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Properties of the Konishi multiplet in N=4 SYM theory
High Energy Physics - Theory · Submitted 2 Apr 2001
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g^2 and g^4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.
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The abstract, sentence by sentence
We study perturbative and non-perturbative properties of the Konishi multiplet in N=4 SYM theory in D=4 dimensions. We compute two-, three- and four-point Green functions with single and multiple insertions of the lowest component of the multiplet, and of the lowest component of the supercurrent multiplet. These computations require a proper definition of the renormalized operator and lead to an independent derivation of its anomalous dimension. The O(g^2) value found in this way is in agreement with previous results. We also find that instanton contributions to the above correlators vanish. From our results we are able to identify some of the lowest dimensional gauge-invariant composite operators contributing to the OPE of the correlation functions we have computed. We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g^2 and g^4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study perturbative and non-perturbative properties of the Konishi multiplet in N=4 SYM theory in D=4 dimensions. | contribution 0.95 | 0.92 | 0.04 | asserted 0.81 |
| s1 | We compute two-, three- and four-point Green functions with single and multiple insertions of the lowest component of the multiplet, and of the lowest component of the supercurrent multiplet. | contribution 0.75 | 0.96 | 0.04 | asserted 1.00 |
| s2 | These computations require a proper definition of the renormalized operator and lead to an independent derivation of its anomalous dimension. | method 0.41 | 0.93 | 0.09 | asserted 1.00 |
| s3 | The O(g^2) value found in this way is in agreement with previous results. | result 0.91 | 0.69 | 0.05 | asserted 0.98 |
| s4 | We also find that instanton contributions to the above correlators vanish. | result 1.00 | 0.96 | 0.07 | asserted 1.00 |
| s5 | From our results we are able to identify some of the lowest dimensional gauge-invariant composite operators contributing to the OPE of the correlation functions we have computed. | result 0.85 | 0.95 | 0.08 | asserted 0.89 |
| s6 | We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g^2 and g^4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions. | result 0.95 | 0.93 | 0.67 | asserted 1.00 |
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The paper
Original abstract
We study perturbative and non-perturbative properties of the Konishi multiplet in N=4 SYM theory in D=4 dimensions. We compute two-, three- and four-point Green functions with single and multiple insertions of the lowest component of the multiplet, and of the lowest component of the supercurrent multiplet. These computations require a proper definition of the renormalized operator and lead to an independent derivation of its anomalous dimension. The O(g^2) value found in this way is in agreement with previous results. We also find that instanton contributions to the above correlators vanish. From our results we are able to identify some of the lowest dimensional gauge-invariant composite operators contributing to the OPE of the correlation functions we have computed. We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g^2 and g^4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.
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References
How the literature uses it
17 arXiv papers cite this in 24 sentences
Papers citing it · 16 sentences without a confident label
Contests it 1 paper
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But this proposal seems to assume the statement of [ref] that the dimension of the Konishi operator does not receive instanton corrections, which does not agrees with the recent calculation in [ref] . ] but this may be useful in future for constructing interpolating functions for other quantities, which are modular invariants and have different behaviours in the classical string regime.
S-duality invariant perturbation theory improved by holography · Further improvement by holographic computation · contest 0.80
Uses its data or values 1 paper
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These can be extracted from the results in [ref] and in the normalisation we use in this chapter they take the values [equation] for $c=2/3(N^2-1)$.
Analytic Bootstrap for Perturbative Conformal Field Theories · Comparing with Konishi · 0.89
Cites it as background 5 papers
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However, there is almost no information on the OPE coefficients apart from early works on 3-point functions of protected operators dual to supergravity modes [ref] , short operators like Konishi [ref] , various operators in the BMN limit as most recently considered in [ref] .
On correlation functions of operators dual to classical spinning string states · Introduction · 0.88
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The helicity and flavour dependent counterparts of the operator $O^1$ was obtained [ref] as conformal descendant of the half-BPS and the $O^2$ was obtained as supersymmetric descendant of Konishi primary [ref] .
The Curious Case of Leading Transcendentality: Three Point Form Factors · Introduction · 0.82
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Consequently, the singlet current acquires a large anomalous dimension of order $λ^1/4$ at strong coupling,[For a detailed study of the Konishi multiplet and the anomaly in $𝒩=4$ SYM, see, e.g., [ref] .
Polarized DIS in N=4 SYM: Where is spin at strong coupling? · Polarized DIS in $𝒩=4$ SYM · 0.90
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