On the OPE of 1/2 BPS Short Operators in N=4 SCFT$_4$

B. Eden; E. Sokatchev

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On the OPE of 1/2 BPS Short Operators in N=4 SCFT$_4$

B. Eden, E. Sokatchev

High Energy Physics - Theory · Submitted 26 Jun 2001

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The authors' main claim Our main result is the identification of all possible protected operators in such OPE's.

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The content of the OPE of two 1/2 BPS operators in N=4 SCFT$_4$ is given by their superspace three-point functions with a third, a priori long operator. For certain 1/2 BPS short superfields these three-point functions are uniquely determined by superconformal invariance. We focus on the cases where the leading ($\theta=0$) components lie in the tensor products $[0,m,0]\otimes[0,n,0]$ and $[m,0,0]\otimes[0,0,n]$ of SU(4). We show that the shortness conditions at the first two points imply selection rules for the supermultiplet at the third point. Our main result is the identification of all possible protected operators in such OPE's. Among them we find not only BPS short multiplets, but also series of special long multiplets which satisfy current-like conservation conditions in superspace.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The content of the OPE of two 1/2 BPS operators in N=4 SCFT$_4$ is given by their superspace three-point functions with a third, a priori long operator.	background 0.96	0.19	0.04	asserted 1.00
s1	For certain 1/2 BPS short superfields these three-point functions are uniquely determined by superconformal invariance.	background 0.96	0.12	0.03	asserted 0.99
s2	We focus on the cases where the leading ($\theta=0$) components lie in the tensor products $[0,m,0]\otimes[0,n,0]$ and $[m,0,0]\otimes[0,0,n]$ of SU(4).	contribution 0.72	0.46	0.02	asserted 0.88
s3	We show that the shortness conditions at the first two points imply selection rules for the supermultiplet at the third point.	result 0.80	0.89	0.04	asserted 1.00
s4	Our main result is the identification of all possible protected operators in such OPE's.	result 0.83	0.96	0.98	asserted 1.00
s5	Among them we find not only BPS short multiplets, but also series of special long multiplets which satisfy current-like conservation conditions in superspace.	result 1.00	0.94	0.12	asserted 1.00

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Original abstract

The content of the OPE of two 1/2 BPS operators in N=4 SCFT$_4$ is given by their superspace three-point functions with a third, a priori long operator. For certain 1/2 BPS short superfields these three-point functions are uniquely determined by superconformal invariance. We focus on the cases where the leading ($\theta=0$) components lie in the tensor products $[0,m,0]\otimes[0,n,0]$ and $[m,0,0]\otimes[0,0,n]$ of SU(4). We show that the shortness conditions at the first two points imply selection rules for the supermultiplet at the third point. Our main result is the identification of all possible protected operators in such OPE's. Among them we find not only BPS short multiplets, but also series of special long multiplets which satisfy current-like conservation conditions in superspace.

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References

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Cited by 14 Pith papers

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

Infinite Chiral Symmetry in Four Dimensions
hep-th 2013-12 conditional novelty 9.0 of 10

Every 4d N=2 superconformal field theory has a protected subsector that behaves as a 2d chiral algebra, with central charges tied to 4d anomalies.
The N=4 Superconformal Bootstrap
hep-th 2013-04 conditional novelty 8.0 of 10

Bootstrap consistency of the stress-tensor four-point function yields nonperturbative upper bounds on unprotected operator dimensions in N=4 superconformal theories, and the extremal spectrum is conjectured to be N=4 ...
$20'$ Five-Point Function from $AdS_5\times S^5$ Supergravity
hep-th 2019-06 conditional novelty 7.0 of 10

A bootstrap built from symmetry, Mellin factorization and two twists produces the complete tree-level five-point function of the 20-prime operator in AdS5 x S5 supergravity, together with new strong-coupling OPE data.
Bootstrap equations for $\mathcal{N}=4$ SYM with defects
hep-th 2016-08 accept novelty 7.0 of 10

Superconformal blocks for half-BPS two-point functions in 4d N=4 SYM with a defect are derived and shown to apply to four systems sharing OSP(4|4) symmetry, yielding polynomial bootstrap equations in a protected subsector.
Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
hep-th 2001-12 accept novelty 7.0 of 10

Superconformal symmetry fixes the four point function of chiral primary operators up to one function of two variables, and the paper uses this to write the operator product expansion in terms of complete supermultiplets.

Show 9 more citing papers

Non-Renormalizability Properties of Quarter-BPS Correlators in $\mathcal{N}$=4 SYM
hep-th 2026-10 conditional novelty 6.0 of 10

Extremal and next-to-extremal four-point functions of general quarter-BPS operators in N=4 SYM exchange only short and semi-short superconformal multiplets, and are therefore independent of the coupling.
Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
hep-th 2019-12 conditional novelty 6.0 of 10

Nonperturbative CFT four-point functions admit a subtracted Mellin representation whose analyticity, Regge growth and Polyakov conditions yield extremal bootstrap functionals acting on OPE data.
Unmixing Supergravity
hep-th 2017-06 accept novelty 6.0 of 10

The paper resolves the mixing of double-trace operators in the supergravity limit of N=4 super Yang-Mills and gives closed-form anomalous dimensions and three-point functions for a large family of them.
More ${\mathcal N}=4$ superconformal bootstrap
hep-th 2016-12 accept novelty 6.0 of 10

Unitarity plus crossing symmetry forces the central charge of any interacting N=4 superconformal field theory to be at least 3/4, and numerical bootstrap bounds on low-lying operator dimensions are computed as a funct...
All three-loop four-point correlators of half-BPS operators in planar N=4 SYM
hep-th 2015-12 accept novelty 6.0 of 10

All planar four-point correlators of half-BPS operators in N=4 SYM are determined up to three loops and expressed through 9 two-loop and 55 three-loop conformal integral functions.
Superconformal Ward Identities and their Solution
hep-th 2004-07 accept novelty 6.0 of 10

The authors derive superconformal Ward identities for four-point functions of arbitrary-rank chiral primary operators in N=2 and N=4 theories and solve them in a form that maps cleanly onto long, short, and semi-short...
On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
hep-th 2002-09 accept novelty 6.0 of 10

At the unitarity threshold a long superconformal multiplet decomposes into four semi-short multiplets, and only the 1/2-BPS [0,p,0] and 1/4-BPS [1,p,1] multiplets are guaranteed to have protected scale dimensions.
The superconformal bootstrap for structure constants
hep-th 2013-10 conditional novelty 5.0 of 10

The authors derive non-perturbative upper bounds on OPE structure constants in N=4 super-Yang-Mills and conjecture the bounds are saturated at S-duality fixed points.
Supersymmetric Gauge Theories and the AdS/CFT Correspondence
hep-th 2002-01 accept novelty 2.0 of 10

A pedagogical review that builds N=4 SYM, Type IIB supergravity, and D3-branes from scratch and then works out how AdS/CFT computes correlation functions and holographic RG flows.

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10 arXiv papers cite this in 13 sentences

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From the representation theory of the 4d $𝒩=4$ superconformal algebra, we know that the tensor product of two stress tensor multiplets takes the following schematic form [ref] [equation] Here we use the notation $𝒳^s/4,s̅/4_[d_1,d_2,d_3](j,j̅)$ to denote the supermultiplets, where $[d_1,d_2,d_3]$ is the R-symmetry Dykin label of the super primary and $(j,j̅)$ are the Lorentz spins.

$20'$ Five-Point Function from $AdS_5\times S^5$ Supergravity · Low-lying operators · 0.80
The constraints of superconformal invariance on this four-point function have been analyzed in detail in, , [ref] .

The N=4 Superconformal Bootstrap · Introduction · 0.97
Schematically we have [ref]

More ${\mathcal N}=4$ superconformal bootstrap · Superconformal block decomposition · 0.81

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