asymptotic properties; in particular the large-L behavior of the second example deserves an explicit verification.
[§2.1] The paper should state clearly which ingredients (ϕ(p), q_r(p), the energy relation (2.7)) are imported from [11] and which are new, so that the reader can separate the novel S-matrix term from the inherited structure.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The paper proposes Bethe equations for quantum strings in a closed $su(2)$ sector and argues that a single added scattering term reproduces all currently known string-spectrum data for those states.

The reading

The paper proposes a set of Bethe equations meant to diagonalize the Hamiltonian of quantum strings on $AdS_5 times S^5$ in a closed $su(2)$ sector, at large string tension and large charge. The proposal keeps the charge densities and phase function of an earlier all-loop gauge-theory Bethe ansatz and changes only the pairwise scattering matrix, adding an infinite sum of charge bilinears. The authors argue that this single modification is enough to reproduce, in one framework, the integral equations for classical spinning strings, the $1/J$ corrections to arbitrary $M$-impurity BMN energies, the known direct-quantization results for $M=2,3$, and the $2(n^2lambda)^{1/4}$ asymptotics of massive string modes. They also speculate that the extra term is the string-side shadow of wrapping interactions and propose an interpolating ansatz with coupling- and length-dependent coefficients.

What carries the argument

The load-bearing object is the S-matrix $$S(p_k,p_j)=frac{$\varphi$(p_k)-$\varphi$(p_j)+i}{$\varphi$(p_k)-$\varphi$(p_j)-i}exp!left(2isum_{r=0}^{infty}left(frac{$g^{2}$}{2}right)^{r+2}left[q_{r+2}(p_k)q_{r+3}(p_j)-q_{r+3}(p_k)q_{r+2}(p_j)right]right),$$ where $phi(p)=frac12cot(frac12 p)sqrt{1+8g^2sin^2(frac12 p)}$ and $q_r(p)$ are the single-excitation charges. The first factor is the ordinary phase-shift factor; the exponential is the new term. The phase function and charges are imported unchanged from the asymptotic gauge-theory ansatz, while the exponential term is absent there. In the thermodynamic limit the exponential term turns into the kernel of the classical spinning-string integral equation; in the near-BMN expansion it supplies the $1/J$ momentum shifts; at strong coupling it alone fixes the leading momentum $p_0=2^{1/4}sqrt{npi}$ and hence the $2(n^2lambda)^{1/4}$ asymptotics.

Extended reading notes

Core claim

The central claim is that, at large string tension and large charge, the quantum string Hamiltonian in the closed $su(2)$ sector is diagonalized by Bethe equations $$$e^{{iLp_k}}$=prod_{jne k}S(p_k,p_j),qquad sum_k p_k=0,$$ with a pairwise S-matrix that differs from the asymptotic gauge-theory one by an extra exponential term built from the single-excitation charges. The authors do not derive the equations from the string $\sigma$ model. Instead they construct them so that their thermodynamic limit is the known integral Bethe equation for classical spinning strings, and then show that the same equations produce the $1/J$ near-BMN corrections for arbitrary $M$ impurities, the previously known direct-quantization results for $M=2$ and $M=3$, and the $2(n^2lambda)^{1/4}$ strong-coupling asymptotics. The claim is therefore an organizing conjecture: one discrete factorized-scattering ansatz accounts for all currently known string data in this sector.

Load-bearing premise

The construction assumes that the quantum-string single-excitation charges $q_r(p)$ and phase function $phi(p)$ are exactly the same as in the asymptotic gauge-theory Bethe ansatz, so that all quantum-string dynamics beyond free propagation is captured by modifying only the pairwise S-matrix.

Editorial extensions

If this is right

If correct, the large-tension, large-charge $su(2)$ string spectrum reduces to solving a finite system of Bethe equations instead of quantizing the full sigma model.
The paper's general formulae give the $1/J$ energy correction for any number $M$ of impurities with distinct mode numbers, and a separate formula covers confluent mode numbers.
The strong-coupling $2(n^2lambda)^{1/4}$ law for level-$n$ massive string modes follows from the new scattering term rather than from the imported charge function.
The proposed interpolating ansatz with coefficients $c_r(g,L)$ gives a concrete target for exact quantization and for organizing wrapping corrections.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The fact that one extra term simultaneously fixes the classical, near-BMN, and strong-coupling limits suggests it is capturing finite-size physics rather than being a fit to any single limit.
A natural next test is the four-impurity $1/J$ correction; if direct quantization matches the general formula, the case for the ansatz becomes much stronger.
If the coefficients $c_r(g,L)$ can be pinned down from string-side $1/J$ or $1/sqrt{lambda}$ corrections, the interpolating equations could become a practical bridge between perturbative gauge theory and string theory.
The paper's own remark that the ansatz does not reproduce the Konishi operator at small length indicates that it should be read as an asymptotic large-$L$, large-$g$ description, not a complete finite-length Bethe ansatz.

Original abstract

We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS_5 x S^5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of arbitrary M-impurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M=2,3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 (n^2 lambda)^(1/4) asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our finding does not in itself cure the disagreements between gauge and string theory, but leads us to speculate about the structure of an interpolating Bethe ansatz for the AdS/CFT system at finite coupling and charge.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. 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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,083 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.95 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.67 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS_5 x S^5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of arbitrary M-impurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M=2,3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 (n^2 lambda)^(1/4) asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our finding does not in itself cure the disagreements between gauge and string theory, but leads us to speculate about the structure of an interpolating Bethe ansatz for the AdS/CFT system at finite coupling and charge.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS_5 x S^5 at large string tension and restricted to certain large charge states from a closed su(2) subsector.	contribution 1.00	0.93	0.31	asserted 0.83
s1	The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations.	contribution 0.79	0.65	0.11	asserted 1.00
s2	We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states.	result 0.98	0.94	0.44	asserted 1.00
s3	Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings.	result 0.98	0.87	0.09	asserted 1.00
s4	Secondly, we explain how to derive the 1/J energy corrections of arbitrary M-impurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory.	result 0.54	0.95	0.11	asserted 1.00
s5	In the special cases M=2,3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 (n^2 lambda)^(1/4) asymptotics of massive string modes at level n.	result 1.00	0.84	0.13	asserted 1.00
s6	Remarkably, this behavior is entirely determined by the novel scattering terms.	interpretation 0.74	0.83	0.17	asserted 1.00
s7	This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory.	interpretation 1.00	0.24	0.07	hedged possibility 0.99
s8	Our finding does not in itself cure the disagreements between gauge and string theory, but leads us to speculate about the structure of an interpolating Bethe ansatz for the AdS/CFT system at finite coupling and charge.	future work 0.53	0.57	0.29	speculative 0.99

What kind of paper the classifier reports this is: theoretical result 0.74 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (29)

[11]

N. Beisert, V. Dippel and M. Staudacher, “A novel long range spin chain and planar N = 4 super Yang-Mills,” hep-th/0405001. – 20 –

View on Pith Pith review arXiv
[14]

V. A. Kazakov, A. Marshakov, J. A. Minahan and K. Zarembo , “Classical / quantum integrability in AdS/CFT,” JHEP 0405 (2004) 024 hep-th/0402207

View on Pith Pith review arXiv 2004
[1]

J. M. Maldacena, “The large N limit of superconformal ﬁeld theories and supergravity,” Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113], hep-th/9711200

View on Pith Pith review arXiv 1998
[2]

D. Berenstein, J. M. Maldacena and H. Nastase, “Strings in ﬂat space and pp waves from N = 4 super Yang Mills,” JHEP 0204 (2002) 013, hep-th/0202021

View on Pith Pith review arXiv 2002
[3]

S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “A semi-classical limit of the gauge/string correspondence,” Nucl. Phys. B 636 (2002) 99, hep-th/0204051

View on Pith Pith review arXiv 2002
[4]

S. Frolov and A. A. Tseytlin, “Semiclassical quantization of rotating superstring in AdS5 × S5,” JHEP 0206 (2002) 007, hep-th/0204226; “Multi-spin string solutions in AdS5 × S5,” Nucl. Phys. B 668 (2003) 77, hep-th/0304255; “Quantizing three-spin string solution in AdS5 × S5,” JHEP 0307 (2003) 016, hep-th/0306130; “Rotating string solutions: AdS/CFT duali...

View on Pith Pith review arXiv 2002
[5]

G. Arutyunov, S. Frolov, J. Russo and A. A. Tseytlin, “Spinning strings in AdS5 × S5 and integrable systems,” Nucl. Phys. B 671, 3 (2003), hep-th/0307191; G. Arutyunov, J. Russo and A. A. Tseytlin, “Spinning strings in AdS5 × S5: New integrable system relations,” Phys. Rev. D 69 (2004) 086009, hep-th/0311004

View on Pith Pith review arXiv 2003
[6]

J. A. Minahan and K. Zarembo, “The Bethe-ansatz for N = 4 super Yang-Mills,” JHEP 0303, (2003) 013, hep-th/0212208

View on Pith Pith review arXiv 2003
[7]

N. Beisert, “The complete one-loop dilatation operator of N = 4 super Yang -Mills theory,” hep-th/0307015; N. Beisert and M. Staudacher, “The N = 4 SYM integrable super spin chain,” hep-th/0307042

View on Pith Pith review arXiv
[8]

N. Beisert, C. Kristjansen and M. Staudacher, “The dilatation operator of N = 4 super Yang-Mills theory,” Nucl. Phys. B 664 (2003) 131, hep-th/0303060; N. Beisert, “Higher loops, integrability and the near BMN limit,” hep-th/0308074; N. Beisert, “The su(2 |3) dynamic spin chain,” Nucl. Phys. B 682 (2004) 487, hep-th/0310252

View on Pith Pith review arXiv 2003
[9]

V. M. Braun, S. E. Derkachov and A. N. Manashov, “Integrability of three-particle evolution equations in QCD,” Phys. Rev. Lett. 81 (1998) 2020 hep-ph/9805225. V. M. Braun, S. E. Derkachov, G. P. Korchemsky and A. N. Manash ov, “Baryon distribution amplitudes in QCD,” Nucl. Phys. B 553 (1999) 355 hep-ph/9902375. A. V. Belitsky, “Renormalization of twist-th...

View on Pith Pith review arXiv 1998
[10]

D. Serban and M. Staudacher, “Planar N = 4 gauge theory and the Inozemtsev long range spin chain,” JHEP 0406 (2004) 001, hep-th/0401057

View on Pith Pith review arXiv 2004
[12]

N. Beisert, J. A. Minahan, M. Staudacher and K. Zarembo, “Stringing spins and spinning strings,” JHEP 0309 (2003) 010, hep-th/0306139; N. Beisert, S. Frolov, M. Staudacher and A. A. Tseytlin, “Precision spectroscopy of AdS/CFT,” hep-th/0308117

View on Pith Pith review arXiv 2003
[13]

G. Arutyunov and M. Staudacher, “Matching higher conserved charges for strings and spins,” JHEP 0403 (2004) 004, hep-th/0310182; “Two-loop commuting charges and the string / gauge duality,” hep-th/0403077

View on Pith Pith review arXiv 2004
[15]

J. Engquist, J. A. Minahan and K. Zarembo, “Yang-Mills duals for semiclassical strings on AdS5 × S5”, hep-th/0310188; J. Engquist, “Higher conserved charges and integrability for spinning strings in AdS5 × S5”, JHEP 0404 (2004) 002, hep-th/0402092; M. Smedback, “Pulsating Strings On AdS5 × S5,” hep-th/0405102; L. Freyhult, “Bethe ansatz and ﬂuctuations in...

View on Pith Pith review arXiv 2004
[16]

M. Kruczenski, “Spin chains and string theory,” hep-th/0311203; M. Kruczenski, A. V. Ryzhov and A. A. Tseytlin, “Large spin limit of AdS5 × S5 string theory and low energy expansion of ferromagnetic spin chains,” hep-th/0403120; H. Dimov and R. C. Rashkov, “A note on spin chain / string duality,” hep-th/0403121. R. Hernandez and E. Lopez, “The SU(3) spin ...

View on Pith Pith review arXiv 2004
[17]

A. Khan and A. L. Larsen, “Spinning pulsating string sol itons in AdS5 × S5,” Phys. Rev. D 69, 026001 (2004), hep-th/0310019; A. L. Larsen and A. Khan, “Novel explicit multi spin string solitons in AdS(5),” Nucl. Phys. B 686, 75 (2004) hep-th/0312184; C. Kristjansen, “Three-spin strings on AdS5 × S5 from N = 4 SYM,” Phys. Lett. B 586 (2004) 106, hep-th/04...

View on Pith Pith review arXiv 2004
[18]

J. G. Russo, “Anomalous dimensions in gauge theories from rotating stri ngs in AdS5 × S5,” JHEP 0206 (2002) 038, hep-th/0205244; J. A. Minahan, “Circular semiclassical string solutions on AdS5 × S5,” Nucl. Phys. B 648 (2003) 203 hep-th/0209047; A. V. Belitsky, A. S. Gorsky and G. P. Korchemsky, “Gauge / string duality for QCD conformal operators,” Nucl. P...

View on Pith Pith review arXiv 2002
[19]

C. G. Callan, H. K. Lee, T. McLoughlin, J. H. Schwarz, I. S wanson and X. Wu, “Quantizing string theory in AdS5 × S5: Beyond the pp-wave,” Nucl. Phys. B 673 (2003) 3, hep-th/0307032; C. G. Callan, T. McLoughlin and I. Swanson, “Holography beyond the Penrose limit,” hep-th/0404007

View on Pith Pith review arXiv 2003
[20]

C. G. Callan, T. McLoughlin and I. Swanson, “Higher impurity AdS/CFT correspondence in the near-BMN limit,” hep-th/0405153

View on Pith Pith review arXiv
[21]

V. I. Inozemtsev, “Integrable Heisenberg-van Vleck chains with variable rang e exchange,” Phys. Part. Nucl. 34 (2003) 166 [Fiz. Elem. Chast. Atom. Yadra 34 (2003) 332], hep-th/0201001

View on Pith Pith review arXiv 2003
[22]

R. R. Metsaev, “Type IIB Green-Schwarz superstring in plane wave Ramond-Ram ond background,” Nucl. Phys. B 625 (2002) 70, hep-th/0112044; R. R. Metsaev and A. A. Tseytlin, “Exactly solvable model of superstring in plane wave Ramond -Ramond background,” Phys. Rev. D 65 (2002) 126004, hep-th/0202109

View on Pith Pith review arXiv 2002
[23]

A. Parnachev and A. V. Ryzhov, “Strings in the near plane wave background and AdS/CFT,” JHEP 0210 (2002) 066, hep-th/0208010

View on Pith Pith review arXiv 2002
[24]

T. J. Stieltjes, “Sur Quelques Theoremes d’Algebre,” Oeuvres Completes, vol. 1, p 440, Noordhoﬀ, Groningen, The Netherlands (1914)

View on Pith 1914
[25]

B. S. Shastry, A. Dhar, Solution of a Generalized Stieltjes Problem , cond-mat/0101464

View on Pith Pith review arXiv
[26]

M. L¨ ubcke and K. Zarembo, “Finite-size corrections to anomalous dimensions in N = 4 SYM theory,” JHEP 0405 (2004) 049, hep-th/0405055

View on Pith Pith review arXiv 2004
[27]

S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B 428 (1998) 105, hep-th/9802109

View on Pith Pith review arXiv 1998
[28]

I. Swanson, “On the integrability of string theory in AdS5 × S5,” hep-th/0405172

View on Pith Pith review arXiv
[29]

R. R. Metsaev and A. A. Tseytlin, Type IIB superstring action in AdS5 × S5 background,” Nucl. Phys. B 533 (1998) 109, hep-th/9805028; R. R. Metsaev, C. B. Thorn and A. A. Tseytlin, “Light-cone superstring in AdS space-time,” Nucl. Phys. B 596 (2001) 151, hep-th/0009171. – 22 –

View on Pith Pith review arXiv 1998

Forward citations

Showing 60 of 69 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. See all 69 Pith citations

Y-system for Scattering Amplitudes
hep-th 2010-02 accept novelty 8.0 of 10

The area of the minimal surface dual to a null polygonal Wilson loop is expressed as the free energy of a TBA system whose equations follow from the integrable structure of the AdS5 sigma model.
Dressing and Wrapping
hep-th 2007-04 accept novelty 8.0 of 10

The dressed asymptotic Bethe ansatz for planar AdS/CFT breaks down at four loops for length-two twist-two operators, because its prediction for the pomeron singularity contradicts the BFKL constraint.
The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
hep-th 2006-10 conditional novelty 8.0 of 10

A direct four-loop computation in N=4 super Yang-Mills gives a cusp anomalous dimension of -29.34 ± 0.05, refuting the Eden-Staudacher Bethe-ansatz prediction of -26.40.
Giant Magnons
hep-th 2006-04 accept novelty 8.0 of 10

Magnons in the planar N=4 SYM spin chain are shown to correspond to giant strings on S5, with momentum equal to the angular separation of the string's endpoints, yielding the strong-coupling dispersion and S-matrix.
Integrability and Transcendentality
hep-th 2006-03 conditional novelty 8.0 of 10

The authors derive an integral equation that predicts the all-loop cusp anomalous dimension f(g) for N=4 SYM, including a new four-loop term, under explicit assumptions about the Bethe ansatz and BMN scaling.

Show 55 more citing papers

Strings as Multi-Particle States of Quantum Sigma-Models
hep-th 2006-03 conditional novelty 8.0 of 10

The thermodynamic limit of the quantum O(2n) sigma-model Bethe ansatz reproduces the classical finite-gap string solutions on S^{2n-1} times R_t via the Zhukovsky map.
Bethe Ansatz in Stringy Sigma Models
hep-th 2006-03 accept novelty 8.0 of 10

The authors derive exact S-matrices and Bethe equations for the Landau-Lifshitz, Alday-Arutyunov-Frolov, and Faddeev-Reshetikhin sigma-models by summing all bubble diagrams.
The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
hep-th 2006-03 accept novelty 8.0 of 10

The paper derives crossing equations for the AdS5xS5 worldsheet S-matrix by constructing generalized rapidities on an elliptic curve, constraining the unknown dressing factor.
Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
hep-th 2005-04 conditional novelty 8.0 of 10

A complete set of asymptotic all-order Bethe equations for planar N=4 SYM with psu(2,2|4) symmetry is proposed, checked to three loops against direct diagonalization, and extended conjecturally to a dual string chain.
The Algebraic Curve of Classical Superstrings on AdS_5xS^5
hep-th 2005-02 accept novelty 8.0 of 10

Every classical solution of the IIB superstring on AdS5 x S5 is captured by a degree 4+4 algebraic curve whose holomorphic integrals yield the energy and other conserved charges.
The Factorized S-Matrix of CFT/AdS
hep-th 2004-12 conditional novelty 8.0 of 10

The paper shows that the S-matrix, not the dilatation operator, is the compact object encoding the spectrum of planar N=4 gauge theory, and derives three-loop S-matrices for the su(1|1) and sl(2) sectors.
On the $AdS_3\times S^3\times S^3\times S^1$ dressing factors
hep-th 2025-12 unverdicted novelty 7.0 of 10

Dressing factors are proposed for the S-matrix of massive worldsheet excitations in AdS3×S3×S3×S1 with mixed RR/NSNS flux that satisfy crossing, unitarity, and reproduce perturbative results for any radius ratio.
The full Quantum Spectral Curve for $AdS_4/CFT_3$
hep-th 2017-01 conditional novelty 7.0 of 10

The authors complete the Quantum Spectral Curve for planar ABJM theory, adding the AdS4 dual system, gluing conditions, and a Q-system for OSp(4|6) that reproduces the Asymptotic Bethe Ansatz in the large-volume limit.
Quantum spectral curve as a tool for a perturbative quantum field theory
hep-th 2014-11 accept novelty 7.0 of 10

A recursive algorithm solves the quantum spectral curve perturbatively for any sl(2) operator in planar N=4 SYM, yielding ten-loop conformal dimensions and a proof that they are multiple zeta-values.
The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
hep-th 2014-06 accept novelty 7.0 of 10

The authors construct the symmetry-fixed worldsheet S-matrix for all fundamental excitations of Type IIB strings on AdS3 x S3 x T4, including massless modes, up to five undetermined dressing factors whose crossing equ...
On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
hep-th 2013-03 conditional novelty 7.0 of 10

The tree-level scattering matrix for massive string excitations on AdS3 x S3 x T4 with mixed RR and NSNS flux depends on the flux-mixing parameter q only through a shifted dispersion relation, e^2 = (p +/- q)^2 + 1 - q^2.
Integrability and the AdS(3)/CFT(2) correspondence
hep-th 2009-12 conditional novelty 7.0 of 10

The Type IIB string on AdS3 x S3 x S3 x S1 is shown to be a classically integrable coset sigma model, with finite-gap and conjectural all-coupling Bethe equations that miss a set of massless modes.
Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
hep-th 2009-03 conditional novelty 7.0 of 10

The paper derives an infinite set of TBA equations for the AdS5 x S5 mirror model and shows that the associated Y-system follows only for rapidities in (-2, 2) and only under an unproven assumption about the dressing phase.
Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
hep-th 2009-02 conditional novelty 7.0 of 10

The authors derive TBA equations for planar AdS/CFT from the mirror Bethe-Yang equations and obtain a Y-system that matches the Gromov-Kazakov-Vieira proposal.
Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
hep-th 2009-02 accept novelty 7.0 of 10

The ordinary and dual superconformal symmetries of tree-level N=4 SYM scattering amplitudes combine into a single infinite-dimensional Yangian algebra.
The all loop AdS4/CFT3 Bethe ansatz
hep-th 2008-07 conditional novelty 7.0 of 10

The authors propose five Bethe equations that, if correct, yield the complete asymptotic energy spectrum of the ABJM AdS4/CFT3 duality at all values of the coupling.
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
hep-th 2008-07 conditional novelty 7.0 of 10

A conjectured multiparticle Luscher formula applied to the AdS string sigma model reproduces the four-loop Konishi wrapping correction previously obtained from perturbative gauge theory.
Superstrings on AdS_4 x CP^3 as a Coset Sigma-model
hep-th 2008-06 accept novelty 7.0 of 10

A coset sigma-model with a Wess-Zumino term reproduces the plane-wave spectrum of type IIA strings on AdS4 x CP3, carries a local fermionic symmetry that removes 8 of 24 fermions, and admits a Lax connection.
Wrapping at four loops in N=4 SYM
hep-th 2007-12 conditional novelty 7.0 of 10

The planar four-loop anomalous dimension of the length-four Konishi descendant in N=4 SYM is 4 + 12g² − 48g⁴ + 336g⁶ + g⁸(−2496 + 576ζ(3) − 1440ζ(5)), with wrapping interactions producing a new ζ(5) term.
On String S-matrix, Bound States and TBA
hep-th 2007-10 accept novelty 7.0 of 10

Unitarity of the mirror S-matrix fixes the AdS5 x S5 string S-matrix essentially uniquely as a meromorphic elliptic function, with the double Wick rotation realized as a quarter-period shift on the rapidity torus.
Transcendentality and Crossing
hep-th 2006-10 accept novelty 7.0 of 10

A specific dressing phase for the planar N=4 SYM S-matrix is derived from crossing symmetry and transcendentality, and its leading four-loop coefficient agrees with an independent computation.
The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
nlin.SI 2006-10 accept novelty 7.0 of 10

The su(2|2)-symmetric S-matrix of the AdS/CFT spin chain coincides, up to an overall factor, with Shastry's R-matrix of the one-dimensional Hubbard model, revealing a hidden supersymmetry in the Hubbard chain.
A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
hep-th 2006-09 conditional novelty 7.0 of 10

A proposed all-orders strong-coupling expression for the AdS5 x S5 string scattering phase satisfies crossing symmetry, reproduces giant-magnon bound states as poles, and is resummed to an analytic form on an infinite...
The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
hep-th 2006-03 accept novelty 7.0 of 10

Frolov, Plefka and Zamaklar derive an exact uniform light-cone gauge-fixed action for the AdS5xS5 superstring and propose a new, compact set of light-cone Bethe equations for its quantum spectrum.
The su(2|2) Dynamic S-Matrix
hep-th 2005-11 accept novelty 7.0 of 10

The su(2|2)-invariant S-matrix of the su(2|3) dynamic spin chain is derived from symmetry alone up to an overall phase and diagonalized to give Bethe equations that confirm an earlier proposal.
The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
hep-th 2004-07 accept novelty 7.0 of 10

The complete one-loop dilatation operator of N=4 super Yang-Mills is fixed by superconformal symmetry, shown to be integrable in the planar limit, and solved by a Bethe ansatz.
Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
hep-th 2017-10 conditional novelty 6.5 of 10

Adding SU(N) colour factors to the hexagon tessellation prescription makes it reproduce tree-level four-point functions with two non-protected operators, and enables a torus tessellation that captures the leading 1/N ...
The $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathrm{S}^3\times\mathrm{S}^1$ worldsheet S matrix
hep-th 2015-05 conditional novelty 6.0 of 10

The worldsheet S matrix for type IIB strings on AdS3 x S3 x S3 x S1 with mixed R-R and NS-NS flux is fixed by the off-shell symmetry algebra up to dressing phases, and the crossing equations those phases must satisfy ...
On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
hep-th 2014-03 conditional novelty 6.0 of 10

The mirror of the eta-deformed AdS5 x S5 string at deformation parameter theta equals the original string at pi minus theta, and this mirror duality is built into proposed TBA equations for the exact finite-size spectrum.
S-matrix for strings on $\eta$-deformed AdS5 x S5
hep-th 2013-12 conditional novelty 6.0 of 10

The bosonic world-sheet S-matrix of the eta-deformed AdS5 x S5 superstring matches the large-tension limit of the q-deformed S-matrix when q = exp(-nu/g) with nu = 2 eta/(1+eta^2).
Dressing phases of AdS3/CFT2
hep-th 2013-06 conditional novelty 6.0 of 10

The two all-loop dressing phases of the AdS3 x S3 x T4 integrable S-matrix are determined by solving the crossing relations, yielding a BES-like phase plus a new term absent in the higher-dimensional cases.
The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
hep-th 2013-03 conditional novelty 6.0 of 10

A symmetry-based bootstrap fixes the all-loop S-matrix of the psu(1,1|2)^2 spin chain up to two dressing phases, yields new Bethe equations, and states the crossing equations those phases must obey.
Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
hep-th 2013-03 conditional novelty 6.0 of 10

Y-systems are constructed for strong-coupling form factors in AdS5 and for multi-operator form factors in AdS3, extending the Maldacena-Zhiboedov AdS3 single-operator result.
A dynamic su(1|1)^2 S-matrix for AdS3/CFT2
hep-th 2012-11 conditional novelty 6.0 of 10

Using the centrally extended su(1|1)^2 symmetry, the authors fix the two-particle S-matrix of the AdS3/CFT2 spin chain up to four scalar phase factors and identify new scattering channels between magnons of different masses.
Integrable Wilson loops
hep-th 2012-03 conditional novelty 6.0 of 10

An open spin-chain and twisted boundary TBA are proposed as the exact, all-coupling description of the generalized cusp anomalous dimension in N=4 super Yang-Mills.
q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
hep-th 2011-12 conditional novelty 6.0 of 10

The authors derive the q-deformed dressing phase that makes the quantum-group S-matrices for AdS5 x S5 magnons satisfy unitarity and crossing, and show only the mirror version has a correct relativistic limit.
An exact slope for AdS/CFT
hep-th 2011-09 conditional novelty 6.0 of 10

The small-spin slope of the minimal scaling dimension in the sl(2) sector is conjectured to equal the Bessel ratio (sqrt(lambda)/J) I'_J(sqrt(lambda))/I_J(sqrt(lambda)) at all coupling and twist.
Integrability, spin-chains and the AdS3/CFT2 correspondence
hep-th 2011-06 conditional novelty 6.0 of 10

An alpha-deformed Zhukovsky map extends the AdS3 x S3 x S3 x S1 Bethe ansatz to all radius ratios, and the alpha to 1 limit of the resulting spin chain is proposed as a route to massless modes.
Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match
hep-th 2011-04 conditional novelty 6.0 of 10

In the Frolov-Tseytlin classical limit, weak-coupling coherent-state computations of three-point structure constants in planar N=4 SYM reproduce the strong-coupling string result, provided the heavy operators differ b...
Superstrings in AdS(2)xS(2)xT(6)
hep-th 2011-04 conditional novelty 6.0 of 10

The complete AdS2 x S2 x T6 superstring admits a Lax connection to quadratic order in fermions, truncates consistently to the PSU(1,1|2) supercoset, and yields a conjectured asymptotic Bethe ansatz for its massive states.
Wronskian Solution for AdS/CFT Y-system
hep-th 2010-10 conditional novelty 6.0 of 10

The full quantum Y-system of planar AdS5/CFT4 is solved in closed form as Wronskian determinants of eight Baxter Q-functions, with explicit large-size asymptotic expressions.
Twisting the Mirror TBA
hep-th 2010-09 conditional novelty 6.0 of 10

Twisting the transfer matrix extends the mirror TBA to periodic, orbifold and beta-deformed strings, giving explicit wrapping corrections and an exact match between orbifold sl(2) and beta-deformed su(2) magnon energi...
String hypothesis for the AdS_5 x S^5 mirror
hep-th 2009-01 accept novelty 6.0 of 10

In the thermodynamic limit, solutions of the mirror-theory Bethe-Yang equations organize into Hubbard-model-like Bethe strings, yielding equations for bound states and string configurations.
Four loop twist two, BFKL, wrapping and strings
hep-th 2008-11 conditional novelty 6.0 of 10

The four-loop wrapping correction to twist-two anomalous dimensions in N=4 SYM, computed from string theory, cancels the spurious poles in the Bethe ansatz result and reproduces the LO and NLO BFKL predictions.
Integrable Spin Chain in Superconformal Chern-Simons Theory
hep-th 2008-07 accept novelty 6.0 of 10

The two-loop dilatation operator of N=6 superconformal Chern-Simons theory equals an alternating 4/4-bar SU(4) spin chain Hamiltonian derived from the Yang-Baxter equation, establishing two-loop integrability.
Supersymmetric Wilson loops on S^3
hep-th 2007-11 conditional novelty 6.0 of 10

A new almost complex structure on AdS4 x S2 makes the string duals of a family of supersymmetric Wilson loops on S3 pseudo-holomorphic, and loops on S2 appear to reduce to two-dimensional Yang-Mills.
Wrapping interactions at strong coupling -- the giant magnon
hep-th 2007-08 conditional novelty 6.0 of 10

A generalized Lüscher formula, applied to the giant magnon and combined with a Borel-resummed BES/BHL dressing factor, reproduces the known classical string finite-size correction exactly.
The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
hep-th 2006-12 accept novelty 6.0 of 10

The AdS5 x S5 string S-matrix satisfies the standard Yang-Baxter equation in a natural 'string' basis, and Beisert's gauge-theory S-matrix is the same object rewritten in a non-local basis that twists the equation.
Finite-size Effects from Giant Magnons
hep-th 2006-06 accept novelty 6.0 of 10

Finite angular momentum string solitons on AdS5 x S5 are constructed and shown to receive exponential corrections to the giant magnon dispersion relation, with the global symmetry algebra breaking at finite size.
Magnon Bound States and the AdS/CFT Correspondence
hep-th 2006-04 conditional novelty 6.0 of 10

An infinite tower of Q-magnon bound states with dispersion Delta - J1 = sqrt(Q^2 + (lambda/pi^2) sin^2(p/2)) is proposed for planar N=4 SYM, checked against the exact S-matrix pole at Q=2 and against a folded-string s...
A Universality Test of the Quantum String Bethe Ansatz
hep-th 2006-04 conditional novelty 6.0 of 10

Independent su(3)-sector data fix the quantum-string dressing-phase coefficients to the same values conjectured from the sl(2) sector, confirming universality and yielding predictions for non-analytic energy correctio...
On AdS_5 x S^5 String S-matrix
hep-th 2006-04 accept novelty 6.0 of 10

The Hernandez-Lopez dressing phase satisfies Janik's crossing functional equation through second order in the strong-coupling expansion.
Quantum corrections to the string Bethe ansatz
hep-th 2006-03 conditional novelty 6.0 of 10

A conjectured set of coefficients for the first quantum correction to the string Bethe ansatz dressing phase reproduces one-loop corrections to rotating-string energies through order 1/J^13.
Strong coupling from the Hubbard model
hep-th 2006-03 conditional novelty 6.0 of 10

Assuming the Hubbard model describes a sector of planar N=4 super Yang-Mills exactly, the paper derives polynomial equations for the dimensions of the Konishi operator and a dimension-5 operator, giving their strong-c...
Exact expressions for quantum corrections to spinning strings
hep-th 2006-02 conditional novelty 6.0 of 10

Quantum corrections to the spinning string energy on R x S3 include non-analytic and exponentially suppressed terms that the string Bethe ansatz misses, arising from transverse and fermionic fluctuations.

See all 69 Pith citations

How the literature uses it

129 arXiv papers cite this in 205 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 132 sentences without a confident label

Uses its method or tool 1 paper

We can now quantize the above classical Bethe equations using the rules of [ref] , formulated for general $Z_4$–cosets in [ref] .

Superstrings in AdS(2)xS(2)xT(6) · Proposal for asymptotic Bethe ansatz equations for the supercoset sector of states · 0.95

Uses its data or values 3 papers

We only need the first three orders of this expansion: [equation] The first line is the AFS tree-level phase [ref] , the second line is the HL one-loop correction [ref] and the third line is taken from [ref] .

World-sheet scattering in AdS_5 x S^5 at two loops · $(2|2)$ S-matrix · 0.83
At weak coupling it is given by $12λ+…$ while at strong coupling it behaves as $2λ^1/4-4+2/λ^1/4+…$ [ref] .

Following Black Hole States · The $1/16$-th BH Fate · 0.91
The parameter $β=β_2,3^(3)$ is the first non-vanishing component of the dressing phase [ref] , whose value $β=4ζ(3)$ has been computed in [ref] .

Wrapping effects in supersymmetric gauge theories · The asymptotic dilatation operator · 0.93

Compares with it 10 papers

This provides the first nontrivial check that goes beyond the tree level AFS [ref] and one-loop HL [ref] dressing factor terms.

World-sheet scattering in AdS_5 x S^5 at two loops · Introduction · 0.86
We find that contribution to the S-matrix from $δh$ ([ref]) exactly matches the leading (nontrivial) contribution from the $2,3$ component of the phase [ref] ,

Iterative Structure of the N=4 SYM Spin Chain · Tests of the proposal for the leading phase contribution · 0.80
Comparing first to Ahn and Bombardelli's [ref] , for the modes on the left the terms of their equation (2.14) we need are [equation] where $x_p_1^±≈x$ for the virtual particle, $x_p_2^±=$ for the physical giant magnon, and the matrix part is thus [equation] For the scalar factor $S_0$, only the classical AFS [ref] term in the BES phase [ref] matters, giving [equation] Then since $X^+=1/X^-+𝒪(1/g)$ we have agreement with the first two terms of [ref] and of [ref], apart from phases $e^-ip_2/2=√(/)$ for the fermions ($1f$ and $3f$) which will arise from going to the string frame.

Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop · Comparison with S-matrices · 1.00

Cites it as background 56 papers

In [ref] , the all-loop asymptotic Bethe ansatz, extending the BDS ansatz to the whole $𝔭𝔰𝔲(2,2|4)$ algebra, was formulated on the grounds of symmetry considerations leading to a proposal for the complete magnon S-matrix, including the extra factor discussed in [ref] , which was called the dressing factor.

Spiky strings and the AdS/CFT correspondence · The all-loop asymptotic Bethe ansatz · 0.93
In the string limit, this is the famous “dressing phase" which took a lot of work to completely pin down in the magnon theory [ref] .

q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit · Introduction · 0.91
We remind that the ABA equations were constructed in [ref] to reproduce the correct finite gap algebraic curve of [ref] in the scaling limit $L∼K_a∼√(λ)$.

PSU(2,2|4) Character of Quasiclassical AdS/CFT · Classical limit · 0.92

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [11]

N. Beisert, V. Dippel and M. Staudacher, “A novel long range spin chain and planar N = 4 super Yang-Mills,” hep-th/0405001. – 20 –

View on Pith Pith review arXiv

[2] [14]

V. A. Kazakov, A. Marshakov, J. A. Minahan and K. Zarembo , “Classical / quantum integrability in AdS/CFT,” JHEP 0405 (2004) 024 hep-th/0402207

View on Pith Pith review arXiv 2004

[3] [1]

J. M. Maldacena, “The large N limit of superconformal ﬁeld theories and supergravity,” Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113], hep-th/9711200

View on Pith Pith review arXiv 1998

[4] [2]

D. Berenstein, J. M. Maldacena and H. Nastase, “Strings in ﬂat space and pp waves from N = 4 super Yang Mills,” JHEP 0204 (2002) 013, hep-th/0202021

View on Pith Pith review arXiv 2002

[5] [3]

S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “A semi-classical limit of the gauge/string correspondence,” Nucl. Phys. B 636 (2002) 99, hep-th/0204051

View on Pith Pith review arXiv 2002

[6] [4]

S. Frolov and A. A. Tseytlin, “Semiclassical quantization of rotating superstring in AdS5 × S5,” JHEP 0206 (2002) 007, hep-th/0204226; “Multi-spin string solutions in AdS5 × S5,” Nucl. Phys. B 668 (2003) 77, hep-th/0304255; “Quantizing three-spin string solution in AdS5 × S5,” JHEP 0307 (2003) 016, hep-th/0306130; “Rotating string solutions: AdS/CFT duali...

View on Pith Pith review arXiv 2002

[7] [5]

G. Arutyunov, S. Frolov, J. Russo and A. A. Tseytlin, “Spinning strings in AdS5 × S5 and integrable systems,” Nucl. Phys. B 671, 3 (2003), hep-th/0307191; G. Arutyunov, J. Russo and A. A. Tseytlin, “Spinning strings in AdS5 × S5: New integrable system relations,” Phys. Rev. D 69 (2004) 086009, hep-th/0311004

View on Pith Pith review arXiv 2003

[8] [6]

J. A. Minahan and K. Zarembo, “The Bethe-ansatz for N = 4 super Yang-Mills,” JHEP 0303, (2003) 013, hep-th/0212208

View on Pith Pith review arXiv 2003

[9] [7]

N. Beisert, “The complete one-loop dilatation operator of N = 4 super Yang -Mills theory,” hep-th/0307015; N. Beisert and M. Staudacher, “The N = 4 SYM integrable super spin chain,” hep-th/0307042

View on Pith Pith review arXiv

[10] [8]

N. Beisert, C. Kristjansen and M. Staudacher, “The dilatation operator of N = 4 super Yang-Mills theory,” Nucl. Phys. B 664 (2003) 131, hep-th/0303060; N. Beisert, “Higher loops, integrability and the near BMN limit,” hep-th/0308074; N. Beisert, “The su(2 |3) dynamic spin chain,” Nucl. Phys. B 682 (2004) 487, hep-th/0310252

View on Pith Pith review arXiv 2003

[11] [9]

V. M. Braun, S. E. Derkachov and A. N. Manashov, “Integrability of three-particle evolution equations in QCD,” Phys. Rev. Lett. 81 (1998) 2020 hep-ph/9805225. V. M. Braun, S. E. Derkachov, G. P. Korchemsky and A. N. Manash ov, “Baryon distribution amplitudes in QCD,” Nucl. Phys. B 553 (1999) 355 hep-ph/9902375. A. V. Belitsky, “Renormalization of twist-th...

View on Pith Pith review arXiv 1998

[12] [10]

D. Serban and M. Staudacher, “Planar N = 4 gauge theory and the Inozemtsev long range spin chain,” JHEP 0406 (2004) 001, hep-th/0401057

View on Pith Pith review arXiv 2004

[13] [12]

N. Beisert, J. A. Minahan, M. Staudacher and K. Zarembo, “Stringing spins and spinning strings,” JHEP 0309 (2003) 010, hep-th/0306139; N. Beisert, S. Frolov, M. Staudacher and A. A. Tseytlin, “Precision spectroscopy of AdS/CFT,” hep-th/0308117

View on Pith Pith review arXiv 2003

[14] [13]

G. Arutyunov and M. Staudacher, “Matching higher conserved charges for strings and spins,” JHEP 0403 (2004) 004, hep-th/0310182; “Two-loop commuting charges and the string / gauge duality,” hep-th/0403077

View on Pith Pith review arXiv 2004

[15] [15]

J. Engquist, J. A. Minahan and K. Zarembo, “Yang-Mills duals for semiclassical strings on AdS5 × S5”, hep-th/0310188; J. Engquist, “Higher conserved charges and integrability for spinning strings in AdS5 × S5”, JHEP 0404 (2004) 002, hep-th/0402092; M. Smedback, “Pulsating Strings On AdS5 × S5,” hep-th/0405102; L. Freyhult, “Bethe ansatz and ﬂuctuations in...

View on Pith Pith review arXiv 2004

[16] [16]

M. Kruczenski, “Spin chains and string theory,” hep-th/0311203; M. Kruczenski, A. V. Ryzhov and A. A. Tseytlin, “Large spin limit of AdS5 × S5 string theory and low energy expansion of ferromagnetic spin chains,” hep-th/0403120; H. Dimov and R. C. Rashkov, “A note on spin chain / string duality,” hep-th/0403121. R. Hernandez and E. Lopez, “The SU(3) spin ...

View on Pith Pith review arXiv 2004

[17] [17]

A. Khan and A. L. Larsen, “Spinning pulsating string sol itons in AdS5 × S5,” Phys. Rev. D 69, 026001 (2004), hep-th/0310019; A. L. Larsen and A. Khan, “Novel explicit multi spin string solitons in AdS(5),” Nucl. Phys. B 686, 75 (2004) hep-th/0312184; C. Kristjansen, “Three-spin strings on AdS5 × S5 from N = 4 SYM,” Phys. Lett. B 586 (2004) 106, hep-th/04...

View on Pith Pith review arXiv 2004

[18] [18]

J. G. Russo, “Anomalous dimensions in gauge theories from rotating stri ngs in AdS5 × S5,” JHEP 0206 (2002) 038, hep-th/0205244; J. A. Minahan, “Circular semiclassical string solutions on AdS5 × S5,” Nucl. Phys. B 648 (2003) 203 hep-th/0209047; A. V. Belitsky, A. S. Gorsky and G. P. Korchemsky, “Gauge / string duality for QCD conformal operators,” Nucl. P...

View on Pith Pith review arXiv 2002

[19] [19]

C. G. Callan, H. K. Lee, T. McLoughlin, J. H. Schwarz, I. S wanson and X. Wu, “Quantizing string theory in AdS5 × S5: Beyond the pp-wave,” Nucl. Phys. B 673 (2003) 3, hep-th/0307032; C. G. Callan, T. McLoughlin and I. Swanson, “Holography beyond the Penrose limit,” hep-th/0404007

View on Pith Pith review arXiv 2003

[20] [20]

C. G. Callan, T. McLoughlin and I. Swanson, “Higher impurity AdS/CFT correspondence in the near-BMN limit,” hep-th/0405153

View on Pith Pith review arXiv

[21] [21]

V. I. Inozemtsev, “Integrable Heisenberg-van Vleck chains with variable rang e exchange,” Phys. Part. Nucl. 34 (2003) 166 [Fiz. Elem. Chast. Atom. Yadra 34 (2003) 332], hep-th/0201001

View on Pith Pith review arXiv 2003

[22] [22]

R. R. Metsaev, “Type IIB Green-Schwarz superstring in plane wave Ramond-Ram ond background,” Nucl. Phys. B 625 (2002) 70, hep-th/0112044; R. R. Metsaev and A. A. Tseytlin, “Exactly solvable model of superstring in plane wave Ramond -Ramond background,” Phys. Rev. D 65 (2002) 126004, hep-th/0202109

View on Pith Pith review arXiv 2002

[23] [23]

A. Parnachev and A. V. Ryzhov, “Strings in the near plane wave background and AdS/CFT,” JHEP 0210 (2002) 066, hep-th/0208010

View on Pith Pith review arXiv 2002

[24] [24]

T. J. Stieltjes, “Sur Quelques Theoremes d’Algebre,” Oeuvres Completes, vol. 1, p 440, Noordhoﬀ, Groningen, The Netherlands (1914)

View on Pith 1914

[25] [25]

B. S. Shastry, A. Dhar, Solution of a Generalized Stieltjes Problem , cond-mat/0101464

View on Pith Pith review arXiv

[26] [26]

M. L¨ ubcke and K. Zarembo, “Finite-size corrections to anomalous dimensions in N = 4 SYM theory,” JHEP 0405 (2004) 049, hep-th/0405055

View on Pith Pith review arXiv 2004

[27] [27]

S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from non-critical string theory,” Phys. Lett. B 428 (1998) 105, hep-th/9802109

View on Pith Pith review arXiv 1998

[28] [28]

I. Swanson, “On the integrability of string theory in AdS5 × S5,” hep-th/0405172

View on Pith Pith review arXiv

[29] [29]

R. R. Metsaev and A. A. Tseytlin, Type IIB superstring action in AdS5 × S5 background,” Nucl. Phys. B 533 (1998) 109, hep-th/9805028; R. R. Metsaev, C. B. Thorn and A. A. Tseytlin, “Light-cone superstring in AdS space-time,” Nucl. Phys. B 596 (2001) 151, hep-th/0009171. – 22 –

View on Pith Pith review arXiv 1998