Connecting giant magnons to the pp-wave: An interpolating limit of $AdS_5 \times S^5$

Ian Swanson; Juan Maldacena

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Connecting giant magnons to the pp-wave: An interpolating limit of $AdS_5 \times S^5$

Juan Maldacena, Ian Swanson

High Energy Physics - Theory · Submitted 11 Dec 2006

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

The authors' main claim After doing a Borel resummation we find that the proposed $S$ matrix reproduces the expected results in the giant-magnon region.

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arXiv IDhep-th/0612079 (version 4)

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CitationIan Swanson, Juan Maldacena. "Connecting giant magnons to the pp-wave: An interpolating limit of $AdS_5 \times S^5$." arXiv:hep-th/0612079 (2006). https://pith.science/paper/XQOUTPO4

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.35 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.84 · mentions code or data availability 0.02.

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We consider a particular large-radius limit of the worldsheet $S$-matrix for strings propagating on $AdS_5 \times S^5$. This limiting theory interpolates smoothly between the so-called plane-wave and giant-magnon regimes of the theory. The sigma model in this region simplifies; it stands as a toy model of the full theory, and may be easier to solve directly. The $S$ matrix of the limiting theory is non-trivial, and receives contributions to all orders in the $\alpha'$ expansion. We analyze a guess for the full worldsheet $S$ matrix that was formulated recently by Beisert, Hernandez and Lopez, and Beisert, Eden, and Staudacher, and take the corresponding limit. After doing a Borel resummation we find that the proposed $S$ matrix reproduces the expected results in the giant-magnon region. In addition, we rely on general considerations to draw some basic conclusions about the analytic structure of the $S$ matrix.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider a particular large-radius limit of the worldsheet $S$-matrix for strings propagating on $AdS_5 \times S^5$.	contribution 0.88	0.81	0.05	asserted 0.94
s1	This limiting theory interpolates smoothly between the so-called plane-wave and giant-magnon regimes of the theory.	result 0.63	0.46	0.36	asserted 1.00
s2	The sigma model in this region simplifies; it stands as a toy model of the full theory, and may be easier to solve directly.	interpretation 0.84	0.26	0.10	hedged possibility 0.61
s3	The $S$ matrix of the limiting theory is non-trivial, and receives contributions to all orders in the $\alpha'$ expansion.	result 0.90	0.48	0.11	asserted 1.00
s4	We analyze a guess for the full worldsheet $S$ matrix that was formulated recently by Beisert, Hernandez and Lopez, and Beisert, Eden, and Staudacher, and take the corresponding limit.	method 0.76	0.74	0.04	asserted 0.94
s5	After doing a Borel resummation we find that the proposed $S$ matrix reproduces the expected results in the giant-magnon region.	result 1.00	0.94	0.51	asserted 1.00
s6	In addition, we rely on general considerations to draw some basic conclusions about the analytic structure of the $S$ matrix.	contribution 0.54	0.82	0.07	asserted 0.69

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

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Original abstract

We consider a particular large-radius limit of the worldsheet $S$-matrix for strings propagating on $AdS_5 \times S^5$. This limiting theory interpolates smoothly between the so-called plane-wave and giant-magnon regimes of the theory. The sigma model in this region simplifies; it stands as a toy model of the full theory, and may be easier to solve directly. The $S$ matrix of the limiting theory is non-trivial, and receives contributions to all orders in the $\alpha'$ expansion. We analyze a guess for the full worldsheet $S$ matrix that was formulated recently by Beisert, Hernandez and Lopez, and Beisert, Eden, and Staudacher, and take the corresponding limit. After doing a Borel resummation we find that the proposed $S$ matrix reproduces the expected results in the giant-magnon region. In addition, we rely on general considerations to draw some basic conclusions about the analytic structure of the $S$ matrix.

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References

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Cited by 10 Pith papers

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

On String S-matrix, Bound States and TBA
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Unitarity of the mirror S-matrix fixes the AdS5 x S5 string S-matrix essentially uniquely as a meromorphic elliptic function, with the double Wick rotation realized as a quarter-period shift on the rapidity torus.
Notes on Superconformal Chern-Simons-Matter Theories
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A large class of three-dimensional N=2 and N=3 Chern-Simons-matter theories is shown to be exactly conformal, and a two-loop large-N computation of long-operator anomalous dimensions is presented as evidence for AdS4 ...
Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
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The exact dispersion relation for light-cone string excitations in AdS3 x S3 x T4 with mixed flux has a central charge linear in worldsheet momentum, fixed by an explicit dyonic giant magnon solution.
Dressing phases of AdS3/CFT2
hep-th 2013-06 conditional novelty 6.0 of 10

The two all-loop dressing phases of the AdS3 x S3 x T4 integrable S-matrix are determined by solving the crossing relations, yielding a BES-like phase plus a new term absent in the higher-dimensional cases.
The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
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A symmetry-based bootstrap fixes the all-loop S-matrix of the psu(1,1|2)^2 spin chain up to two dressing phases, yields new Bethe equations, and states the crossing equations those phases must obey.

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Exciting the GKP string at any coupling
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The spectrum of excitations around the long GKP string is expressed as all-loop dispersion relations parameterized by the solution to the BES equation, with the SO(6) symmetry restoration mechanism identified.
Konishi operator at intermediate coupling
hep-th 2010-06 conditional novelty 6.0 of 10

Solving the Konishi TBA equations numerically up to λ ≈ 2046 pushes the first critical coupling above 5300 and indicates a nonzero 1/λ term in the strong-coupling expansion.
The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
hep-th 2006-12 accept novelty 6.0 of 10

The AdS5 x S5 string S-matrix satisfies the standard Yang-Baxter equation in a natural 'string' basis, and Beisert's gauge-theory S-matrix is the same object rewritten in a non-local basis that twists the equation.
Towards integrability for AdS3/CFT2
hep-th 2014-06 accept novelty 3.0 of 10

A self-contained review that assembles, from previously published work, the symmetry-fixed all-loop S matrix and Bethe ansatz for massive AdS3 x S3 x T4 string excitations, including a crossing-symmetric proposal for ...
Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
hep-th 2010-12 accept novelty 2.0 of 10

Across the deformations, orbifolds and open-chain setups surveyed, all-loop integrability survives only where the bulk spin chain is undeformed N=4 SYM and the difference sits in twisted, orbifold or open boundary conditions.

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32 arXiv papers cite this in 67 sentences

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Papers citing it · 43 sentences without a confident label

Builds on it 1 paper

For example, it would be nice to perform the same analysis for the supersymmetric form of the model given in [ref] .

Reduced Sigma-Model on O(N): Hamiltonian Analysis and Poisson Bracket of Lax Connection · Introduction and Summary · 0.90

Uses its method or tool 4 papers

Since the full $_5×^5$ sigma-model [ref] is quite complicated we make use of the simplifying limit proposed recently by Maldacena and Swanson [ref] .

World-sheet scattering in AdS_5 x S^5 at two loops · Introduction · 0.94
[equation] Note also that under the rescaling ([ref]), $T_++$ given in ([ref]) takes the form [equation] and hence the Virasoro constraint $T_++=0$ implies the constraint [equation] In the same way the rescaling ([ref]) performed on $T_–$ implies [equation] In summary, we have two constraints in the theory [equation] Following [ref] we can move to a gauge fixed Lagrangian by defining new coordinates [equation] Then it is easy to see that [equation] where we have used ([ref]).

Reduced Sigma-Model on O(N): Hamiltonian Analysis and Poisson Bracket of Lax Connection · Reduced $O(N)$ Sigma Model · 0.81
Nevertheless we can still probe parts of the amplitude by using the near-flat-space (NFS) limit of [ref] .[See [ref] for related work in $AdS_3$ and $AdS_4$.] This limit can be thought of as a subsector of the BMN string in which we keep only the leading terms under a large worldsheet Lorentz boost: p_±→ĝ^∓1/2 p_±, χ_±→ĝ^∓1/4χ_± .

Scattering in AdS(2)/CFT(1) and the BES Phase · Near-flat-space amplitudes and truncation · 0.93

Compares with it 3 papers

However, at the two-loop level there are sunset diagrams which induce radiative corrections to the dispersion relation that agree with the predicted near-flat limit of the dispersion relation in [ref] .

World-sheet scattering in AdS_5 x S^5 at two loops · Introduction · 0.98
For the quadratic terms, we write $ℒ_4^NFS=ℒ_BB+ℒ_BF+ℒ_FF$, and the all-boson term is the simplest: [equation] For the term mixing bosons and fermions (writing $ψ̅ ψ=ψ̅_aψ^a$ and $ω̅ ω=ω̅^αω_α$) we have: [equation] At this order, the powers of $g$ under the boost [ref] are the same as in the $AdS_5×S^5$ case [ref] : terms with two right-moving fermions and $∂_-$ scale correctly as $g$.

The Near-Flat-Space and BMN Limits for Strings in AdS4 x CP3 at One Loop · The near-flat-space limit · 0.94
We will show that the latters admit three qualitatively distinct regimes, that parallel the ones found for a magnon over the BMN vacuum [ref] .

Exciting the GKP string at any coupling · Strong coupling regimes · 0.82

Cites it as support 1 paper

The asymptotic Bethe equations also pass multiple tests in the near-flat-space limit [ref] .

Iterative Structure of the N=4 SYM Spin Chain · Introduction · 0.96

Cites it as background 14 papers

For further details on the derivation and the quantization of the model, we refer to our one-loop form factor computation [ref] , to the perturbative S-matrix calculations [ref] and, of course, to the original work [ref] .

Comments on World-Sheet Form Factors in AdS/CFT · Near-Flat World-Sheet Theory · 0.94
The limit proposed by Maldacena and Swanson in [ref] can be viewed as a partial restoration of this decoupling, by virtue of the fact that one light-like worldsheet momentum is taken to be much larger than the other, $p_-≫p_+$.

The Near-Flat-Space and BMN Limits for Strings in AdS4 x CP3 at One Loop · Introduction · 0.83
Another limit which will be important below is the so-called near-flat, or Maldacena-Swanson, limit [ref] .

Worldsheet Form Factors in AdS/CFT · String Worldsheet Theory · 0.93

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