On Three-point Functions in the AdS_4/CFT_3 Correspondence

Agnese Bissi; Ara Martirosyan; Charlotte Kristjansen; Marta Orselli

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On Three-point Functions in the AdS_4/CFT_3 Correspondence

Agnese Bissi, Charlotte Kristjansen, Ara Martirosyan, Marta Orselli

High Energy Physics - Theory · Submitted 6 Nov 2012

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

The authors' main claim We show that when normalized by the three-point function of three BPS operators the heavy-heavy-light correlation function agrees, in the Frolov-Tseytlin limit, with its string theory counterpart which we calculate holographically.

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arXiv ID1211.1359 (version 2)

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CitationAgnese Bissi, Ara Martirosyan, Charlotte Kristjansen, Marta Orselli. "On Three-point Functions in the AdS_4/CFT_3 Correspondence." arXiv:1211.1359 (2012). https://pith.science/paper/JSAZX7UE

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We calculate planar, tree-level, non-extremal three-point functions of operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we generalize the determinant representation, found by Foda for the three-point functions of the SU(2) sector of N=4 SYM, to the present case and find that the ABJM result up to normalization factors factorizes into a product of two N=4 SYM correlation functions. Secondly, we treat the case where two operators are heavy and one is light and BPS, using a coherent state description of the heavy ones. We show that when normalized by the three-point function of three BPS operators the heavy-heavy-light correlation function agrees, in the Frolov-Tseytlin limit, with its string theory counterpart which we calculate holographically.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We calculate planar, tree-level, non-extremal three-point functions of operators belonging to the SU(2) x SU(2) sector of ABJM theory.	contribution 1.00	0.96	0.08	asserted 1.00
s1	First, we generalize the determinant representation, found by Foda for the three-point functions of the SU(2) sector of N=4 SYM, to the present case and find that the ABJM result up to normalization factors factorizes into a product of two N=4 SYM correlation functions.	result 0.56	0.91	0.28	asserted 1.00
s2	Secondly, we treat the case where two operators are heavy and one is light and BPS, using a coherent state description of the heavy ones.	method 0.62	0.89	0.06	asserted 0.63
s3	We show that when normalized by the three-point function of three BPS operators the heavy-heavy-light correlation function agrees, in the Frolov-Tseytlin limit, with its string theory counterpart which we calculate holographically.	result 1.00	0.92	0.47	asserted 1.00

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Original abstract

We calculate planar, tree-level, non-extremal three-point functions of operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we generalize the determinant representation, found by Foda for the three-point functions of the SU(2) sector of N=4 SYM, to the present case and find that the ABJM result up to normalization factors factorizes into a product of two N=4 SYM correlation functions. Secondly, we treat the case where two operators are heavy and one is light and BPS, using a coherent state description of the heavy ones. We show that when normalized by the three-point function of three BPS operators the heavy-heavy-light correlation function agrees, in the Frolov-Tseytlin limit, with its string theory counterpart which we calculate holographically.

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3 arXiv papers cite this in 3 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

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Various developments subsequently generalized it to the computation of the correlation functions-including three-point functions and hexagon approach [ref] , four- point functions [ref] , octagon [ref] , three-point functions [ref] and the exact overlap formula in spin chain [ref] .

Integrable Boundary States from Maximal Giant Gravitons in ABJM Theory · Introduction · 0.93

What it cites · 43 sentences without a confident label

Uses the method or tool of 11 papers

The prescription of [ref] gives in our case [Note that the unconventional powers of $κ$ are due to a rescaling of the time coordinate (see App. [ref]).]

Holographic three-point functions of semiclassical states · The holographic approach · 0.94
The prescription of [ref] gives in our case [Note that the unconventional powers of $κ$ are due to a rescaling of the time coordinate (see App. [ref]).]

Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match · The holographic approach · 0.94
The prescription of [ref] gives in our case [Note that the unconventional powers of $κ$ are due to a rescaling of the time coordinate (see App. [ref]).]

Holographic 3-point function at one loop · The holographic approach · 0.94

Uses data or values from 1 paper

Moreover, from Appendix A of [ref] we have $n_6=j$, $n_1=n_2=p=J-j$, $n_3=j$.

Giant Gravitons on AdS_4 x CP^3 and their Holographic Three-point Functions · The holographic approach · 0.83

Compares with 1 paper

Note that, apart from a different normalization, this is precisely the square of the result of [ref] for operators in the $SU(2)$ sector of $𝒩$=4 SYM theory.

Classical Limit of the Three-Point Function from Integrability · The coherent state approach · 1.00

Cites as background 14 papers

The holographic dual of ABJM theory is given by type IIA string theory on $_4×P^3$ [ref] with metric

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Type IIA string theory on $AdS_4×P^3$ and its $SU(2)×SU(2)$ sigma model limit. · 0.99
More recently, strong coupling results were obtained for the case of two giant gravitons and one tiny graviton, all BPS [ref] .

Giant Gravitons on AdS_4 x CP^3 and their Holographic Three-point Functions · Introduction · 0.92
The spectral problem of ABJM theory is believed to be integrable [ref] in much the same way as the spectral problem of $N=4$ SYM [ref] .

Superstrings on AdS_4 x CP^3 as a Coset Sigma-model · Three-point functions in the $SU(2)×SU(2)$ sector of ABJM theory · 0.87

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