Finite-Size Effects for Dyonic Giant Magnons

Ryo Suzuki; Yasuyuki Hatsuda

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Finite-Size Effects for Dyonic Giant Magnons

Yasuyuki Hatsuda, Ryo Suzuki

High Energy Physics - Theory · Submitted 6 Jan 2008

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

The authors' main claim By careful choice of poles in the su(2|2)^2-invariant S-matrix, we find agreement of the two results, which makes possible to predict the (leading) finite-size correction for dyonic giant magnons to all orders in the 't Hooft coupling.

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We compute finite-size corrections to dyonic giant magnons in two ways. One is by examining the asymptotic behavior of helical strings of hep-th/0609026 as elliptic modulus k goes to unity, and the other is by applying the generalized Luscher formula for mu-term of arXiv:0708.2208 to the situation in which incoming particles are boundstates. By careful choice of poles in the su(2|2)^2-invariant S-matrix, we find agreement of the two results, which makes possible to predict the (leading) finite-size correction for dyonic giant magnons to all orders in the 't Hooft coupling.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute finite-size corrections to dyonic giant magnons in two ways.	contribution 0.83	0.96	0.05	asserted 0.99
s1	One is by examining the asymptotic behavior of helical strings of hep-th/0609026 as elliptic modulus k goes to unity, and the other is by applying the generalized Luscher formula for mu-term of arXiv:0708.2208 to the situation in which incoming particles are boundstates.	method 0.99	0.71	0.05	asserted 0.97
s2	By careful choice of poles in the su(2\|2)^2-invariant S-matrix, we find agreement of the two results, which makes possible to predict the (leading) finite-size correction for dyonic giant magnons to all orders in the 't Hooft coupling.	result 0.93	0.95	0.86	asserted 0.98

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Original abstract

We compute finite-size corrections to dyonic giant magnons in two ways. One is by examining the asymptotic behavior of helical strings of hep-th/0609026 as elliptic modulus k goes to unity, and the other is by applying the generalized Luscher formula for mu-term of arXiv:0708.2208 to the situation in which incoming particles are boundstates. By careful choice of poles in the su(2|2)^2-invariant S-matrix, we find agreement of the two results, which makes possible to predict the (leading) finite-size correction for dyonic giant magnons to all orders in the 't Hooft coupling.

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References

Forward citations

Cited by 6 Pith papers

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

Exploring the mirror TBA
hep-th 2009-11 conditional novelty 7.0 of 10

Excited-state mirror TBA equations for sl(2) two-particle states are state-dependent and change form at infinitely many critical values of the 't Hooft coupling, the first for Konishi estimated near lambda of about 774.
Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
hep-th 2009-03 conditional novelty 7.0 of 10

The paper derives an infinite set of TBA equations for the AdS5 x S5 mirror model and shows that the associated Y-system follows only for rapidities in (-2, 2) and only under an unproven assumption about the dressing phase.
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
hep-th 2008-07 conditional novelty 7.0 of 10

A conjectured multiparticle Luscher formula applied to the AdS string sigma model reproduces the four-loop Konishi wrapping correction previously obtained from perturbative gauge theory.
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.
Four loop twist two, BFKL, wrapping and strings
hep-th 2008-11 conditional novelty 6.0 of 10

The four-loop wrapping correction to twist-two anomalous dimensions in N=4 SYM, computed from string theory, cancels the spurious poles in the Bethe ansatz result and reproduces the LO and NLO BFKL predictions.

Show 1 more citing papers

Five-loop Konishi from the Mirror TBA
hep-th 2010-02 conditional novelty 4.0 of 10

The mirror TBA reproduces, numerically, the five-loop Konishi anomalous dimension previously obtained from generalized Lüscher formulae, supporting the consistency of the AdS/CFT TBA system.

How the literature uses it

36 arXiv papers cite this in 70 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 · 50 sentences without a confident label

Uses its method or tool 2 papers

In order to calculate explicitly the $μ$-term from Eq. ([ref]), we shall follow basically the calculations of [ref] .

Finite-size effects of beta-deformed AdS_5/CFT_4 at strong coupling · The $μ$-term calculation · 0.99
Following the contour prescription of [ref] , this contribution enters with a minus, thus doubling the result.

Real and Virtual Bound States in L\"uscher Corrections for CP3 Magnons · Leading $μ$-term for the dyonic magnon · 0.99

Compares with it 8 papers

Explicit computations of each factor in ([ref]) are exactly the same as those in [ref] .

Finite-size Effect of the Dyonic Giant Magnons in N=6 super Chern-Simons Theory · Symmetric DGM state · 0.96
Once again these finite size corrections are related by a simple rescaling of the 't Hooft coupling, to the result obtained in [ref] , again exactly as predicted in [ref] .

Integrable Subsectors from Holography · Finite size Dyonic Giant Magnon · 0.96
When comparing to [ref] , note that $cosh(θ/2)=ℰ/2√(2λ)sin(p'/2)$.

Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J · Finite-size corrections · 0.99

Cites it as background 8 papers

During the last years, finite-size effects have been studied on the string side too in a number of papers [ref] , based mainly on direct string methods or on the Lüscher approach.

Wrapping effects in supersymmetric gauge theories · Introduction · 0.97
Indeed it would be extremely interesting to investigate for example the bound states $S$-matrix and the mirror [ref] counterpart of the sector we considered, in order to study wrapping effects also at weak coupling (see [ref] for $N=4$ SYM) and finite-size effects for dyonic giant magnons in $ℂℙ^3$ (see [ref] for string computations and [ref] for string and Lüscher-terms results in $N=4$ SYM).

Finite-Size Corrections of the $\mathbb{CP}^3$ Giant Magnons: the L\"{u}scher terms · Conclusions · 0.86
On the string theory side there have been recent papers addressing this issue and studying finite size contributions in the spectrum of magnons [ref] .

Finite-size effects in the superconformal beta-deformed N=4 SYM · Introduction · 0.80

What it cites · 89 sentences without a confident label

Builds on 2 papers

Firstly, we analyze the asymptotic behavior of helical strings of [ref] in the limit when they nearly reduce to an array of dyonic giant magnons, and determined the leading finite -$J_1$ correction to the energy-spin relation.

A Perspective on Classical Strings from Complex Sine-Gordon Solitons · Introduction · 0.82
In Appendix [ref], we briefly review derivation of the generalized Lüscher formula, slightly modifying the argument of [ref] to the case of our interest.

Wrapping interactions at strong coupling -- the giant magnon · Introduction · 0.93

Uses the method or tool of 6 papers

The diagrammatic technique developed in [ref] turns out to be useful for this purpose, where they showed how simple and double poles of the $su(2|2)^2 S$-matrix are related to particular exchange of physical particles.

Singularities of the Magnon Boundstate S-Matrix · Introduction · 1.00
The diagrammatic technique developed in [ref] turns out to be useful for this purpose, where they showed how simple and double poles of the $su(2|2)^2 S$-matrix are related to particular exchange of physical particles.

On the Singularities of the Magnon S-matrix · Introduction · 1.00
Now using the residue of the Green function in [ref] , we can perform integration over $q^1$ and get the expression [equation] where $I_a$ is the integrand coming from the sum $I_abc^+ + I_abc^- +J_abc+K_ab$ and explicitly given by [equation] where the momentum vectors $p$ and $q$ are both on-shell.

Wrapping interactions at strong coupling -- the giant magnon · Review of the Generalized Lüscher Formula · 0.92

Uses data or values from 1 paper

The rescaled energy $E$ and the spins $J_j$ $(j=1,2)$ were evaluated in [ref] .

A Perspective on Classical Strings from Complex Sine-Gordon Solitons · Helical strings with two spins near $k=1$ · 0.88

Compares with 6 papers

Thus we obtain the elementary-boundstate $S$-matrix as [equation] where $Σ(y, X)$ and $s_b (y, X)$ are given by [equation] Interestingly, the following formula holds[There is an identity for the spectral parameters of elementary magnons: [equation] ] [equation] which agree with the recent results of [ref] .

Four-loop perturbative Konishi from strings and finite size effects for multiparticle states · The $su(2|2)^2 S$-matrix and its singularity · 0.88
Thus we obtain the elementary-boundstate $S$-matrix as [equation] where $Σ(y, X)$ and $s_b (y, X)$ are given by [equation] Interestingly, the following formula holds[There is an identity for the spectral parameters of elementary magnons: [equation] ] [equation] which agree with the recent results of [ref] .

The S-matrix of String Bound States · The $su(2|2)^2 S$-matrix and its singularity · 0.88
Collecting the results [ref] and [ref], the energy-spin relation [ref] becomes [equation] This is consistent with the finite -$J_1$ correction to giant magnons in the literature [ref] if we set $θ=0$ and $cos2ω_2 = 1$.

Finite-size Effects from Giant Magnons · Helical strings with two spins near $k=1$ · 0.96

Cites as background 25 papers

In this appendix, we give a brief review on the generalized Lüscher formula proposed by Janik and Łukowski [ref] .

Wrapping interactions at strong coupling -- the giant magnon · Review of the Generalized Lüscher Formula · 0.85
Moreover in [ref] , they proposed “string" $S$-matrix which satisfies the standard Yang-Baxter equation, while “gauge" $S$-matrix of [ref] satisfies the twisted Yang-Baxter equation.

The su(2|2) Dynamic S-Matrix · Introduction · 0.93
Moreover in [ref] , they proposed “string" $S$-matrix which satisfies the standard Yang-Baxter equation, while “gauge" $S$-matrix of [ref] satisfies the twisted Yang-Baxter equation.

The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring · Introduction · 0.93

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