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## Interacting finite-size magnons

Venue: | J. Phys. A41 |

Citations: | 14 - 0 self |

### Citations

5606 | The large N limit of superconformal field theories and supergravity
- Maldacena
- 1998
(Show Context)
Citation Context ...k 38 A Elliptic functions 40 11 Introduction The solution to the problem of finding the spectrum of the N = 4 super-Yang-Mills dilatation operator or equivalently, by the conjectured AdS/CFT duality =-=[1]-=- [2], that of finding the energies of quantum strings on AdS5 × S5 has seen significant progress in recent times. In particular the discovery that the perturbative dilatation operator in the planar li... |

1499 |
Handbook of Mathematical Functions with formulas, graphs and mathematical tables, 10th Edition
- Abramowitz, Stegun
- 1972
(Show Context)
Citation Context ...c Newton Institute in Cambridge and the organizers of the SIS workshop, where this work was initiated, for their kind hospitality. A Elliptic functions We use the conventions of Abramowitz and Stegun =-=[58]-=-. The elliptic integrals of first, second and third kind are defined, respectively, as ∫ ϕ dθ F(ϕ|m) := √ , (A.1) 2 1 − m sin θ 0 ∫ ϕ √ E(ϕ|m) := 1 − m sin 2 θ dθ , (A.2) 0 ∫ ϕ dθ Π(n, ϕ|m) := 0 (1 − ... |

884 |
Strings in flat space and pp waves from
- Berenstein, Maldacena, et al.
(Show Context)
Citation Context ...tal excitations and the two body S-matrix provide a complete description of the theory in infinite volumes. That the fundamental excitation, the magnon, dispersion relation is given by the BMN result =-=[5]-=- ∆ = √ 1 + λ p sin2 π 2 (1.1) was shown to follow from the existence of global symmetries preserved by the spin chain vacuum state [6]. The relevant S-matrix for studying the infinite volume spectrum ... |

393 |
Tseytlin, “Type IIB superstring action
- Metsaev, A
- 1998
(Show Context)
Citation Context ...e center of mass frame. 2 From strings on × S 2 to sine-Gordon Superstrings living in a AdS5 × S5 background can be described by the Green-SchwarzPSU(2,2|4) Metsaev-Tseytlin action for the supercoset =-=[46]-=-. We will focus on closed SO(1,4)×SO(5) bosonic strings moving in an R×S 2 subspace, which as we are only interested in classical solutions, is a consistent truncation. We fix part of the world-sheet ... |

279 | Bethe ansatz for quantum strings
- Arutyunov, Frolov, et al.
(Show Context)
Citation Context ...ed phase by the global symmetries in [6]. Furthermore an asymptotic strong coupling expansion for the phase itself was conjectured by Beisert, Hernandez and Lopez in [8] based on perturbative results =-=[9]-=- and compatibility with the crossing symmetry as formulated by [10]. This conjecture was subsequently extended by Beisert, Eden and Staudacher [11], via an inspired “analytic continuation”, to a weak ... |

247 |
Long-range psu(2,2|4) Bethe ansaetze for gauge theory and strings
- Beisert, Staudacher
(Show Context)
Citation Context ...coupling expansion which begins at fourth order in a loop expansion and which has passed several checks against perturbative calculations [12]. This S-matrix provides, via the asymptotic Bethe ansatz =-=[13]-=-, predictions for the all-order anomalous dimensions of operators with infinitely large charges. Nonetheless there remain several outstanding issues amongst which is the pressing question of what happ... |

239 | The factorized S-matrix of CFT/AdS
- Staudacher
- 2005
(Show Context)
Citation Context ...2 π 2 (1.1) was shown to follow from the existence of global symmetries preserved by the spin chain vacuum state [6]. The relevant S-matrix for studying the infinite volume spectrum was introduced by =-=[7]-=- and, remarkably, was fixed up to an overall undetermined phase by the global symmetries in [6]. Furthermore an asymptotic strong coupling expansion for the phase itself was conjectured by Beisert, He... |

232 |
Integrable Hamiltonian Systems and Interactions Through Quadratic Constraints
- Pohlmeyer
- 1976
(Show Context)
Citation Context ...cult to find explicit solutions that are simple enough to manipulate. Instead it is possible to make use of the relation between strings on R × S 2 and sine-Gordon theory which was first described in =-=[36]-=- and discussed in the context of AdS/CFT by [37,38]. This purely classical correspondence relates the string equations of motion and constraints to the sine-Gordon equation of motion: in the simplest ... |

226 | The AdS5×S5 superstring worldsheet S-matrix and crossing symmetry, Phys. Rev. D73
- Janik
- 2006
(Show Context)
Citation Context ...c strong coupling expansion for the phase itself was conjectured by Beisert, Hernandez and Lopez in [8] based on perturbative results [9] and compatibility with the crossing symmetry as formulated by =-=[10]-=-. This conjecture was subsequently extended by Beisert, Eden and Staudacher [11], via an inspired “analytic continuation”, to a weak coupling expansion which begins at fourth order in a loop expansion... |

219 | The su(2|2) dynamic S-matrix
- Beisert
- 2008
(Show Context)
Citation Context ...ation, the magnon, dispersion relation is given by the BMN result [5] ∆ = √ 1 + λ p sin2 π 2 (1.1) was shown to follow from the existence of global symmetries preserved by the spin chain vacuum state =-=[6]-=-. The relevant S-matrix for studying the infinite volume spectrum was introduced by [7] and, remarkably, was fixed up to an overall undetermined phase by the global symmetries in [6]. Furthermore an a... |

162 |
A crossing-symmetric phase for
- Beisert, Hernandez, et al.
(Show Context)
Citation Context ... fixed up to an overall undetermined phase by the global symmetries in [6]. Furthermore an asymptotic strong coupling expansion for the phase itself was conjectured by Beisert, Hernandez and Lopez in =-=[8]-=- based on perturbative results [9] and compatibility with the crossing symmetry as formulated by [10]. This conjecture was subsequently extended by Beisert, Eden and Staudacher [11], via an inspired “... |

154 | Magnon bound states and the AdS/CFT correspondence
- Dorey
(Show Context)
Citation Context ...gh this obstacle could be overcome by considering the string moving on a orbifold of the S5 [26]. Just as the giant magnon, a string moving on an S2 ⊂ S5 , could be generalized to dyonic bound states =-=[27]-=-, strings in S3 , their finite size counterparts can be similarly generalized [28] and the corrections to the dispersion relation calculated [29]. Another method makes use of arguments of Lüscher [30]... |

153 | Wrapping interactions and a new source of corrections to the spin-chain / string duality, Nucl. Phys. B736
- Ambjorn, Janik, et al.
- 2006
(Show Context)
Citation Context ...gher loop terms in the spin chain Hamiltonian give rise to so called wrapping-interactions which spoil the application of the Bethe ansatz. General considerations using the thermodynamic Bethe ansatz =-=[14]-=- show that the wrapping effects will generically occur at the L-th loop order for spin chains of length L and more concretely it was shown [15] that the anomalous dimensions for finite-spin twisttwo o... |

145 |
Volume dependence of the energy spectrum in massive Quantum Field Theories. 2
- Luscher
- 1986
(Show Context)
Citation Context ...[27], strings in S3 , their finite size counterparts can be similarly generalized [28] and the corrections to the dispersion relation calculated [29]. Another method makes use of arguments of Lüscher =-=[30]-=-, generalized to the non-Lorentz invariant world-sheet theory [31], to use the asymptotic S-matrix to calculate the leading order exponential corrections to the dispersion relation. Indeed this method... |

110 |
The Zamolodchikov-Faddeev algebra for
- Arutyunov, Frolov, et al.
(Show Context)
Citation Context ...two-loops [20]. Furthermore it has been shown that the conjectured S-matrix is consistent with the Zamolodchikov-Faddeev algebra following from the conjectured integrability of the string sigma-model =-=[21]-=-. One particularly elegant result by Hofman and Maldacena [22] is the construction of the string dual to the elementary spin chain excitation, the giant magnon, which has a classical dispersion relati... |

105 |
Aspects of semiclassical strings
- Mandal, Suryanarayana, et al.
(Show Context)
Citation Context ...overy that the perturbative dilatation operator in the planar limit is described by an integrable spin-chain Hamiltonian [3] and of the existence of classical integrability for the string sigma model =-=[4]-=- has lead to the introduction of a range of new powerful tools. As is the case for many integrable models the dispersion relation for the fundamental excitations and the two body S-matrix provide a co... |

91 | Connecting giant magnons to the pp-wave: An interpolating limit
- Maldacena, Swanson
(Show Context)
Citation Context ...y. This world-sheet 2S-matrix can be calculated perturbatively and has been show to reproduce the tensor structure [18] of the exact conjectured S-matrix at leading order and, in the near-flat limit =-=[19]-=-, reproduce the phase to two-loops [20]. Furthermore it has been shown that the conjectured S-matrix is consistent with the Zamolodchikov-Faddeev algebra following from the conjectured integrability o... |

90 | Wrapping interactions at strong coupling – the giant magnon,” Phys
- Janik, Lukowski
(Show Context)
Citation Context ...rly generalized [28] and the corrections to the dispersion relation calculated [29]. Another method makes use of arguments of Lüscher [30], generalized to the non-Lorentz invariant world-sheet theory =-=[31]-=-, to use the asymptotic S-matrix to calculate the leading order exponential corrections to the dispersion relation. Indeed this method can be extended to calculate not merely classical corrections but... |

89 |
The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory, Phys. Rev. D75
- Bern, Czakon, et al.
- 2007
(Show Context)
Citation Context ...cher [11], via an inspired “analytic continuation”, to a weak coupling expansion which begins at fourth order in a loop expansion and which has passed several checks against perturbative calculations =-=[12]-=-. This S-matrix provides, via the asymptotic Bethe ansatz [13], predictions for the all-order anomalous dimensions of operators with infinitely large charges. Nonetheless there remain several outstand... |

81 |
World-sheet scattering
- Klose, McLoughlin, et al.
(Show Context)
Citation Context ...atrix for the resulting massive, non-Lorentz invariant, integrable world-sheet theory. This world-sheet 2S-matrix can be calculated perturbatively and has been show to reproduce the tensor structure =-=[18]-=- of the exact conjectured S-matrix at leading order and, in the near-flat limit [19], reproduce the phase to two-loops [20]. Furthermore it has been shown that the conjectured S-matrix is consistent w... |

69 |
Bethe ansatz for quantum strings,” JHEP 0410
- Arutyunov, Frolov, et al.
- 2004
(Show Context)
Citation Context ...ed phase by the global symmetries in [6]. Furthermore an asymptotic strong coupling expansion for the phase itself was conjectured by Beisert, Hernandez and Lopez in [8] based on perturbative results =-=[9]-=- and compatibility with the crossing symmetry as formulated by [10]. This conjecture was subsequently extended by Beisert, Eden and Staudacher [11], via an inspired “analytic continuation”, to a weak ... |

64 |
Circular semiclassical string solutions on
- Minahan
(Show Context)
Citation Context ...finite size corrections the breather solutions found by Hofman and Maldacena. In addition we are able to compare our solution for the case of J = 0 with the pulsating circular string found by Minahan =-=[45]-=- where we find agreement. Furthermore using the relation between the momentum, phaseshift and oscillation number we identify the dispersion relation for the single and double magnon solutions. For the... |

63 |
Dressing the giant magnon
- Kalousios, Spradlin, et al.
(Show Context)
Citation Context ...h magnons having real kinematic variables. In order to see this one must go to the larger space ×S3 where it can be shown that they arise from the two-charge magnon solutions of Spradlin and Volovich =-=[44]-=-. Not having the periodic solutions for this larger sector we are not able to unambiguously determine whether the same interpretation persists for the string solutions corresponding to both the fluxon... |

58 |
The Bethe-Ansatz for N = 4 super Yang-Mills,” JHEP 0303, 013 (2003), hep-th/0212208
- Minahan, Zarembo
- 2003
(Show Context)
Citation Context ...AdS5 × S5 has seen significant progress in recent times. In particular the discovery that the perturbative dilatation operator in the planar limit is described by an integrable spin-chain Hamiltonian =-=[3]-=- and of the existence of classical integrability for the string sigma model [4] has lead to the introduction of a range of new powerful tools. As is the case for many integrable models the dispersion ... |

58 | Finite-size effects from giant magnons
- Arutyunov, Frolov, et al.
(Show Context)
Citation Context ...consider the finite volume corrections coming from the finite angular momentum, J, analogues of the giant magnons. The dispersion relation for such finite angular momentum solutions was calculated in =-=[25]-=- for a variety of gauge choices. The resulting corrections to the single magnon dispersion relation were exponentially suppressed in the effective string length and gauge dependent. The gauge dependen... |

57 |
Classical Lumps and Their Quantum Descendants,” 1975 Erice lectures, reprinted in: S. Coleman, Aspects of Symmetry (Cambridge
- Coleman
- 1985
(Show Context)
Citation Context ...otion, this condition can be cast into the differential form T(∆) d∆ = 2π dn , (5.3) where ∆ denotes the energy of the system. These semi-classical methods are also valid for field theories, see e.g. =-=[51]-=-. Applying (5.3) to the finite-J giant magnon solution and our two-magnon solutions gives us the excitation energy, ∆ = E − J, in terms of the action variable n. For the magnon breathers this directly... |

56 | Gauge invariant finite size spectrum of the giant magnon”, Phys - Astolfi, Forini, et al. |

53 |
On the dynamics of finite-gap solutions in classical string theory
- Dorey, Vicedo
(Show Context)
Citation Context ...sponding to these multi-magnon states. Discouragingly the string equations of motion are non-linear and while, by using standard finite-gap methods, it is possible to find a general abstract solution =-=[35]-=- it is difficult to find explicit solutions that are simple enough to manipulate. Instead it is possible to make use of the relation between strings on R × S 2 and sine-Gordon theory which was first d... |

52 |
Wrapping interactions and the genus expansion of the 2- point function of composite operators
- Sieg, Torrielli
(Show Context)
Citation Context ... scattering amplitudes. Relatedly, direct perturbative calculations of the four-loop anomalous dimension of the length four Konishi operator have shown the presence of wrapping effects [16], see also =-=[17]-=-. (It should be mentioned that there is currently a discrepancy between these independent calculations.) The string duals to operators with infinite charges are quantum states of the worldsheet theory... |

50 |
A perspective on classical strings from complex sine-Gordon solitons,” Phys
- Okamura, Suzuki
- 2007
(Show Context)
Citation Context ...of the S5 [26]. Just as the giant magnon, a string moving on an S2 ⊂ S5 , could be generalized to dyonic bound states [27], strings in S3 , their finite size counterparts can be similarly generalized =-=[28]-=- and the corrections to the dispersion relation calculated [29]. Another method makes use of arguments of Lüscher [30], generalized to the non-Lorentz invariant world-sheet theory [31], to use the asy... |

45 |
Finite size effects for giant magnons on physical strings,” arXiv:0801.2064 [hep-th
- Minahan, Sax
(Show Context)
Citation Context ...certainly provide checks of whatever conjectures are made. Already studies of multi giant magnon states at leading order in exponential corrections have been carried out using algebraic curve methods =-=[34]-=-. For a more concrete description we would like to find string solutions corresponding to these multi-magnon states. Discouragingly the string equations of motion are non-linear and while, by using st... |

44 |
Unified approach to strings and vortices with soliton solutions, Phys. Rev. D14
- Lund, Regge
- 1976
(Show Context)
Citation Context ...hen considered quantum mechanically. The Pohlmeyer reduction or reformulation has been generalized to other systems; for example the O(4) sigma model, which is equivalent to complex sine-Gordon [36], =-=[47]-=-, and interestingly the full superstring on the supercoset PSU(2,2|4) SO(1,4)×SO(5) [38]. Because of the special properties of the superstring in the AdS5 × S5 , for one the theory is conformal even q... |

44 |
Finite-size Effects from Giant Magnons”, Nucl.Phys
- Arutyunov, Frolov, et al.
(Show Context)
Citation Context ...consider the finite volume corrections coming from the finite angular momentum, J, analogues of the giant magnons. The dispersion relation for such finite angular momentum solutions was calculated in =-=[25]-=- for a variety of gauge choices. The resulting corrections to the single magnon dispersion relation were exponentially suppressed in the effective string length and gauge dependent. The gauge dependen... |

41 |
How accurate is the quantum string Bethe ansatz
- Schafer-Nameki, Zamaklar, et al.
(Show Context)
Citation Context ...f quantum corrections to the energies of rigid spinning strings were shown to disagree with the predictions of from the Bethe ansatz with corrections that are exponentially small in the string length =-=[24]-=-. An alternative approach has been to consider the finite volume corrections coming from the finite angular momentum, J, analogues of the giant magnons. The dispersion relation for such finite angular... |

41 |
Mass scale in the sine-Gordon model and its reductions
- Zamolodchikov
- 1995
(Show Context)
Citation Context ...rdon theory simplifies dramatically in this “UV” regime essentially becoming the theory of a free scalar on a circle and it has proved useful to study the theory as a perturbation from this CFT, e.g. =-=[55]-=-. For the string theory the underlying theory is of course already conformal however this symmetry can be spontaneously broken by expanding the gauge fixed theory about a non-trivial classical solutio... |

38 | Analylical description of ultrashort optical pulse propagation in a resonsnt medium - Lamb - 1971 |

38 | A symplectic structure for string theory on integrable backgrounds
- Dorey, Vicedo
(Show Context)
Citation Context ...utions. There are explicit formulas in terms of Riemann theta functions for sine-Gordon three-phase solutions [56] though at this point one may as well use the generic string solutions constructed in =-=[35, 57]-=-. The three - magnon result would of course also be interesting as it may shine light on the question of what are the useful quantities to generalize to arbitrary magnon states. The three phase soluti... |

36 |
Nonperturbative methods and extended hadron models in field theory. 2. Two-dimensional models and extended hadrons,” Phys
- Dashen, Hasslacher, et al.
- 1974
(Show Context)
Citation Context ...erfeld condition is only valid for large n and does not include any zero-point energy. To include this effect one should use the WKB approximation as generalized by Dashen, Hasslacher and Neveu (DHM) =-=[53]-=- to solitons in quantum field theories (this was done for the decompactified limit by [54]). 5.1 Single magnon at finite J We apply our method to the single magnon case as a check and as an example of... |

29 |
Sine-Gordon-like action for the Superstring
- Mikhailov, Schafer-Nameki
- 2008
(Show Context)
Citation Context ...enough to manipulate. Instead it is possible to make use of the relation between strings on R × S 2 and sine-Gordon theory which was first described in [36] and discussed in the context of AdS/CFT by =-=[37,38]-=-. This purely classical correspondence relates the string equations of motion and constraints to the sine-Gordon equation of motion: in the simplest case the giant magnon corresponds to the kink solut... |

23 | Quantum corrections to spinning strings - Schafer-Nameki, Zamaklar, et al. |

20 |
Finite-Size Effects for Dyonic Giant Magnons,” arXiv:0801.0747 [hep-th
- Hatsuda, Suzuki
(Show Context)
Citation Context ... S2 ⊂ S5 , could be generalized to dyonic bound states [27], strings in S3 , their finite size counterparts can be similarly generalized [28] and the corrections to the dispersion relation calculated =-=[29]-=-. Another method makes use of arguments of Lüscher [30], generalized to the non-Lorentz invariant world-sheet theory [31], to use the asymptotic S-matrix to calculate the leading order exponential cor... |

18 |
Semiclassical Scattering of Quantized Nonlinear Waves,” Phys
- Jackiw, Woo
- 1975
(Show Context)
Citation Context ...30nor with boundaries and will be modified by the presence of a phase shift describing these interactions. We make use of the usual quantum mechanical relation, which can be extended to field theory =-=[52]-=-, between the time delay and this phase. This can then be used to describe the scattering of solitons, a result which was used in the context of giant magnon scattering [22], and we will use analogous... |

17 | An action variable of the sine-Gordon model
- Mikhailov
- 2006
(Show Context)
Citation Context ...enough to manipulate. Instead it is possible to make use of the relation between strings on R × S 2 and sine-Gordon theory which was first described in [36] and discussed in the context of AdS/CFT by =-=[37,38]-=-. This purely classical correspondence relates the string equations of motion and constraints to the sine-Gordon equation of motion: in the simplest case the giant magnon corresponds to the kink solut... |

16 |
Gauge theory correlators from non-critical string theory
- Phys
- 1998
(Show Context)
Citation Context ... A Elliptic functions 40 11 Introduction The solution to the problem of finding the spectrum of the N = 4 super-Yang-Mills dilatation operator or equivalently, by the conjectured AdS/CFT duality [1] =-=[2]-=-, that of finding the energies of quantum strings on AdS5 × S5 has seen significant progress in recent times. In particular the discovery that the perturbative dilatation operator in the planar limit ... |

7 |
Spectral theory for the periodic sine-Gordon equation: a concrete viewpoint
- Forest
- 1982
(Show Context)
Citation Context ...by the number of independent arguments, called phases, on which they depend. For example the finite-J one magnon solution of [25] corresponds to the single phase kinktrain of sine-Gordon theory, e.g. =-=[39]-=-. In this work we make use of the known two-phase solutions of sine-Gordon theory [40]. These were constructed using the Lamb ansatz [41] where the sine-Gordon field, φ(x, t), is assumed to be of the ... |

5 |
On the singularities of the magnon S-matrix
- Dorey, Hofman, et al.
(Show Context)
Citation Context ...s and magnon ‘breathers’ 1 . All of these solutions are periodic in time as well as in the spatial 1We call the reconstruction of breather-like sine-Gordon solutions magnon breathers. As discussed in =-=[43]-=- in the decompactification limit they are superpositions of BPS magnons carrying opposite charges and with both magnons having real kinematic variables. In order to see this one must go to the larger ... |

4 |
Wrapping Interactions and the Konishi Operator”, arXiv:0801.1661 [hep-th
- Keeler, Mann
(Show Context)
Citation Context ... of high energy scattering amplitudes. Relatedly, direct perturbative calculations of the four-loop anomalous dimension of the length four Konishi operator have shown the presence of wrapping effects =-=[16]-=-, see also [17]. (It should be mentioned that there is currently a discrepancy between these independent calculations.) The string duals to operators with infinite charges are quantum states of the wo... |

4 |
Periodic finite-zone solutions of the sine-Gordon equation, Funct
- Bobenko
- 1984
(Show Context)
Citation Context ... Another path, but perhaps just as complicated, would be to construct the three magnon solutions. There are explicit formulas in terms of Riemann theta functions for sine-Gordon three-phase solutions =-=[56]-=- though at this point one may as well use the generic string solutions constructed in [35, 57]. The three - magnon result would of course also be interesting as it may shine light on the question of w... |

3 |
Exact solutions of the sine-Gordon equation describing oscillations in a long (but finite) Josephson junction
- Costabile, Parmentier, et al.
- 1978
(Show Context)
Citation Context ...le the finite-J one magnon solution of [25] corresponds to the single phase kinktrain of sine-Gordon theory, e.g. [39]. In this work we make use of the known two-phase solutions of sine-Gordon theory =-=[40]-=-. These were constructed using the Lamb ansatz [41] where the sine-Gordon field, φ(x, t), is assumed to be of the form φ(x, t) = 2 arctanF(t)G(x) , (1.3) with F and G even functions satisfying ordinar... |

3 | Reduced sigma-model on AdS5 × S 5 :one-loop scattering amplitudes
- Klose, Zarembo
(Show Context)
Citation Context ...alculated perturbatively and has been show to reproduce the tensor structure [18] of the exact conjectured S-matrix at leading order and, in the near-flat limit [19], reproduce the phase to two-loops =-=[20]-=-. Furthermore it has been shown that the conjectured S-matrix is consistent with the Zamolodchikov-Faddeev algebra following from the conjectured integrability of the string sigma-model [21]. One part... |

2 |
Boxing with
- Eden
(Show Context)
Citation Context ... scattering amplitudes. Relatedly, direct perturbative calculations of the four-loop anomalous dimension of the length four Konishi operator have shown the presence of wrapping effects [16], see also =-=[17]-=-. (It should be mentioned that there is currently a discrepancy between these independent calculations.) The string duals to operators with infinite charges are quantum states of the worldsheet theory... |

2 |
Semiclassical scaling functions of sine-Gordon model
- Mussardo, Riva, et al.
(Show Context)
Citation Context ... carry out a proper WKB analysis of these solitonic solutions à la DHN which would correctly account for the zero-point contributions (within the context of sine-Gordon theory this was carried out by =-=[58]-=-). For the string states corresponding to the breathers the relation between the quantum number and the energy is straightforward and we directly find the exponentially suppressed corrections. While t... |

1 |
An action variable of the sine-Gordon
- Mikhailov
(Show Context)
Citation Context ...enough to manipulate. Instead it is possible to make use of the relation between strings on R × S 2 and sine-Gordon theory which was first described in [36] and discussed in the context of AdS/CFT by =-=[37,38]-=-. This purely classical correspondence relates the string equations of motion and constraints to the sine-Gordon equation of motion: in the simplest case the giant magnon corresponds to the kink solut... |

1 |
Soliton and differential geometry”, in: “Soliton theory and its
- Hesheng
- 1995
(Show Context)
Citation Context ... solution is in general a very non-trivial problem, fortunately it is possible to make use of the classical relations between sine-Gordon theory and the geometry of constant curved surfaces, see e.g. =-=[42]-=-. We explicitly integrate the equations describing the string surfaces, find their embedding for all values of their parameters, and calculate their global charges. We find a rich moduli space of soli... |

1 |
Abelian Functions and Solitons”, Univ. of Wroclaw Report No. 373 (unpublished
- Matveev
- 1976
(Show Context)
Citation Context ...e of some periodic solutions counting kinks is misleading and does not lead to a sensible classification. In fact, the general n-phase solution can be written down in terms of Riemann theta functions =-=[48]-=-. Here we are only interested in the special but broad class of the two-phase solutions which can be written in Lamb form [41] φ(σ, τ) = 2 arctanF(τ)G(σ) . (3.2) They were first studied in [40] as a d... |

1 |
Equivalent circuits and analogs of the Josephson effect
- Fulton
- 1977
(Show Context)
Citation Context ...his string in target space is finite. 2 In solid state physics the usual nomenclature is ‘fluxon’ for the fluxon oscillation, ‘breather’ for the fluxon breather and ‘plasmon’ for the plasmon breather =-=[49]-=-. 7(a) Single kink (b) Kink–anti-kink scattering (c) Breather (d) Kink train (elem) (e) Fluxon oscillation (elem) (f) Fluxon breather (elem) (g) Kink train (doub) (h) Fluxon oscillation (doub) (i) Fl... |

1 |
Über den Schnitt von
- Chebyshev
- 1946
(Show Context)
Citation Context ...erlaps with itself. In the chosen gauge, the coordinate τ also represents time. The coordinate lines which correspond to light-cone coordinates on the world sheet are what is known as a Chebyshev net =-=[50]-=- in the mathematical literature. These nets are characterized by the condition that in any net quadrangle the opposite sides are equal; here this condition is contained in (2.7). The angle 2φ between ... |