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A basis for large operators in N=4 SYM with orthogonal gauge group
High Energy Physics - Theory · Submitted 8 Jan 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For these operators, the large N limit of correlation functions is not captured by summing only the planar diagrams.
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The abstract, sentence by sentence
We develop techniques to study the correlation functions of "large operators" whose bare dimension grows parametrically with N, in SO(N) gauge theory. We build the operators from a single complex matrix. For these operators, the large N limit of correlation functions is not captured by summing only the planar diagrams. By employing group representation theory we are able to define local operators which generalize the Schur polynomials of the theory with gauge group U(N). We compute the two point function of our operators exactly in the free field limit showing that they diagonalize the two point function. We explain how these results can be used to obtain the exact free field answers for correlators of operators in the trace basis.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We develop techniques to study the correlation functions of "large operators" whose bare dimension grows parametrically with N, in SO(N) gauge theory. | contribution 0.99 | 0.94 | 0.13 | asserted 0.99 |
| s1 | We build the operators from a single complex matrix. | method 0.60 | 0.91 | 0.04 | asserted 1.00 |
| s2 | For these operators, the large N limit of correlation functions is not captured by summing only the planar diagrams. | result 0.73 | 0.70 | 0.37 | asserted 1.00 |
| s3 | By employing group representation theory we are able to define local operators which generalize the Schur polynomials of the theory with gauge group U(N). | contribution 0.54 | 0.90 | 0.16 | asserted 0.99 |
| s4 | We compute the two point function of our operators exactly in the free field limit showing that they diagonalize the two point function. | result 0.96 | 0.96 | 0.18 | asserted 1.00 |
| s5 | We explain how these results can be used to obtain the exact free field answers for correlators of operators in the trace basis. | contribution 0.46 | 0.91 | 0.19 | asserted 0.92 |
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The paper
Original abstract
We develop techniques to study the correlation functions of "large operators" whose bare dimension grows parametrically with N, in SO(N) gauge theory. We build the operators from a single complex matrix. For these operators, the large N limit of correlation functions is not captured by summing only the planar diagrams. By employing group representation theory we are able to define local operators which generalize the Schur polynomials of the theory with gauge group U(N). We compute the two point function of our operators exactly in the free field limit showing that they diagonalize the two point function. We explain how these results can be used to obtain the exact free field answers for correlators of operators in the trace basis.
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References
How the literature uses it
18 arXiv papers cite this in 37 sentences
Papers citing it · 29 sentences without a confident label
Builds on it 2 papers
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Using the results of [ref] we now immediately find[Recall that as symmetric group representations we have $d_R=d_R^c$.
Operators, Correlators and Free Fermions for SO(N) and Sp(N) · $Sp(N)$ gauge theory · 0.88
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A natural generalization of the work presented here is to develop the analogous discussion for $SO(N)/SP(N)$ gauge groups, building on earlier work at zero and weak coupling [ref] .
Quarter-BPS states, multi-symmetric functions and set partitions · Summary and Outlook · 0.89
Uses its method or tool 3 papers
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To proceed with these sums, we will use a useful result by Howe [ref] (see also a result by Mizukawa, proposition 4.1 in [ref] , and also [ref] or a more recent use of it in [ref] ): ∑_γ∈S_n[S_2] χ^R(γ) = |S_n[S_2]| m^R where $m^R= 1$ if $R$ is an “even” partition, that is, all its row lengths are even, and $m^R=0$ otherwise.
On the counting of $O(N)$ tensor invariants · The counting as a Kronecker sum · 0.90
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We use these partitions $ν$ (see [ref] ) to construct $σ_4ν∈S_2n$ with cycle structure given by multiplying each of the parts of $ν$ by 4.
Operators, Correlators and Free Fermions for SO(N) and Sp(N) · Multi trace Correlators · 0.80
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To tackle these sums, we use a result by Howe [ref] (see also [ref] ): $∑_γ∈S_n[S_2] χ^R(γ) = |S_n[S_2]| m^R$, where $m^R= 1$ if $R$ is an “even” partition, and $m^R=0$ otherwise.
On the counting tensor model observables as $U(N)$ and $O(N)$ classical invariants · Algebras and representation theoretic bases · 0.92
Cites it as background 2 papers
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To start, recall the discussion of [ref] : operators of the form ([ref]) are the complete set of operators that can be built without using $ϵ^i_1 i_2⋯i_N$.
Operators, Correlators and Free Fermions for SO(N) and Sp(N) · Counting · 0.84
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Half-BPS operators in these theories have been studied in [ref] and it would be interesting to consider single-particle operators in that context.
Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM · Conclusions · 0.85
What it cites · 7 sentences without a confident label
Builds on 1 paper
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This again generalizes results that are known for the $U(N)$ gauge theory [ref] .
From Schurs to Giants in ABJ(M) · Introduction · 0.96
Cites as support 2 papers
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In this case, the large $N$ limit of correlation function is not captured by summing only the planar diagrams [ref] , so that correlation functions of large operators are sensitive to the non-planar structure of the theory.
Giant Gravitons in Conformal Field Theory · Introduction · 0.98
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In fact, from existing group theory results we know that the irrep $[A]$ of $S_n[S_2]$ is always subduced once [ref] .
Wreath Product Generalizations of the Triple $(S_{2n},H_{n},\phi)$ and Their Spherical Functions · $SO(N)$ gauge theory · 0.97
Cites as background 20 papers
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A detailed study of the spectral problem of $N=4$ super Yang-Mills with these gauge groups has been carried out in [ref] .
On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group · Introduction · 0.80
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For the theory with gauge group $U(N)$ the technology for computing n-point correlators is rather well developed [ref] .
From Schurs to Giants in ABJ(M) · Discussion and future directions · 0.93
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Progress on the study of the finite $N$ physics has been rapid and we now know of a number of bases of local operators that diagonalize the free field two point function [ref] and we know how to diagonalize the one-loop dilatation operator [ref] for certain operators dual to giant graviton branes [ref] .
Exact Multi-Matrix Correlators · Introduction · 0.85
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