On the prosaic origin of the double poles in the sine-GordonS-matrix

Coleman, Sidney; Thun, H.J.

doi:10.1007/bf01609466

Cited by 106 publications

(103 citation statements)

References 3 publications

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“…(3.2)-(3.4) specialise for the different operators we are interested in. 4 Multi-scattering singularities usually show up as higher order poles in two dimensions (they lead to anomalous thresholds in four dimensions) [25]. In the present case a simultaneous vanishing of the residues reduces the singularities to simple poles [24].…”

Section: Form Factorsmentioning

confidence: 63%

Universal amplitude ratios in the two-dimensional q-state Potts model and percolation from quantum field theory

1998

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We consider the scaling limit of the two-dimensional q-state Potts model for q ≤ 4. We use the exact scattering theory proposed by Chim and Zamolodchikov to determine the one and two-kink form factors of the energy, order and disorder operators in the model. Correlation functions and universal combinations of critical amplitudes are then computed within the two-kink approximation in the form factor approach. Very good agreement is found whenever comparison with exact results is possible. We finally consider the limit q → 1 which is related to the isotropic percolation problem. Although this case presents a serious technical difficulty, we predict a value close to 74 for the ratio of the mean cluster size amplitudes above and below the percolation threshold. Previous estimates for this quantity range from 14 to 220.

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Section: Form Factorsmentioning

confidence: 63%

Universal amplitude ratios in the two-dimensional q-state Potts model and percolation from quantum field theory

1998

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“…. Other poles in the scalar factor do not correspond to bound states but rather to anomalous thresholds [108,109]. The full set of (bound state) Bethe-Yang equations can be used to compute energies of various string states as long as the string length is asymptotically large, however to describe exact energies at finite volume we will have to go to the mirror theory.…”

Section: The S-matrix Of the Adsmentioning

confidence: 99%

Integrability of the ${\rm Ad}{{{\rm S}}_{5}}\times {{{\rm S}}^{5}}$ superstring and its deformations

Tongeren

Stijn²

2014

J. Phys. A: Math. Theor.

103

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This article reviews the application of integrability to the spectral problem of strings on AdS 5 × S 5 and its deformations. We begin with a pedagogical introduction to integrable field theories culminating in the description of their finite-volume spectra through the thermodynamic Bethe ansatz. Next, we apply these ideas to the AdS 5 × S 5 string and in later chapters discuss how to account for particular integrable deformations. Through the AdS/CFT correspondence this gives an exact description of anomalous scaling dimensions of single trace operators in planar N = 4 supersymmetry Yang-Mills theory, its 'orbifolds', and β and γ-deformed supersymmetric Yang-Mills theory. We also touch upon some subtleties arising in these deformed theories. Furthermore, we consider complex excited states (bound states) in the su(2) sector and give their thermodynamic Bethe ansatz description. Finally we discuss the thermodynamic Bethe ansatz for a quantum deformation of the AdS 5 × S 5 superstring S-matrix, with close relations to among others Pohlmeyer reduced string theory, and briefly indicate more recent developments in this area.

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“…The matrix S bns (θ) contains various types of poles. i) simple and double poles inside the physical sheet beyond the imaginary axis, which are redundant from our point of view as they are of a tachyonic nature, ii) double poles on the imaginary axis which can be explained by the usual "box diagrams" corresponding to the Coleman-Thun mechanism [40], iii) simple poles in the non-physical sheet which can be interpreted as unstable particles (see e.g. [33] and references therein) and iv) one simple pole on the imaginary axis inside the physical sheet at θ = iπ/2 + inνK ℓ which is associated to a soliton produced as an n th -breathers-soliton bound state.…”

Section: Soliton-breather Amplitudesmentioning

confidence: 99%

Breathers in the elliptic sine-Gordon model

Castro-Alvaredo

Fring

2003

J. Phys. A: Math. Gen.

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Abstract: We provide new expressions for the scattering amplitudes in the solitonantisoliton sector of the elliptic sine-Gordon model in terms of cosets of the affine Weyl group corresponding to infinite products of q-deformed gamma functions. When relaxing the usual restriction on the coupling constants, the model contains additional bound states which admit an interpretation as breathers. These breather bound states are unavoidably accompanied by Tachyons. We compute the complete S-matrix describing the scattering of the breathers amonst themselves and with the soliton-antisoliton sector. We carry out various reductions of the model, one of them leading to a new type of theory, namely an elliptic version of the minimal D Permanentn+1 -affine Toda field theory.

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On the prosaic origin of the double poles in the sine-GordonS-matrix

Abstract: We show that the apparently exotic double poles in the sine-Gordon S-matrix are nothing but ordinary anomalous thresholds.

Cited by 106 publications

References 3 publications

Universal amplitude ratios in the two-dimensional q-state Potts model and percolation from quantum field theory

Universal amplitude ratios in the two-dimensional q-state Potts model and percolation from quantum field theory

Integrability of the ${\rm Ad}{{{\rm S}}_{5}}\times {{{\rm S}}^{5}}$ superstring and its deformations

Breathers in the elliptic sine-Gordon model

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