5-loop Konishi from linearized TBA and the XXX magnet

Arpad Hegedus; Janos Balog

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5-loop Konishi from linearized TBA and the XXX magnet

Janos Balog, Arpad Hegedus

High Energy Physics - Theory · Submitted 22 Feb 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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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. The proof is based on the relation between this linear system and the XXX model TBA equations.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	result 0.81	0.91	0.93	asserted 1.00
s1	The proof is based on the relation between this linear system and the XXX model TBA equations.	method 0.99	0.49	0.07	asserted 1.00

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Original abstract

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. The proof is based on the relation between this linear system and the XXX model TBA equations.

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References

Forward citations

Cited by 13 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...
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...

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Integrability, spin-chains and the AdS3/CFT2 correspondence
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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.
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.

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42 arXiv papers cite this in 73 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 1 paper

We show numerically that the corresponding result perfectly agrees with the one recently obtained via the generalized Luscher formulae.

Five-loop Konishi from the Mirror TBA · 0.96

Papers citing it · 55 sentences without a confident label

Builds on it 4 papers

Due to the similarities between the TBA equations of the orbifolded model and the undeformed model, it is easily seen that $δℛ_k$ will satisfy the equations discussed in [ref] , albeit with a different source term.

Orbifolded Konishi from the Mirror TBA · TBA approach · 0.88
The proof is a generalization of that used for the case of the Konishi operator in [ref] .

The Bajnok-Janik formula and wrapping corrections · Introduction · 0.96
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

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
We will do this analytically by applying the method developed in [ref] .

Twisting the Mirror TBA · Quantization of momentum and exact Bethe equation · 0.99
The crucial observation in the procedure of [ref] is that we can explicitly construct Y-functions for the XXX-spin chain that satisfy an equation which strongly resembles the TBA equation of relevance for us, just with a different source term.

Integrability of the AdS_5 x S^5 superstring and its deformations · TBA approach · 0.85

Compares with it 4 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 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 · 27 sentences without a confident label

Uses the method or tool of 1 paper

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

Five-loop Konishi from the Mirror TBA · Linearized TBA equations · 0.94

Compares with 1 paper

It is easy to check that in this gauge we have [equation] Since $t̂_m$ ($m≥1$) has no roots in the physical strip we can write [equation] and by taking the $∂_k$ derivative we obtain [equation] $ρ_k$ can now be written as [equation] Calculating the derivative we find [equation] Putting everything together, we find the result [equation] This is precisely the same (up to a sign) as ([ref]), the result obtained by using the generalized Lüscher formalism [ref] .

Five loop Konishi from AdS/CFT · Calculation of $ρ_k$ · 0.98

Cites as background 7 papers

The key point of the proof is to recognize that the coefficient functions $A_M|vw$ of the linear problem ([ref]) are related to the $Y$-functions of the inhomogeneous spin-$1/2$ XXX chain [ref] and that (with a different source term) the linear problem ([ref]) is identical to the variation of the TBA equations[In this case the term TBA is used in the sense of finite size effects.] of the XXX magnet with respect to the inhomogeneity parameters.

Bethe Ansatz and Classical Hirota Equation · Introduction · 0.84
The TBA equations were derived first for the ground state [ref] .

Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal · Introduction · 0.92
The TBA equations were derived first for the ground state [ref] .

Integrability for the Full Spectrum of Planar AdS/CFT II · Introduction · 0.92

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