Extracting OPE coefficient of Konishi at four loops

Vasco Gon\c{c}alves

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Extracting OPE coefficient of Konishi at four loops

Vasco Gonçalves

High Energy Physics - Theory · Submitted 7 Jul 2016

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

The authors' main claim We compute in this short note the OPE coefficient of two 20' operators and the Konishi.

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We compute in this short note the OPE coefficient of two 20' operators and the Konishi. We use the OPE decomposition of a four point function of four 20' operators and the method of asymptotic expansions to compute the integrals at the order that it is needed.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute in this short note the OPE coefficient of two 20' operators and the Konishi.	contribution 0.88	0.96	0.64	asserted 1.00
s1	We use the OPE decomposition of a four point function of four 20' operators and the method of asymptotic expansions to compute the integrals at the order that it is needed.	method 1.00	0.92	0.07	asserted 1.00

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We compute in this short note the OPE coefficient of two 20' operators and the Konishi. We use the OPE decomposition of a four point function of four 20' operators and the method of asymptotic expansions to compute the integrals at the order that it is needed.

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References

Forward citations

Cited by 3 Pith papers

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

Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
hep-th 2019-06 conditional novelty 8.0 of 10

A TBA boundary-state construction yields a finite-coupling formula for structure constants of two giant gravitons and one single-trace operator in planar N=4 SYM.
Bootstrapping Holographic Theories in the Planar Limit
hep-th 2026-09 conditional novelty 6.0 of 10

Bootstrap plus localization, with no integrability input, reproduces single-trace operator dimension bounds that match independent predictions in planar N=4 SYM and in an N=2 open-string dual.
Structure constants at wrapping order
hep-th 2017-02 conditional novelty 6.0 of 10

A renormalization procedure tames wrapping-order divergences in the hexagon approach to structure constants, yielding a Luscher-type formula that reproduces the four-loop Konishi OPE coefficient.

How the literature uses it

24 arXiv papers cite this in 36 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 · 21 sentences without a confident label

Builds on it 2 papers

The results of this paper confirm and extend the analysis of [ref] .

Half-BPS half-BPS twist two at four loops in N=4 SYM · Introduction · 0.90
This will be a simple extension of the analysis that has been done for four-point conformal integrals [ref] .

Higher-Point Integrands in N=4 super Yang-Mills Theory · Asymptotic Expansions · 0.96

Uses its method or tool 4 papers

This method was introduced in [ref] and has been applied recently to compute five-loop p-integrals and structure constants in $𝒩=4$ SYM [ref] .

All five-loop planar four-point functions of half-BPS operators in $\mathcal N=4$ SYM · Asymptotic Expansions · 0.91
The integration in parametric space is possible for these integrals following an algorithm introduced in [ref] and implemented in Maple in [ref] [We have also checked the results using the method of asymptotic expansions [ref] . ].

Decagon at Two Loops · Feynman integrals · 0.99
To overcome this problem (at least partially), we will apply the method of asymptotic expansion [ref] to these higher-point integrals.

Higher-Point Integrands in N=4 super Yang-Mills Theory · OPE of the Integrated Correlator · 1.00

Uses its data or values 3 papers

In particular, we obtain [equation] while the lower loop $F^(n)$ were computed in [ref] .

Konishi OPE coefficient at the five loop order · From integrals to conformal data · 0.80
This OPE coefficient is currently known through four loops [ref] (see [ref] for the earlier loop orders) (C^∙∘∘/C^∘∘∘)^2 = 1/6-2g^2+(28+12ζ_3)g^4-(384+64ζ_3+200ζ_5)g^6 + (4976+656ζ_3+1960ζ_5+144ζ_3^2+2940ζ_7)g^8 + O(g^10) , where $g^2 = λ/(4π)^2$ is the 't Hooft coupling and $ζ_z = ζ(z)$ is the Riemann zeta function.

Structure constants at wrapping order · Introduction · 0.91
Similarly, the OPE coefficient with $T_2$ gives [ref] C_T_2 T_2 𝒪_𝒦 = 1 - 3 2 N g__YM^2/4 π^2 + …= 1 - 6N λ/m+ O(1/m^2) .

Large charge meets semiclassics in $\mathcal{N}=4$ super Yang-Mills · HHLL Four-point functions: OPE analysis · 0.93

Compares with it 2 papers

At weak coupling, we found that our upper bounds are close to being saturated by the four-loop weak coupling estimates [ref] for a remarkably large range of couplings.

Bootstrapping $\mathcal{N}=4$ super-Yang-Mills on the conformal manifold · Discussion · 0.99
Our analysis confirms the result of [ref] for $α_4(2)$, which is in itself a valuable piece of information because the calculation is large enough to offer space for errors.

Half-BPS half-BPS twist two at four loops in N=4 SYM · Waves and Conclusions · 0.98

Cites it as background 4 papers

The principle of uniform transcendentality (PUT) is a remarkable feature based on numerous observations [ref] , albeit unproven, which states that certain kinds of scattering amplitudes and form factors in $N=4$ can be expressed purely in terms of functions having UT.

The Curious Case of Leading Transcendentality: Three Point Form Factors · Principle of uniform transcendentality · 0.98
It is an observed [ref] , albeit unproven fact that certain kinds of scattering amplitudes in $N=4$ SYM exhibit uniform transcendentality (UT) i.e. those can be expressed in terms of polylogarithmic functions of uniform degree 2L with constant coefficients, where L denotes the loop order.

Two-loop Doubly Massive Four-Point Amplitude Involving a half-BPS and Konishi Operator · Behaviour of Leading Transcendental Terms · 0.90
The recent paper [ref] considers the leading terms in an asymptotic expansion for the entire set of integrals.

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations · Introduction · 0.88

What it cites · 18 sentences without a confident label

Uses the method or tool of 5 papers

The method to compute the first two integrals in ([ref]) was presented in the appendix of [ref] .

Five-loop Konishi in N=4 SYM · Master integrals · 0.98
We are interested in evaluating the integrals $j_21$ and $j_22$ in a Laurent expansion in $2ϵ=d-4$ [equation] Imposing that the each conformal integral that appears in the planar part of the four point function ([ref]) are finite in the limit $ϵ→0$ and conformal fixes their values[In our computations we have used $G$-scheme and for the planar master integrals we have used [ref] .]

Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals · Master integrals · 0.93
We will review briefly how the method works on $4$ loop integral that appears in this four point function[More details on the method can be found in [ref] .] [equation] where the point $x_4$ was sent to infinity and $x_1$ to $0$ using conformal invariance of the integral.

Three-loop universal structure constants in N=4 susy Yang-Mills theory · Asymptotic expansions · 0.93

Uses data or values from 3 papers

At this point any conformal integral is given by a combination of master integrals, whose values have been determined in an $ϵ$ expansion [equation] up transcendentality seven [ref] [Notice that transcendentality is enough for our purposes.

Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals · Asymptotic expansions · 0.86
At this point any conformal integral is given by a combination of master integrals, whose values have been determined in an $ϵ$ expansion [equation] up transcendentality seven [ref] [Notice that transcendentality is enough for our purposes.

Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM · Asymptotic expansions · 0.86
These have been computed in [ref] [equation] The constants $b_i$ and $c_i$ are obtained using [equation] Plugging these values in ([ref]) we obtain again ([ref]) and also the values for $j_22,1$ and $j_22,1$ [equation]

Five-loop Konishi in N=4 SYM · Master integrals · 0.87

Cites as background 1 paper

The structure of the four point function of $20'$ operators can be written in a compact form [ref] [equation] with the tree level result given by [equation] and the loop level by [equation] where $a$ is the t'Hoft coupling $a=g^2N_c/(4π^2)$ and $R$ contains all the dependence on the polarization vectors $Y$ [equation] The function $f^(l)(x_1,…,x_4+l)$ possesses an hidden permutation symmetry $S_4+l$ and this, together with imposing the correct OPE behavior, has led to a complete description of its form up to a high loop order [ref] .

Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM · Four point function and OPE limit · 0.82

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