Generalized bootstrap equations for N=4 SCFT

Agnese Bissi; Luis F. Alday

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Generalized bootstrap equations for N=4 SCFT

Luis F. Alday, Agnese Bissi

High Energy Physics - Theory · Submitted 23 Apr 2014

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

The authors' main claim The resulting conformal bootstrap equations impose non-trivial bounds for the scaling dimension of unprotected local operators transforming in various representations of the R-symmetry group.

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We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling dimension of unprotected local operators transforming in various representations of the R-symmetry group. These bounds generalize recent bounds for operators in the singlet representation, arising from consistency of the four-point function of the stress-energy tensor multiplet.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories.	contribution 0.99	0.91	0.06	asserted 0.85
s1	The resulting conformal bootstrap equations impose non-trivial bounds for the scaling dimension of unprotected local operators transforming in various representations of the R-symmetry group.	result 0.99	0.87	0.63	asserted 1.00
s2	These bounds generalize recent bounds for operators in the singlet representation, arising from consistency of the four-point function of the stress-energy tensor multiplet.	interpretation 0.45	0.58	0.33	asserted 1.00

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Original abstract

We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling dimension of unprotected local operators transforming in various representations of the R-symmetry group. These bounds generalize recent bounds for operators in the singlet representation, arising from consistency of the four-point function of the stress-energy tensor multiplet.

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References

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Cited by 20 Pith papers

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How the literature uses it

37 arXiv papers cite this in 44 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 · 20 sentences without a confident label

Uses its data or values 1 paper

For $𝒩=4$ SYM, the GFFT and $R$ data was computed using conformal symmetry [ref] , and then used to obtain the 1-loop correction in [ref] .

6d (2,0) and M-theory at 1-loop · Introduction · 0.84

Compares with it 1 paper

As a consistency check we reproduced some of the bounds first obtained in [ref] and improved on some of those by pushing the numerics.

Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills · Summary of results · 0.99

Cites it as background 22 papers

The conformal bootstrap [ref] in $D>2$ dimensions has produced remarkable results, including numerical bounds on operator dimensions and OPE coefficients [ref] , analytical constraints [ref] , and recently a precise conjecture for the $ℤ_2$-even spectrum of the 3D Ising model [ref] .

Bootstrapping Mixed Correlators in the 3D Ising Model · Introduction · 0.99
In the past few years the $𝒩=4$ superconformal bootstrap approach [ref] has obtained a relatively satisfying upper bounds on the dimensions of the unprotected leading twist operators by studying the four-point function (see also [ref] ) \begin ⟨𝒪_20'^I_1(x_1 ) 𝒪_20'^I_2(x_2 ) 𝒪_20'^I_3(x_3 ) 𝒪_20'^I_4(x_4 )⟩, \end where $𝒪_20'^I$ is a superconformal primary scalar operator of dimension two in energy-momentum tensor multiplets transforming as $20'$ representation in $SU(4)_R$.

S-duality invariant perturbation theory improved by holography · The $𝒩=4$ superconformal bootstrap · 0.85
A partial list of references on the numerical conformal bootstrap is [ref] ; see also a most recent paper, Ref. [ref] , and the recent review [ref] for a more complete list.

Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach · Introduction and result · 0.91

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Uses the method or tool of 2 papers

From the comparison between the bounds for $Λ=9$ and $Λ=11$ it seems one should be able to improve the bounds found in this paper, by increasing the number of derivatives or by applying more efficient methods, e.g. as in [ref] or [ref] .

Carving Out the Space of 4D CFTs · Discussion · 0.93
From the comparison between the bounds for $Λ=9$ and $Λ=11$ it seems one should be able to improve the bounds found in this paper, by increasing the number of derivatives or by applying more efficient methods, e.g. as in [ref] or [ref] .

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Equations [ref] and [ref] exactly agree with the equations found by [ref] .

The N=4 Superconformal Bootstrap · Generalized bootstrap equations · 1.00

Cites as background 2 papers

Bootstrap equations with this structure appear when studying CFT's with global symmetries and were analyzed in [ref] .

Bounds in 4D Conformal Field Theories with Global Symmetry · Setup · 0.91
As shown in [ref] , the conformal bootstrap equation can be used to put upper bounds to the dimensions of leading twist primary operators appearing in the OPE $ϕ×ϕ$.

Bounding scalar operator dimensions in 4D CFT · Introduction · 0.80

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