Pith. Sign in

REVIEW

Konishi operator at intermediate coupling

PaperPDF from arXiv

data files

ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Sergey Frolov

High Energy Physics - Theory · Submitted 25 Jun 2010 · 75 references

Pith's verdict: A solid, honest numerical push on the Konishi TBA — but the λ_cr > 5300 headline is one fit choice, not a bound, and the author knows it.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 10, 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.

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

How Pith checks papers →

· 3 major objections · 7 minor · Ask about this paper · The compiled record · Read the full review →
Challenge this review Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1006.5032 (version 2)
Pith IDWXQIJ36D, Pith's permanent record of this paper and its review
CitationSergey Frolov. "Konishi operator at intermediate coupling." arXiv:1006.5032 (2010). https://pith.science/paper/WXQIJ36D
Cite this reviewBibTeX for Pith's review of this paper
Claim paper

Why Pith says this

Highlight any text to comment on it.

Referee report

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

The paper

The paper claims

Solving the mirror thermodynamic Bethe ansatz numerically up to 't Hooft coupling $2046$, Frolov argues that the Konishi operator's first critical coupling lies above $5300$ — far beyond the earlier estimate of $774$ — and that its strong-c

The reading

The Konishi operator is the shortest nontrivial operator in maximally supersymmetric Yang–Mills theory, and its anomalous dimension as a function of 't Hooft coupling is a benchmark test of the AdS/CFT correspondence. Frolov solves numerically the excited-state thermodynamic Bethe ansatz equations proposed for two-particle states of the $sl(2)$ sector, reaching $g=7.2$, i.e. $lambda approx 2046$, and uses the solutions to ask whether those equations break down at some critical coupling. The answer he extracts is that the first critical value is most likely above $lambda approx 5300$, roughly seven times the estimate obtained from the large-$J$ asymptotic solution, so the entire range studied is still an intermediate-coupling regime. Fitting the energy to a series in $1/lambda^{1/4}$ reproduces the leading and first subleading coefficients $2$ and $2$, sets the constant and $1/sqrt{lambda}$ terms to zero, but leaves a nonzero $1/lambda$ coefficient, which would mean the strong-coupling expansion is not in powers of $1/sqrt{lambda}$. A by-product is a new integral representation of the BES dressing phase built from elliptic integrals of the third kind, which substantially cuts the computation time.

What carries the argument

The load-bearing object is the set of simplified and hybrid TBA equations for two-particle $sl(2)$ states, which determine the $Y$-functions $Y_{M|w}$, $Y_{M|vw}$, $Y_pm$ and $Y_Q$ together with the exact Bethe equation for the root $w$; the Konishi energy is $E_K = 2 + 2sqrt{1+4g^2sin^2(p/2)} - sum_Q int frac{dtilde p}{2pi} log(1+Y_Q)$. Because the critical coupling is where particular $Y$-functions at $u=0$ vanish ($Y_2$, $Y_pm$, $Y_{1|vw}+1$), the numerics can address the existence of critical values directly rather than by analogy with the asymptotic solution. The technical enabler is a new representation of the BES dressing phase $Theta$ as a one-dimensional integral over $t in [0,1]$ of elliptic $Pi$-functions times $logGamma$ factors, valid in all four string/mirror kinematic regions, plus companion $Psi$-function integrals; this is what makes solving up to $lambda approx 2046$ practical.

Extended reading notes

Core claim

The paper's central claim is that the excited-state TBA equations for Konishi-like states stay valid far beyond the coupling at which the large-$J$ asymptotic $Y$-functions would place a critical point. Solving the equations up to $g=7.2$ and extrapolating the vanishing of $Y_2(0,g)$, $Y_pm(0,g)$ and $Y_{1|vw}(0,g)+1$ gives $g_{rm cr}^{(1)} > 11.6$, that is $lambda_{rm cr}^{(1)} > 5300$ and probably $5300 < lambda_{rm cr}^{(1)} < 5700$, against the earlier estimate $lambda_{rm cr}^{(1)} approx 774$. On the way the data pin down the large-$lambda$ series: imposing $c_{-1}=2$, $c_0=0$, $c_1=2$, $c_2=0$, the remaining coefficients stabilise around $c_3 approx -3.26$, $c_4 approx 2.53$, $c_5 approx 4.03$, giving $E_K = 2lambda^{1/4} + 2/lambda^{1/4} - 3.26/lambda^{3/4} + 2.53/lambda + 4.03/lambda^{5/4}$. That function fits the numerical data as well as the alternative with all even coefficients set to zero, but it has a nonvanishing $c_4$, so the expansion appears to run in powers of $1/lambda^{1/4}$ rather than $1/sqrt{lambda}$.

Load-bearing premise

The fit assumes the large-$lambda$ expansion contains only powers of $1/lambda^{1/4}$ with no $loglambda$ terms, and that exponentially small corrections are already negligible at $lambda lesssim 2046$; the author notes that a $0.0002$ precision floor could by itself account for the nonzero $c_4$.

Editorial extensions

If this is right

  • The first critical coupling of the Konishi operator is $lambda_{rm cr}^{(1)} > 5300$, most likely in the window $5300$–$5700$, rather than the $approx 774$ suggested by the large-$J$ asymptotic solution.
  • The strong-coupling expansion of the Konishi energy is in powers of $1/lambda^{1/4}$ with $c_{-1}=c_1=2$, $c_0=c_2=0$ and $c_4 approx 2.53$ nonzero, so the earlier prediction that only powers of $1/sqrt{lambda}$ appear is not confirmed.
  • The computed energies agree with the earlier canonical-TBA results to about $0.0015$ across the overlapping range, supporting the equivalence of the two TBA formulations for Konishi-like states.
  • The $Y_Q$ contributions to the energy grow nearly linearly with $g$ over the range studied, which raises the possibility that the exact Bethe root asymptotes to a constant below $2$ and that critical values are absent altogether.

Reading between the lines

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

  • If the near-linear growth of the $Y_Q$ energy contribution persists, the exact Bethe root would settle below $2$ while the flat-space string spectrum is still recovered from the Bethe–Yang equations, so either the growth saturates at larger $g$ or the route from TBA to the flat-space spectrum needs rethinking.
  • A nonzero $c_4$ would break the pattern suggested by the free-fermion model of the $su(1|1)$ sector, where the expansion is in $1/lambda^{1/4}$ only up to an overall factor; comparing the fitted $c_4$ against the next order of the semiclassical string expansion would discriminate between the two pictures.
  • The new elliptic-integral form of the dressing phase, combined with a Newton-method solver of the kind used for the Hubbard model, should make $lambda approx 5000$ reachable and turn the extrapolated critical coupling into a measured one.
  • If no critical value exists for Konishi, the equations would remain valid at all couplings, which changes what wrapping corrections mean for short operators and would make the intermediate-coupling regime the generic one rather than a transient.
Original abstract

TBA equations for two-particle states from the sl(2) sector proposed by Arutyunov, Suzuki and the author are solved numerically for the Konishi operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained is used to analyze the properties of Y-functions and address the issue of the existence of the critical values of the coupling. In addition we find a new integral representation for the BES dressing phase which substantially reduces the computational time.

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, 2,961 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.84 · compares with prior results 0.28 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

TBA equations for two-particle states from the sl(2) sector proposed by Arutyunov, Suzuki and the author are solved numerically for the Konishi operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained is used to analyze the properties of Y-functions and address the issue of the existence of the critical values of the coupling. In addition we find a new integral representation for the BES dressing phase which substantially reduces the computational time.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 TBA equations for two-particle states from the sl(2) sector proposed by Arutyunov, Suzuki and the author are solved numerically for the Konishi operator descendent up to 't Hooft's coupling lambda ~ 2046. method 0.50 0.84 0.25 asserted 1.00
s1 The data obtained is used to analyze the properties of Y-functions and address the issue of the existence of the critical values of the coupling. contribution 0.49 0.92 0.18 asserted 0.98
s2 In addition we find a new integral representation for the BES dressing phase which substantially reduces the computational time. contribution 0.73 0.96 0.12 asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.95 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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

Figures
Figure 1. Black dots represent the numerical solution of the TBA equations for the Konishi state energy EK(λ). The brown (upper) curve represents the solution of the Bethe-Yang equation, and the red (lower) curve is the graph of 2√4 λ which is the large λ asymptote of EK(λ). The range of the coupling constant is from g = 0.1, λ = 0.39 to g = 7.2, λ = 2046.56. ææ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æææææææææææææææææææææææææææææææææ 1 2 3 4 5 6 7 g 6 8 10 12 14 16 EKHgL
Figure 2. Here black dots, the brown and red curves are the same as in
Figure 3. This is the graph of the contribution of EY to the energy. It obviously shows a linear growth starting already with g ∼ 2. æ æ æ æ æ ææææ æ æ æ æ æ æ æ æ æ æ æ æ æ æææææææææææææææææææææææææææææææææææææææææææææææ 1 2 3 4 5 6 7 g 1.5 1.6 1.7 1.8 1.9 2.0 2.1 wHgL
Figure 4. The black dots represent our numerical solution of the exact Bethe equation, and the brown curve is the graph of the corresponding solution of the Bethe-Yang equation. The exact Bethe root w(g) reaches its minimum at g ≈ 1, and g ≈ 1.6 is the inflection point. wasym, respectively. The numerical data of the computation of the Bethe root w are in the table (6.2) in Appendix. One sees that w is still pretty far from 2 which is the large g asymptotic value of wasym, and that the exact Bethe root is noticably smaller than wasym. The corresponding exact momentum p is not small at these…
Figure 5. The graphs of the derivative of Edis and EY with respect to g. equations for Konishi-like states [29, 28] might be valid for any value of g. Also, this would mean that the strong coupling limit of multi-particle states with finite number of particles and J (short operators in dual field theory) is very different from the near flat space limit discussed in [59, 64] where the rapidities asymptote to 2, and one can study states with J ∼ √g. The puzzle then is that the full spectrum of string theory in flat space can be reproduced already in the near flat space limit [59], and if w does…
Figure 6. On the left figure graphs of five Y1-functions with different values of g are shown, and on the right figure the graph of Y1(0, g) as a function of g is plotted. case and for g ∼ 7, Y1 increases only as g 3/2 . This behavior is different from both the asymptotic Y1–function g-dependence and the exponential growth required by the scenario discussed above. This also shows clearly that the values of g we have reached are not large enough, and we are still analyzing the intermediate coupling regime. What happens at larger values of g remains to be understood. 3. Y-functions In this…
Figure 7. The graphs of √g∂gY1(0, g) and √g∂gY1(1, g) definitely show that Y1 grows as g 3/2 . 1 2 3 4 5 6 7 g 0.5 1.0 1.5 EY1 1 2 3 4 5 6 7 g 0.05 0.10 0.15 0.20 0.25 ¶gEY1
Figure 8. These are the plots of EY1 and ∂gEY1 . explained by insufficient numerical precision. The scenario with w∞ < 2 would be realized only if ∂gEY1 asymptotes to a positive constant
Figure 9. shows plots of Y2-functions. One sees that they exhibit a rather intricate g dependence. The maximum value of Y2 increases with g and shifts to the right towards u = 2. 0.5 1.0 1.5 2.0 u 0.1 0.2 0.3 0.4 Y2 Hu,gL; g = 1.6, 3.0, 4.4, 5.8, 7.2 1 2 3 4 5 6 7 g 0.01 0.02 0.03 Y2 H0,gL
Figure 10. These are the plots of EY2 and ∂gEY2 . 0.5 1.0 1.5 2.0 2.5u 0.01 0.02 0.03 0.04 0.05 0.06 Y3 Hu,gL; g = 1.6, 3.0, 4.4, 5.8, 7.2 1 2 3 4 5 6 7 g 0.01 0.02 0.03 0.04 Y3 H0,gL
Figure 11. On the left figure graphs of five Y3-functions with different values of g are shown, and on the right figure the graph of Y3(0, g) as a function of g is plotted. Even though Y3 is so small its contribution to the energy is also increasing linearly with g, see
Figure 12. These are the plots of EY3 and ∂gEY3 . Next we discuss Y±-functions, see Figures 13 and 14. The first subcritical value can be also determined from Y± because their values vanish at u = 0, and they are – 12 –
Figure 13. Y−-functions assumed to have the following expansions8 Y±(0, g) ∼ g − g¯ (1) cr + · · · . Using again the linear fit, we get the following results for Y−(0, g) g0 Fit g0 Fit g0 Fit 6.2 0.0035(g − 8.93) 6.3 0.0034(g − 8.98) 6.4 0.0033(g − 9.03) 6.5 0.0033(g − 9.08) 6.6 0.0032(g − 9.13) 6.7 0.0031(g − 9.18) 6.8 0.0030(g − 9.23) 6.9 0.0030(g − 9.28) 7. 0.0029(g − 9.33) (3.3) The results in the table (3.3) are obviously compatible with those in table (3.1) but the estimated subcritical values ¯g (1) cr in (3.3) appear to be slightly less than the ones from (3.1). A better estimate of…
Figure 14. Y+- and Y−-functions are approaching 0 at u = 0 with g increasing. For g > g¯ (1) cr they become positive at u = 0, and asymptote to their ground state value Y gr st ± = 1 for very large g. 0.5 1.0 1.5 2.0 2.5 3.0 3.5 u -1 1 2 3 Y1 vwHu,gL; g = 1.6, 3.0, 4.4, 5.8, 7.2 1 2 3 4 5 6 7 g -0.9 -0.8 -0.7 -0.6 -0.5 Y1 vwH0,gL
Figure 15. Y1|vw-function is approaching −1 at u = 0 with g increasing. It also approaches its ground state value at u = ∞ faster for larger g. mines the first critical value of g because its value at u = 0 has the following behavior in the vicinity of g = g (1) cr Y1|vw(0, g) + 1 ∼ (g − g (1) cr ) 2 + · · · . Using the quadratic fitting function c2(g − g¯ (1) cr ) 2 , we get the following results g0 Fit g0 Fit g0 Fit 6.2 0.0028(g − 11.52)2 6.3 0.0028(g − 11.54)2 6.4 0.0028(g − 11.55)2 6.5 0.0028(g − 11.57)2 6.6 0.0028(g − 11.59)2 6.7 0.0027(g − 11.60)2 6.8 0.0027(g − 11.62)2 6.9 0.002
Figure 16. Y2|vw-function is approaching 0 at u = 0 with g increasing. It also approaches its ground state value at u = ∞ faster for larger g. 1 2 3 4 u 10 20 30 40 50 60 70 Y1 wHu,gL; g = 1.6, 3.0, 4.4, 5.8, 7.2 1 2 3 4 5 6 7 g 10 20 30 40 50 60 70 Y1 wH0,gL
Figure 17. On the left figure graphs of five Y1|w-functions with different values of g are shown, and on the right figure the graph of Y1|w(0, g) as a function of g is plotted. The first subcritical value can be also determined from Y2|vw, see
Figure 18. On the left and right figures the graphs of c−1 and c0 as functions of g1 are plotted. The fitting is done without any constraint imposed on ci . To better visualize the results in
Figure 19. On the left and right figures the graphs of c0 and c1 as functions of g1 are plotted. The fitting is done with c−1 = 2. æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ 4.5 5.0 5.5 6.0 6.5 7.0æ g1 2.02 2.04 2.06 2.08 c1Hg1L æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ 4.5 5.0 5.5 6.0 6.5 7.0 g1 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 c2Hg1L
Figure 20. On the left and right figures the graphs of c1 and c2 as functions of g1 are plotted. The fitting is done with c−1 = 2 and c0 = 0. c0 is to 0 the closer c1 is to 2. One sees that for the range of λ we are analyzing the contribution of the constant term is much smaller than the one of the subleading term c1/ √4 λ and, therefore, it is reasonable to assume that c0 = 0. Fixing now the leading and constant coefficients to be 2 and 0, respectively, one finds the results in table (4.4) and
Figure 21. On the left and right figures the graphs of c2 and c3 as functions of g1 are plotted. The fitting is done with c−1 = 2, c0 = 0 and c1 = 2. However c2 is increasing and becomes very close to 0 for g1 = 6.9. Since the coefficient c1 is so close to 2, let us proceed by fixing c−1 = 2, c0 = 0, and c1 = 2. Then, one obtains the following table and
Figure 22. On the left and right figures the graphs of c2 and c3 as functions of g1 are plotted. The fitting is done with c−1 = 2, c0 = 0 and c1 = 2. To continue we use the average value of c3, and fit the coefficients c4 and c5. Then, we use the average value of c4, and fit the coefficient c5. Finally, taking the average value of c5, we find the following fitting function g0 = 1.4 : EK(λ) = 2√4 λ + 2 √4 λ − 3.26 λ 3/4 + 2.53 λ + 4.03 λ 5/4 . (4.7) Obviously, the fitting function is different from (1.1), in particular the coefficient c4 is not small and gives a significant contribution to the…
Figure 23. Black dots represent the difference between the computed values of the Konishi energy and its fitting function (4.7): ∆EK = EK − EK. Green squares on the left picture represent a similar difference with E GKV K where the fitting function E GKV K (λ) = 2√4 λ + 2 √4 λ − 2.94 λ3/4 + 8.83 λ5/4 is obtained by using our data and setting c−1 = c1 = 2 and c0 = c2 = c4 = 0. On the right picture green squares represent the difference of EK and the fitting function in (1.2). æ æ æ æ æ æ æ æ æ æ æ æ æ æ 0.2 0.4 0.6 0.8 1.0 1.2 1.4g 1 2 3 4 EK - 2 Λ 14 æ æ æ æ æ æ æ æ æ æ æ æ æ æ 0.2 0.4 0.6…
Figure 24. Black dots represent the difference between the energy and its leading large λ asymp￾totic, EK − 2 √4 λ. Red (upper) curve is the graph of EK − 2 √4 λ. Green curve on the left picture is the graph of E GKV K (λ) − 2 √4 λ, and on the right picture it is the difference between the fitting function (1.3) and 2√4 λ. The red curve works very well starting already with g = 0.3, λ = 3.55. computation for g ∼ 7.0 is not 0.0001 but about 0.0002, and if the contribution of exponentially suppressed terms is of order 0.0002 for g ∼ 2, then this could explain the left plot on
Figure 25. The black dots represent the difference between the values of the Konishi energy we obtained and those from [29]. One sees that our results agree with those of [29] with 0.0015 precision for almost all values of g. 5. Conclusion In this paper we solved the TBA equations for the Konishi operator descendent from the sl(2) sector proposed by Arutyunov, Suzuki and the author [28] up to ’t Hooft’s coupling λ ≈ 2046. At this value the iterations converge very slowly. It would be important to improve the numerical algorithm and approach closer to the first critical value of λ, and go…

Figures reproduced from arXiv:1006.5032 by the authors.

References
How later papers used it

47 later papers cite it

Evidence: substantial. 43 of the citing papers share no author with it, and 10 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 71 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 3 papers · 1 by the same authors

  • Used a method similar to the one used in this paper, with the advantage of easily keeping track of the explicit shape of the Y-functions.

    The spectrum of tachyons in AdS/CFT (2013) · 0.95 · paraphrased: the licence does not allow quoting

  • Found the representation of the dressing phase as presented in this paper most convenient in solving the equation numerically.

    Lifting asymptotic degeneracies with the Mirror TBA (2011) · 0.99 · paraphrased: the licence does not allow quoting

By the same authors

  • Used the same code as this paper, with minor modifications, for the J=4, n=1 state beyond its (sub)critical value.

    Scaling dimensions from the mirror TBA (2012) (same authors) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

47 arXiv papers cite this in 71 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 · 48 sentences without a confident label

Uses its method or tool 3 papers
Uses its data or values 3 papers
Compares with it 9 papers
Cites it as background 4 papers

What it cites · 65 sentences without a confident label

Contests 2 papers
Builds on 9 papers
  • The analysis in [ref] was then extended to prove the agreement analytically first for the Konishi operator [ref] , and then for an arbitrary twist-two operator [ref] reproducing the results in [ref] .[The five-loop computations in [ref] were based on [ref] where the four-loop anomalous dimension of the Konishi operator was computed and shown to agree with the direct field theory result [ref] .

    Wrapping at four loops in N=4 SYM · Introduction · 0.84

  • The analysis in [ref] was then extended to prove the agreement analytically first for the Konishi operator [ref] , and then for an arbitrary twist-two operator [ref] reproducing the results in [ref] .[The five-loop computations in [ref] were based on [ref] where the four-loop anomalous dimension of the Konishi operator was computed and shown to agree with the direct field theory result [ref] .

    Four-loop perturbative Konishi from strings and finite size effects for multiparticle states · Introduction · 0.84

  • The analysis in [ref] was then extended to prove the agreement analytically first for the Konishi operator [ref] , and then for an arbitrary twist-two operator [ref] reproducing the results in [ref] .[The five-loop computations in [ref] were based on [ref] where the four-loop anomalous dimension of the Konishi operator was computed and shown to agree with the direct field theory result [ref] .

    The Four-Loop Konishi in N=4 SYM · Introduction · 0.84

Uses the method or tool of 3 papers
  • We solve numerically the excited states TBA equations [ref] for the Konishi operator up to 't Hooft's coupling $λ≈2046$, and use the data obtained to analyze the behavior of Y-functions.

    Exploring the mirror TBA · Introduction · 0.95

  • One possible improvement would be to use Newton's method for solving the TBA equations as it was done for the Hubbard model in [ref] .

    TBA Equations of 1D Hubbard Model and High-Temperature Expansion · Conclusion · 0.99

  • We used in our computation a new integral representation for the BES dressing phase [ref] which significantly reduces the computational time.

    Transcendentality and Crossing · Introduction · 1.00

Uses data or values from 1 paper
  • Analyzing the results obtained, the authors of [ref] found the following fitting function for the Konishi state energy or, equivalently, for the conformal dimension of the dual Konishi operator E_K^GKV()=√()(2.0004+1.988/ √()-2.60/+6.2/^3/2) .

    Exact AdS/CFT spectrum: Konishi dimension at any coupling · Introduction · 0.95

Compares with 7 papers
  • These terms are known to appear in the strong coupling expansion of the Bethe-Yang equations [ref] .] we found convincingly that the first nontrivial subleading coefficient $c_1$ is equal to 2 and the coefficient $c_2$ vanishes in agreement with the previous prediction [ref] .

    Exact AdS/CFT spectrum: Konishi dimension at any coupling · Conclusion · 0.80

  • These terms are known to appear in the strong coupling expansion of the Bethe-Yang equations [ref] .] we found convincingly that the first nontrivial subleading coefficient $c_1$ is equal to 2 and the coefficient $c_2$ vanishes in agreement with the previous prediction [ref] .

    On the strong coupling expansion in the su(1|1) sector of N=4 SYM · Conclusion · 0.80

  • These terms are known to appear in the strong coupling expansion of the Bethe-Yang equations [ref] .] we found convincingly that the first nontrivial subleading coefficient $c_1$ is equal to 2 and the coefficient $c_2$ vanishes in agreement with the previous prediction [ref] .

    Konishi at strong coupling from ABE · Conclusion · 0.80

Cites as background 8 papers
  • It is known that at large values of 't Hooft's coupling the energy of the Konishi state can be expanded in an asymptotic series in powers of $1/ √()$ asexp E_K()=2 √()+c_0+c_1/ √()+c_2/√()+c_3/^3/4+c_4/+c_5/^5/4+ ⋯ , where the leading $2 √()$ behavior follows from the string spectrum in flat space [ref] , and can be reproduced from the asymptotic Bethe ansatz [ref] .

    Bethe Ansatz for Quantum Strings · Konishi state energy · 0.89

  • It is known that at large values of 't Hooft's coupling the energy of the Konishi state can be expanded in an asymptotic series in powers of $1/ √()$ asexp E_K()=2 √()+c_0+c_1/ √()+c_2/√()+c_3/^3/4+c_4/+c_5/^5/4+ ⋯ , where the leading $2 √()$ behavior follows from the string spectrum in flat space [ref] , and can be reproduced from the asymptotic Bethe ansatz [ref] .

    Gauge Theory Correlators from Non-Critical String Theory · Konishi state energy · 0.89

  • The large $λ$ perturbative expansion of the light-cone string sigma model (see [ref] for a review) allows one to have any of the coefficients $c_i$ nonvanishing.

    Foundations of the AdS_5 x S^5 Superstring. Part I · Konishi state energy · 0.91

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.