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Large spin expansion of semiclassical 3-point correlators in AdS_5 x S^5
High Energy Physics - Theory · Submitted 13 Dec 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Remarkably, in all of these cases the large J expansion of the 3-point correlator has the same structure as expected in perturbative (tree-level and one-loop) dual gauge theory.
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The abstract, sentence by sentence
3-point correlators in AdS_5xS^5 string theory in which two states are "heavy" (have large quantum numbers) and the third is "light" (here chosen as chiral primary scalar) can be computed semiclassically in terms of the "light" vertex operator evaluated on the classical string solution sourced by the two "heavy" operators. We observe that in the case when the "heavy" operators represent BPS states there is an ambiguity in the computation depending on whether the mass shell (or marginality) condition is imposed before or after integration over the world sheet. We show that this ambiguity is resolved in a universal way by defining the BPS correlator as a limit of the one with non-BPS "heavy" states. We consider several examples with "heavy" states represented by folded or circular spinning strings in AdS_5xS^5 that admit a point-like BMN-type limit when one S^5 spin J is much larger than the others. Remarkably, in all of these cases the large J expansion of the 3-point correlator has the same structure as expected in perturbative (tree-level and one-loop) dual gauge theory. We conjecture that, like the leading chiral primary correlator term, the coefficients of the first few subleading terms are also protected, i.e. should be the same at strong and weak coupling.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 3-point correlators in AdS_5xS^5 string theory in which two states are "heavy" (have large quantum numbers) and the third is "light" (here chosen as chiral primary scalar) can be computed semiclassically in terms of the "light" vertex operator evaluated on the classical string solution sourced by the two "heavy" operators. | background 0.89 | 0.12 | 0.09 | asserted 0.98 |
| s1 | We observe that in the case when the "heavy" operators represent BPS states there is an ambiguity in the computation depending on whether the mass shell (or marginality) condition is imposed before or after integration over the world sheet. | result 0.78 | 0.82 | 0.05 | asserted 0.99 |
| s2 | We show that this ambiguity is resolved in a universal way by defining the BPS correlator as a limit of the one with non-BPS "heavy" states. | result 0.53 | 0.93 | 0.25 | asserted 1.00 |
| s3 | We consider several examples with "heavy" states represented by folded or circular spinning strings in AdS_5xS^5 that admit a point-like BMN-type limit when one S^5 spin J is much larger than the others. | contribution 0.80 | 0.75 | 0.04 | asserted 0.98 |
| s4 | Remarkably, in all of these cases the large J expansion of the 3-point correlator has the same structure as expected in perturbative (tree-level and one-loop) dual gauge theory. | result 0.99 | 0.88 | 0.40 | asserted 0.97 |
| s5 | We conjecture that, like the leading chiral primary correlator term, the coefficients of the first few subleading terms are also protected, i.e. should be the same at strong and weak coupling. | interpretation 0.82 | 0.19 | 0.37 | speculative 1.00 |
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Original abstract
3-point correlators in AdS_5xS^5 string theory in which two states are "heavy" (have large quantum numbers) and the third is "light" (here chosen as chiral primary scalar) can be computed semiclassically in terms of the "light" vertex operator evaluated on the classical string solution sourced by the two "heavy" operators. We observe that in the case when the "heavy" operators represent BPS states there is an ambiguity in the computation depending on whether the mass shell (or marginality) condition is imposed before or after integration over the world sheet. We show that this ambiguity is resolved in a universal way by defining the BPS correlator as a limit of the one with non-BPS "heavy" states. We consider several examples with "heavy" states represented by folded or circular spinning strings in AdS_5xS^5 that admit a point-like BMN-type limit when one S^5 spin J is much larger than the others. Remarkably, in all of these cases the large J expansion of the 3-point correlator has the same structure as expected in perturbative (tree-level and one-loop) dual gauge theory. We conjecture that, like the leading chiral primary correlator term, the coefficients of the first few subleading terms are also protected, i.e. should be the same at strong and weak coupling.
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References
How the literature uses it
11 arXiv papers cite this in 16 sentences
Papers citing it · 8 sentences without a confident label
Cites it as background 7 papers
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Holographic three-point functions of giant gravitons have been studied extensively in the literature [ref] , with some discrepancies and ambiguities appearing between the holographic and gauge theoretic computations in the case of off-diagonal extremal correlators and for AdS giant gravitons.
Orbit Averaging Coherent States: Holographic Three-Point Functions of AdS Giant Gravitons · Introduction · 0.91
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[For recent work on holographic 3-point functions see [ref] .]
Holographic 3-point function at one loop · Introduction, summary and conclusion · 1.00
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On the other hand, the case $Ø_3= (Z^j)$ is the case which has been most extensively studied in the literature recently at strong coupling [ref] .
Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match · $Ø_3= (Z^j)$ and (ignoring) mixing with double traces · 0.96
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