Five-loop Konishi from the Mirror TBA

Gleb Arutyunov; Ryo Suzuki; Sergey Frolov

REVIEW

Five-loop Konishi from the Mirror TBA

Gleb Arutyunov, Sergey Frolov, Ryo Suzuki

High Energy Physics - Theory · Submitted 9 Feb 2010 · 41 references

Pith's verdict: A careful, honest consistency check of the mirror TBA at five loops — the number is borrowed, the TBA-side machinery is the contribution, and the abstract oversells the precision slightly.

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arXiv ID1002.1711 (version 2)

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CitationGleb Arutyunov, Ryo Suzuki, Sergey Frolov. "Five-loop Konishi from the Mirror TBA." arXiv:1002.1711 (2010). https://pith.science/paper/ERLB2N54

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Editor's note

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Bottom line: this is a validation paper, not a new-result paper, and it's a good one. The five-loop Konishi anomalous dimension is quoted from Bajnok-Hegedus-Janik-Lukowski [30]; what Arutyunov-Frolov-Suzuki actually do is linearize the simplified mirror TBA around the asymptotic solution, solve numerically for the auxiliary Y_{1|vw}, and show that the resulting order-g^8 correction δR_k to the asymptotic Bethe equations cancels the Lüscher-side Φ^(8) (eq. 3.10). That is a real piece of work — the coupled TBA system is not something you can eyeball, and getting a clean numerical handle on Y_{1|vw} through the iteration (2.17) is the substance here. The closing observation that Φ^(8) can be written as -Σ∫(1/4π)∂_w Y^o_M (eq. 3.12) is the most interesting line in the paper and deserves more than the one paragraph it gets; it hints at a transfer-matrix structure that might generalize beyond Konishi, and the authors flag the distinction from the trace-of-derivative-S-matrix form honestly in the footnote and closing paragraph. Credit where due: the linearization is laid out explicitly, the kernels are given, and the comparison is done term by term rather than as a black-box total, which is the right way to expose a discrepancy if one existed. On the soft spots: the abstract's 'perfectly agrees' [abstract:s1] is a bit ahead of Table 1, where the relative agreement degrades from 5×10^{-8} at M=2 to about 1% at M=6. The stress-test note is right that there's no convergence study, grid size, or residual analysis. But the absolute residuals sit at a roughly constant 10^{-8}–10^{-9} across M, which reads like a fixed precision floor rather than a growing disagreement, and the total is dominated by the well-converged M=2 term. So the concern is real but modest, and I would not weight it heavily. The reader's 'circularity' worry I'd push back on: yes, both routes descend from the same mirror S-matrix, but the TBA is a coupled integral system and the Lüscher formula is a perturbative diagrammatic expansion — showing they agree is not trivial even inside one framework. The authors themselves say an analytic proof would be important, so that limitation is acknowledged, not hidden. The uniqueness of the iteration (text after eq. 2.17) is asserted rather than proved, but the banded, exponentially decaying kernel makes non-uniqueness implausible. Who should read it: anyone working on the exact-spectrum program, and anyone who wants a worked example of how to linearize an excited-state TBA. Worth a serious referee — the technical content is solid and the check is the kind of thing the subfield needs on record.

Referee report

Significance

This is a useful and timely consistency check of the mirror TBA at the first order (g^8) at which the auxiliary Y-functions contribute non-trivially to the modification of the asymptotic Bethe ansatz; at four loops the leading finite-size correction is already built into the excited-state TBA, so five loops is the first genuinely non-trivial test. The comparison is falsifiable and is carried out term-by-term in the Y_M expansion, which is the right level of granularity for diagnosing a mismatch. The paper is also candid about its scope: it states in the introduction that the task reduces to showing that the TBA correction agrees with Φ^(8) of Ref. [30], and it states that an analytic proof would be important. Two caveats temper the significance. First, the TBA and the generalized Lüscher formulae both descend from the same mirror S-matrix and the same asymptotic Y-functions (Eq. 2.9), so the agreement is a check of internal consistency of the TBA system rather than a comparison of two independent first-principles derivations; the non-triviality lies in the fact that the two expressions (3.9) and (3.11) look structurally different. Second, the paper does not itself compute Δ^(10);it

Major objections (3)

[Abstract, sentence s1; Table 1] The abstract states that the TBA result 'perfectly agrees' with the Lüscher result, but Table 1 shows the relative difference growing monotonically from about 4.8×10^-6 at M=2 to about 9.6×10^-3 at M=6. The authors attribute this to the higher-M contributions being small and requiring more computing time, but no grid size, discretization, iteration truncation criterion, or residual analysis is given anywhere in the paper. The absolute residuals in Table 1 are not constant: they fall from about 5.2×10^-8 at M=2 to about 4.7×10^-10 at M=6, so the degradation in relative terms cannot be dismissed simply as a fixed precision floor. Without an error budget the reader cannot distinguish 'agreement to numerical precision' from 'agreement to the precision achieved here,' and the word 'perfectly' in the abstract is not calibrated by the evidence presented. Please supply a convergence study (e.g., variation of the result with grid spacing and iteration depth) and either quantify the achieved precision or soften the abstract wording to something like 'agrees within numerical precision'.
[Table 1; Eqs. (3.9)–(3.11)] The central claim of the paper is Eq. (3.10), δR_k + Φ^(8)(u_k) = 0, which concerns the full quantities δR_1 and −Φ^(8)(u_1). Table 1, however, compares only the individual Y_M contributions, and the M=1 term is asserted to match 'trivially' without being shown. Since the sum is dominated by M=2, the omission of the summed comparison is not likely to change the conclusion, but it is the quantity named in Eq. (3.10) and should be reported explicitly, together with an estimate of the truncation error from dropping M>6. Relatedly, the decomposition of the Y_{1|vw} contribution into the pieces Y^[M]_{1|vw} defined in Eq. (2.17) should be justified in one sentence: by linearity of Eq. (2.13) the sum over n reproduces Y_{1|vw}, but the text does not spell this out, and a reader could be left with the impression that the comparison is being made between different objects.
[Text following Eq. (2.17); Eq. (2.13)] The text after Eq. (2.17) states that the solution is 'unambiguously well-defined provided that the homogeneous equation has only the trivial solution Y_{M|vw} = 0,' but this proviso is neither proved nor checked numerically. Because Y_{1|vw} feeds directly into δR_k through Eq. (3.9), the uniqueness of the solution is load-bearing for the comparison with Φ^(8): if the homogeneous equation admitted a non-trivial solution, the extracted Y_{1|vw} would be ambiguous and the agreement in Table 1 would not be well defined. The banded, exponentially decaying kernel makes non-uniqueness implausible, and Figure 1 is consistent with convergence, but the paper should either give an argument (for example, from the spectrum of the kernel Ω in Eq. 2.14) or demonstrate numerically that the iteration converges to the same solution from different initial guesses and grid sizes.

Minor objections (9)

[Title; Abstract, sentence s0] The title and the abstract's first sentence read as if the five-loop anomalous dimension is derived in this paper, whereas the body is explicit that the number follows from Ref. [30] once the TBA correction is shown to match Φ^(8). The introduction states this clearly, so this is a matter of framing, but rewording the title or the abstract's first sentence to reflect that the paper establishes the equivalence of the two routes would better match the content.
[Table 1, 'Lüscher' column] The caption should state explicitly that the entries in the 'Lüscher' column are computed here from Eq. (3.11) and are not taken from Ref. [30], and that the entries in the 'TBA' column exclude the first line of Eq. (3.9) and the first term of Eq. (3.11), as the caption already notes for the latter.
[Eq. (2.9)] The expansion of Y^o_Q in Eq. (2.9) is written through O(g^10), while the text below Eq. (2.7) states that the next corrections to Y^o_Q start from g^16. Please clarify whether the O(g^10) term in (2.9) is needed anywhere or is retained only for completeness.
[Eq. (2.10)] At w = 1/√3 the expression (w^2−3)/(w^2+1) equals −2, so the asymptotic values Y^o_+ = Y^o_- are negative. A brief remark on the sign convention for the asymptotic y-particle Y-functions would help the reader, since Y-functions are usually positive.
[Figure 1] The caption does not state the value of w used, the range of u plotted, or the normalization of the vertical axis beyond the division by g^8. These should be given so the figure can be reproduced.
[Eq. (3.9), footnote 3] The footnote explains that the principal value prescription can be dropped because A_{1|vw} vanishes at u = u_k. It would be clearer to state in the main text that the integrand is regular at u = u_k, rather than only in the footnote.
[Eq. (3.12) and footnote 4] The closing observation that the transfer-matrix expression and the S-matrix-derivative expression 'must be distinguished in the general situation' is intriguing but unexplained. One or two sentences indicating what distinguishes them, or in what class of observables they are expected to differ, would make the remark useful rather than cryptic.
[Introduction] The statement that 'the exact Bethe equations at order g^8 involve a leading correction to a single auxiliary function Y_{1|vw}' deserves a sentence of justification, since Eq. (3.1) also contains Y_{M|w} and Y_±; the text later argues that Y_{M|w} starts at g^10 and that the Y_± convolutions are higher order, but this reasoning is spread across Sections 2 and 3 and would be clearer if collected.
[Typesetting] There are several minor typesetting issues: the author name 'L¨ uscher' is broken across a space in the abstract and elsewhere; spacing is missing in places such as 'eqs.(2.6)' and 'the latter being given'; and the reference list uses inconsistent formatting for arXiv numbers. These do not affect the physics.

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The paper

The paper claims

The mirror thermodynamic Bethe ansatz, linearized around the Konishi state, reproduces the five-loop correction to the asymptotic Bethe equations obtained independently from generalized Lüscher formulae, term by term in the auxiliary $Y$-fu

The reading

This paper asks whether the thermodynamic Bethe ansatz (TBA) for the mirror of the $AdS_5$ x $S^5$ superstring — the current candidate for an exact spectrum of planar $N=4$ super Yang-Mills — reproduces the five-loop anomalous dimension of the Konishi operator that was obtained by an entirely different route, the generalized Lüscher (finite-volume) formulae. The authors do not recompute the five-loop number itself; they isolate the single new ingredient, the order-$g^8$ correction $R_k$ to the asymptotic Bethe-Yang equations, and show numerically that $R_k + (8)(u_k) = 0$ holds against the Lüscher-derived $(8)$ of the earlier work. The check matters because five loops is the first order at which the auxiliary $Y$-functions of the TBA — not just the main $Y_Q$'s fixed by infinite-volume scattering data — feed into the answer. Agreement means the coupled TBA system is behaving exactly as the perturbative finite-size expansion demands, which is the sharpest available test of the proposed spectral equations at weak coupling.

What carries the argument

The load-bearing object is the linearized TBA kernel $Omega_{QM}(u,v) = delta_{QM} delta(u-v) - delta_{Q,M-1} A_{M-1|vw}(u) s(u-v) - delta_{Q,M+1} A_{M+1|vw}(u) s(u-v)$, with $A_{M|vw} = Y^o_{M|vw}/(1+Y^o_{M|vw})$ taking the explicit rational form given in the text and $s(u) = 1/(4 cosh(pi u/2))$. Inverting or iterating this kernel converts the known asymptotic $Y^o_{M+1}$ into the correction $Y_{M|vw}$, and only $Y_{1|vw}$ is needed because the exact Bethe equation in the representation used here contains no $Y_{M|w}$ at all and only $Y_{1|vw}$ from the $M|vw$ tower. The second piece of machinery is the exact Bethe equation itself, quoted from the authors' earlier hybrid-TBA derivation, whose imaginary part is written as $pi(2n_k+1) = J p_k + i sum_j log S^{sl(2)}_{1*1*}(u_j,u_k) + R_k$; the statement that $R_k$ vanishes asymptotically for any $g$ is what allows the shift from the asymptotic rapidities to be discarded, leaving $R_k$ alone as the object to compare.

Extended reading notes

Core claim

The authors linearize the simplified mirror TBA equations around the large-$J$ asymptotic solution, writing each $Y$-function as $Y^o(1+Y)$, and then expand further in the coupling with $J$ fixed to 2 (the Konishi value). They show that at order $g^8$ only the $M|vw$-string functions survive: the $M|w$-strings and the $y$-particle combinations enter at $g^{10}$ or higher, and the $Q$-particle equations would only correct $Y^o_Q$ at $g^{16}$. The surviving linear system, $Y_{M|vw} = (A_{M-1|vw}Y_{M-1|vw} + A_{M+1|vw}Y_{M+1|vw}) * s - Y^o_{M+1} * s$, is solved numerically by iterating an inhomogeneous version, and the resulting $Y_{1|vw}$ is inserted into the exact Bethe equation in the representation of the authors' earlier work. In this way they obtain the order-$g^8$ shift $R_k$ as an explicit sum of convolutions of the asymptotic $Y^o_M$ with known kernels plus a term built from $A_{1|vw}Y_{1|vw}$. Comparing with the Lüscher-side quantity $(8)$ of the earlier five-loop paper, they find that the individual contributions attached to each $Y^o_M$ agree numerically, with absolute differences of order $10^{-8}$ to $10^{-10}$ for $M = 2$ through $6$ and relative differences from about $5$ x $10^{-6}$ at $M=2$ growing to about $10^{-2}$ at $M=6$, the degradation attributed to the smallness of the higher-$M$ contributions. The paper closes with an observation: the Lüscher expression can be rewritten as $-sum_M int du, partial_w Y^o_M(u)/(4)$, a derivative of the transfer matrix with the level-matching condition imposed first, resembling a known result in the $O(4)$ model, whereas the generalized Lüscher formula involves the trace of the derivative of the $S$-matrix with respect to the mirror rapidity; the two coincide here but the authors state they must be distinguished in general.

Load-bearing premise

The numerical iteration that produces $Y_{1|vw}$ is assumed to converge to the unique solution of the linearized equation, which the authors state requires the homogeneous equation to admit only the trivial solution; if that failed, the extracted correction would be ambiguous and the comparison with the Lüscher result would not be well defined.

Editorial extensions

If this is right

The five-loop Konishi anomalous dimension quoted from the Lüscher computation, including its $g^{10}$ coefficients in $zeta(3)^2$, $zeta(3)$, $zeta(5)$, $zeta(7)$ and a rational term, gains independent support from the TBA side.
Because auxiliary $Y_{M|vw}$ functions first contribute at order $g^8$, any weak-coupling treatment of wrapping that keeps only the main $Y_Q$'s will miss the five-loop correction; the coupled system cannot be truncated at that order.
The correction can be recast as a transfer-matrix derivative, $-sum_M int du, partial_w Y^o_M(u)/(4)$, giving a compact form for the finite-size shift that parallels a known result in the $O(4)$ model.
The same machinery extends to other twist-two operators, so the reciprocity and BFKL constraints imposed on the five-loop twist-two dimensions become checkable against the TBA at the same order.

Reading between the lines

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

If the numerical match can be promoted to an analytic identity, the TBA and the Lüscher resummation would be two computations of one and the same quantity, and the auxiliary $Y$-system would be the natural bookkeeping device for wrapping corrections at all orders rather than only the first few.
The distinction the authors flag between the transfer-matrix derivative and the trace of the $S$-matrix derivative is a live fork: for states other than Konishi the two prescriptions should give different answers, which would be a sharp and cheap discriminator between candidate all-order formulae.
A direct five-loop field-theory computation of the Konishi anomalous dimension, once available, would be the arbiter if the two methods ever disagreed; the present agreement is a consistency check between two approximations of the same integrable structure, not an external measurement.
The precision loss at higher $M$ is a numerical artifact of small contributions, but it also hints that a resummed treatment of the $M$ tower would be more informative than a term-by-term comparison.

Original abstract

We use the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model to derive the five-loop anomalous dimension of the Konishi operator. We show numerically that the corresponding result perfectly agrees with the one recently obtained via the generalized Luscher formulae. This constitutes an important test of the AdS/CFT TBA system.

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, 2,895 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.19 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We use the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model to derive the five-loop anomalous dimension of the Konishi operator. We show numerically that the corresponding result perfectly agrees with the one recently obtained via the generalized Luscher formulae. This constitutes an important test of the AdS/CFT TBA system.

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 use the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model to derive the five-loop anomalous dimension of the Konishi operator.	contribution 0.70	0.96	0.49	asserted 1.00
s1	We show numerically that the corresponding result perfectly agrees with the one recently obtained via the generalized Luscher formulae.	result 0.99	0.93	0.27	asserted 1.00
s2	This constitutes an important test of the AdS/CFT TBA system.	interpretation 1.00	0.47	0.37	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.53.

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.** In the upper picture the profiles of the functions Y1|vw/g8 (blue) and Y2|vw/g8 (purple) are depicted. They are obtained by solving numerically eq.(2.13). The lower picture contains the profiles of YM|vw/g8 for M = 2, 3, 4, 5. The absolute value of YM|vw decreases as M increases. • M|vw-strings: M ≥ 1 , Y0|vw = 0 YM|vw = (AM−1|vwYM−1|vw + AM+1|vwYM+1|vw) ⋆ s − Y o M+1 ⋆ s. (2.11) • y-particles Y+ = Y− 2Y+ = 2A1|vwY1|vw ⋆ s − Y o Q ⋆ s + 2Y o Q ⋆ KQ1 xv ⋆ s , (2.12) where all the TBA kernels are taken at their leading order. In fact, as we will see below, the correction to th

Figures reproduced from arXiv:1002.1711 by the authors.

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N. Beisert, V. Dippel and M. Staudacher, “A novel long ra nge spin chain and planar N = 4 super Yang-Mills,” JHEP 0407 (2004) 075 [arXiv:hep-th/0405001]. – 13 –

View on Pith Pith review arXiv 2004
[37]

N. Beisert, “The su(2 |2) dynamic S-matrix,” Adv. Theor. Math. Phys. 12 (2008) 945 [arXiv:hep-th/0511082]

View on Pith Pith review arXiv 2008
[38]

P. Dorey and R. Tateo, “Excited states by analytic conti nuation of TBA equations,” Nucl. Phys. B 482 (1996) 639 [arXiv:hep-th/9607167]

View on Pith Pith review arXiv 1996
[39]

P. Dorey and R. Tateo, “Excited states in some simple per turbed conformal ﬁeld theories,” Nucl. Phys. B 515 (1998) 575 [arXiv:hep-th/9706140]

View on Pith Pith review arXiv 1998
[40]

G. Arutyunov and S. Frolov, “The Dressing Factor and Cro ssing Equations,” J. Phys. A 42 (2009) 425401 [arXiv:0904.4575 [hep-th]]

View on Pith Pith review arXiv 2009
[41]

N. Gromov, V. Kazakov and P. Vieira, “Finite Volume Spec trum of 2D Field Theories from Hirota Dynamics,” JHEP 0912 (2009) 060 [arXiv:0812.5091 [hep-th]]. – 14 –

View on Pith Pith review arXiv 2009

Forward citations

Cited by 17 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Quantum spectral curve for AdS_5/CFT_4
hep-th 2013-05 conditional novelty 8.0 of 10

A finite nonlinear Riemann-Hilbert system on four Q-functions and a 4x4 matrix replaces the infinite TBA equations for the planar N=4 SYM spectrum.
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.
Solving the AdS/CFT Y-system
hep-th 2011-10 conditional novelty 7.0 of 10

The infinite AdS5/CFT4 Y-system is reduced to a finite set of nonlinear integral equations using analyticity and a quantum Z4 symmetry, and checked against Konishi-operator numerics.
TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
hep-th 2011-08 accept novelty 7.0 of 10

Two independent finite-volume methods, Lüscher corrections and the thermodynamic Bethe ansatz, agree exactly for the ground-state energy of twisted AdS/CFT, yielding the first double-wrapping correction and a six-loop...
Exploring the mirror TBA
hep-th 2009-11 conditional novelty 7.0 of 10

Excited-state mirror TBA equations for sl(2) two-particle states are state-dependent and change form at infinitely many critical values of the 't Hooft coupling, the first for Konishi estimated near lambda of about 774.

Show 12 more citing papers

T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
hep-th 2015-10 conditional novelty 6.0 of 10

A Grassmannian exterior-form formalism solves the Hirota T-system on T-hooks and yields a twisted Quantum Spectral Curve that reproduces the gamma-twisted BMN vacuum energy at single-wrapping order.
Cutting through form factors and cross sections of non-protected operators in N=4 SYM
hep-th 2014-10 accept novelty 6.0 of 10

A correction rule lets on-shell unitarity compute Konishi form factors in D=4-2epsilon, yielding two-loop two-point and one-loop three-point results and an infrared-finite decay rate whose logarithm gives the known tw...
Correlation functions of local composite operators from generalized unitarity
hep-th 2012-09 accept novelty 6.0 of 10

Generalized unitarity, previously used for scattering amplitudes, is extended to compute momentum-space correlation functions of local operators, yielding new n-point correlators of BPS and twist-2 operators in N=4 su...
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.
Quantum folded string and integrability: from finite size effects to Konishi dimension
hep-th 2011-02 conditional novelty 6.0 of 10

The Konishi operator's anomalous dimension at strong coupling is derived analytically as 2λ^{1/4} - 4 + 2/λ^{1/4}, confirming earlier numerical Y-system predictions.
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...
Konishi operator at intermediate coupling
hep-th 2010-06 conditional novelty 6.0 of 10

Solving the Konishi TBA equations numerically up to λ ≈ 2046 pushes the first critical coupling above 5300 and indicates a nonzero 1/λ term in the strong-coupling expansion.
Extended Y-system for the $AdS_5/CFT_4$ correspondence
hep-th 2010-05 conditional novelty 6.0 of 10

The AdS5/CFT4 TBA equations, including the dressing kernel, follow from the Y-system supplemented by local square-root discontinuity relations via Cauchy's theorem.
Towards integrability for AdS3/CFT2
hep-th 2014-06 accept novelty 3.0 of 10

A self-contained review that assembles, from previously published work, the symmetry-fixed all-loop S matrix and Bethe ansatz for massive AdS3 x S3 x T4 string excitations, including a crossing-symmetric proposal for ...
Integrability of the AdS_5 x S^5 superstring and its deformations
hep-th 2013-10 unverdicted novelty 2.0 of 10

The review organizes how integrability and the thermodynamic Bethe ansatz give exact finite-volume spectra for the AdS5 x S5 superstring and several integrable deformations.
DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
hep-th 2019-08 unverdicted

A review of known results on DGLAP and BFKL equations in N=4 SYM, from weak-coupling perturbation theory to strong coupling via AdS/CFT and integrability, with no new derivations.

How later papers used it

54 later papers cite it

Evidence: substantial. 44 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 13 of the 84 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

1 paper by the same authors is listed below: 1 used its method or tool.

Uses its method or tool 1 of 3 papers with this label · 1 by the same authors

By the same authors

Followed the same strategy as this paper by employing the exact Bethe equations in their hybrid form.

Twisting the Mirror TBA (2010) (same authors) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

54 arXiv papers cite this in 84 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 2 papers

Using the linearized TBA equations recently obtained in [arXiv:1002.1711] we show analytically that the 5-loop anomalous dimension of the Konishi operator agrees with the result obtained previously from the generalized Luscher formulae.

5-loop Konishi from linearized TBA and the XXX magnet · 0.96
We obtain an analytic result at five loops in the planar limit and observe perfect agreement with the prediction based on integrability in AdS/CFT.

Five-loop Konishi in N=4 SYM · 0.85

Papers citing it · 66 sentences without a confident label

Contests it 1 paper

This will be given by the solution of the following linearized set of TBA equations: [We note that in [ref] there is an erroneous term in Eq. (2.7): $-Y^0_Q⋆s$ should be instead $-Y^0_Q⋆K_Q$, as in ([ref]).] [equation] where [equation]

TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT · NLO expansion · contest 0.90

Builds on it 1 paper

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] .

Konishi operator at intermediate coupling · Introduction · 0.84

Uses its method or tool 3 papers

[ref] and the coefficient functions $D_m(u)$ are the inverses of the functions $A_m|vw(u)$ given by ([ref]).

5-loop Konishi from linearized TBA and the XXX magnet · Linearized TBA equations · 0.94
Rescaling the variables $u→u/g$, $u_k→u_k/g$, $r̂^(m)_j→ξ_m;j/g$ and $δr^(m)_j→δξ_m;j/g$ and making similar considerations as in [ref] and [ref] it can be shown that the Bethe equations ([ref]) up to $O(g^8)$ can be expressed by the leading $O(g^8)$ expressions of the $Y^o_Q$ functions and with the solution of a linear problem coming from ([ref]).

The Bajnok-Janik formula and wrapping corrections · The Bajnok-Janik formula · 0.93
Following the same strategy as employed in [ref] , we employ the exact Bethe equations in their hybrid form ([ref]).

Twisting the Mirror TBA · Quantization of momentum and exact Bethe equation · 0.98

Compares with it 5 papers

In this manner, we obtain an analytic result for the Konishi anomalous dimension at five loops in planar $𝒩=4$ SYM theory and observe perfect agreement with the prediction based on integrability in AdS/CFT [ref] .

Five-loop Konishi in N=4 SYM · Introduction · 0.97
Our computations check the complete (both horizontal and vertical parts of the) $Y$-system, and go beyond the five-loop calculations presented in [ref] , which checked at the single wrapping order only the vertical part.

TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT · Conclusion · 0.83
The task is much more complicated than in the case of the Konishi operator [ref] because in ([ref]) the correction $δr_0$ appears explicitly, together with $𝒴_1|vw$.

Exceptional Operators in N=4 super Yang-Mills · Cancellation of the most $ϕ$-divergent terms · 0.91

Cites it as support 1 paper

Even more impressively, it lead to correct predictions for the dimension of the Konishi operator both at large [ref] and at small [ref] 't Hooft coupling.

First-principles derivation of the AdS/CFT Y-systems · Introduction · 0.96

Cites it as background 3 papers

These equations were proposed in [ref] , following the discovery of the Y-system [ref] , and passed a number of important checks [ref] .

Solving the AdS/CFT Y-system · Equivalence of FiNLIE to the TBA equations · 0.97
On the other hand, the Thermodynamic Bethe Ansatz based on the mirror theory [ref] was advanced as a tool to capture the exact string spectrum in both the 't Hooft coupling constant $λ$ and the size $L$ of the system [ref] .

On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra · Introduction · 0.83
In the result of such investigations the set of TBA equations and the Y-system were formulated [ref] .

Twist-2 at five loops: Wrapping corrections without wrapping computations · Introduction · 0.84

What it cites · 29 sentences without a confident label

Uses the method or tool of 4 papers

We exploit here the exact Bethe equations in a different representation which is derived from the hybrid TBA equation for $Y_1$ discussed in [ref] . ] admit the following representation π(2n_k+1) = L p_k +i∑_j=1^N logS_(2)^1_*1_*(u_j,u_k) +Im U ExactBAEIm - 2∑_M=1^∞log(1+Y_M )⋆( Im K^Σ_M1_* - s⋆Im K_vwx^M-1,1_* ) + 2 log(1+Y_1|vw)⋆(Im s̃-i s ⋆̂ K^y1_*) - 2log1-Y_-1-Y_+s⋆Im K^11_*_vwx -ilog(1- 1/Y_-)(1- 1/Y_+) K^y1_* .

Exploring the mirror TBA · Correction to the asymptotic Bethe equations · 0.89
In what follows it is convenient to use the simplified TBA equations derived in [ref] .

Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model · Linearizing the TBA system · 0.99
In what follows it is convenient to use the simplified TBA equations derived in [ref] .

Simplified TBA equations of the AdS_5 x S^5 mirror model · Linearizing the TBA system · 0.99

Uses data or values from 1 paper

According to [ref] , the quantity $Φ^(8)$ was found to be Φ^(8)(u_k)=∑_M=1^∞∫_-∞^∞du Y_M^o(u)× ×1/π[ -u-u_k/(M+1)^2+(u-u_k)^2-u-u_k/(M-1)^2+(u-u_k)^2+u_k/-1+M^2+u^2-u_k^2] .

Five loop Konishi from AdS/CFT · Correction to the asymptotic Bethe equations · 0.87

Compares with 2 papers

Then, using this result for $Y_1|vw$ we evaluate numerically the correction to the exact Bethe equations and find that it agrees with $Φ^(8)$ of [ref] with a sufficiently high precision.

Five loop Konishi from AdS/CFT · Introduction · 0.97
The right hand side involves the derivative of the transfer matrix, and looks similar to the known result for the $O(4)$ model [ref] .

Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics · Correction to the asymptotic Bethe equations · 0.87

Cites as background 4 papers

Recently there has been interesting progress on its precise formulation and in deriving some consequences of the corresponding spectral equations [ref] - [ref] .

String hypothesis for the AdS_5 x S^5 mirror · Introduction · 0.98
Recently there has been interesting progress on its precise formulation and in deriving some consequences of the corresponding spectral equations [ref] - [ref] .

Exploring the mirror TBA · Introduction · 0.98
The mirror Thermodynamic Bethe Ansatz (TBA) is generalization of the relativistic TBA [ref] and offers a tool to determine the spectrum of the $$ superstring [ref] .

On String S-matrix, Bound States and TBA · Introduction · 0.96

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.

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