Perspective on classical strings from complex sine-Gordon solitons

Okamura, Keisuke; Suzuki, Ryō

doi:10.1103/physrevd.75.046001

Cited by 72 publications

(130 citation statements)

References 39 publications

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“…Our conventions have the advantage of producing a much simpler set of frequencies (27). The conventions of [3] agree with those of [5], since they obtain the same frequency shifts although without writing a formula like (67). We observe that our conventions produce off-shell frequencies which vanish as the new pole is taken to infinity: Ω(y → ∞) = 0.…”

Section: Conventions and The Vacuummentioning

confidence: 79%

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Quantum strings and the AdS4/CFT3 interpolating function

Abbott

Aniceto

Bombardelli

2010

J. High Energ. Phys.

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The existence of a nontrivial interpolating function h(λ) is one of the novel features of the new AdS 4 /CFT 3 correspondence involving ABJM theory. At strong coupling, most of the investigation of semiclassical effects so far has been for strings in the AdS 4 sector. Several cutoff prescriptions have been proposed, leading to different predictions for the constant term in the expansion h(λ) = λ/2 + c + . . .. We calculate quantum corrections for giant magnons, using the algebraic curve, and show by comparing to the dispersion relation that the same prescriptions lead to the same values of c in this CP 3 sector. We then turn to finite-J effects, where a comparison with the Lüscher F-term correction shows a mismatch for one of the three sum prescriptions. We also compute some dyonic and higher F-terms for future comparisons.

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Section: Conventions and The Vacuummentioning

confidence: 79%

“…The coefficient a 0,1 contains the classical (order √ λ) corrections to the magnon's energy, of they type studied by [66,47,67,68] 16 and, using algebraic curves, by [72,34,4]. Its one-loop part was calculated for the AdS 5 × S 5 case by [39], who found agreement with the subleading Lüscher µ-term calculation of [73].…”

Section: Finite-j Effectsmentioning

confidence: 83%

Quantum strings and the AdS4/CFT3 interpolating function

Abbott

Aniceto

Bombardelli

2010

J. High Energ. Phys.

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“…2 For references on (generalizations of) giant magnons, see [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In a recent paper [26], new interpolating limit of AdS 5 × S 5 was considered.…”

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confidence: 99%

Emergent classical strings from matrix model

Hatsuda

Okamura

2007

J. High Energy Phys.

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Generalizing the idea of hep-th/0509015 by Berenstein, Correa, and Vázquez, we study many-magnon states in an SU(2) sector of a reduced matrix quantum mechanics obtained from N = 4 SU(N) super Yang-Mills on R × S 3 . Generic Q-magnon states are described as a chain of "string-bits" joining Q + 1 eigenvalues of background matrices which form a 1/2 BPS circular droplet in the large N limit. We will concentrate on infinitely long states whose first and last eigenvalues localize at the edge of the droplet. Each constituent string-bit has a complex quasi-momentum in general, while the total quasi-momentum P of the state is real. For given Q and P , the minimum energy of the chain of string-bits is realized when the Q + 1 eigenvalues are equally spaced on one and the same line segment joining the two outmost eigenvalues localized on the edge with angular difference P . Such configuration of bound string-bits precisely reproduces the dispersion relation for dyonic giant magnons in classical string theory. We also show the emergence of two-spin folded/circular strings in special infinite spin limit as particular configurations of closed chains of string-bits.

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“…In a more recent paper [16], a family of solutions to the string equations of motion on R × S 3 was found by exploiting its connection with the complex sine-Gordon model via Pohlmeyer's reduction. These solutions nicely interpolate between folded/circular strings on the one hand and dyonic giant magnons on the other, the latter being obtained in the J 1 → ∞ limit.…”

Section: )mentioning

confidence: 99%

“…This apparent dilemma is resolved by noting that the general finite-gap solution to the equations of a closed string moving through R × S 3 , constructed in [14,15], are valid for all values of the R-charges J 1 and J 2 . It therefore ought to be possible to obtain dyonic giant magnon solutions as a special limit of finite-gap solutions when J 1 → ∞, and in particular recover the condensate cut representation of [8] in this limit.In a more recent paper [16], a family of solutions to the string equations of motion on R × S 3 was found by exploiting its connection with the complex sine-Gordon model via Pohlmeyer's reduction. These solutions nicely interpolate between folded/circular strings on the one hand and dyonic giant magnons on the other, the latter being obtained in the J 1 → ∞ limit.…”

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confidence: 99%

Giant magnons and singular curves

Vicedo

2007

J. High Energy Phys.

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We obtain the giant magnon of Hofman-Maldacena and its dyonic generalisation on R × S 3 ⊂ AdS 5 × S 5 from the general elliptic finite-gap solution by degenerating its elliptic spectral curve into a singular curve. This alternate description of giant magnons as finite-gap solutions associated to singular curves is related through a symplectic transformation to their already established description in terms of condensate cuts developed in hep-th/0606145. IntroductionRecently, a certain limit of the AdS/CFT correspondence was proposed by Hofman and Maldacena [1] in which the 't Hooft coupling λ is held fixed allowing for a direct interpolation between the gauge theory (λ ≪ 1) and string theory (λ ≫ 1). In the Hofman-Maldacena (HM) limit, the energy E (or conformal dimension ∆ = E) and a U(1) R-charge J 1 both become infinite with the difference E − J 1 held fixed. On the string side, using static gauge X 0 = κτ , the energy density E = √ λκ/2π is uniform along the string so that the string effectively becomes infinitely long in this limit. Likewise on the gauge side, the dual singletrace conformal operator of the form tr(Z J 1 W J 2 ) clearly becomes infinitely long in this limit. If we relax the trace condition then we are able to consider elementary excitations on the gauge side given by infinitely long operators of the formThe trace condition is equivalent to the requirement that the total momentum of all excitations should vanish. The single excitation (0.1), which violates the momentum condition, describes a 'magnon' of momentum p with dispersion relation [2,3,4,5,6] E − J 1 = 1 + λ π 2 sin 2 p 2 .At large λ this state is described by a classical string solution on the real line called a 'giant magnon' which was identified in [1]. It corresponds to a solitonic solution of the infinite string embedded in an R × S 2 subsector of AdS 5 × S 5 .Subsequently, solitonic solutions of the infinite string moving through R × S 3 referred to as 'dyonic giant magnons' were identified in [2] and constructed in [7]. These solutions carry an extra finite U(1) R-charge J 2 and have the following dispersion relationThey correspond on the gauge side to bound states of J 2 magnons given by infinitely long operators of the form .).A general description of such dyonic giant magnons was then proposed in [8] using the language of finite-gap solutions and spectral curves [9,10,11,12,13], still restricting attention to the R × S 3 sector. In this framework, every solution is characterised by a spectral curve Σ equipped with an Abelian integral p called the quasi-momentum, such that the pair (Σ, dp) encodes the integrals of motion of the solution. A single dyonic giant magnon can 1 be described by a condensate cut B 1 from x 1 tox 1 on the spectral curve [8], whose presence can be traced down to the existence of a nonvanishing a-period for the differential of the quasi-momentum a dp ∈ 2πZ.The ensuing multivaluedness of the Abelian integral p(x) can equivalently be described in terms of simple poles of p(x) at the end points x 1...

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Perspective on classical strings from complex sine-Gordon solitons

Cited by 72 publications

References 39 publications

Quantum strings and the AdS4/CFT3 interpolating function

Quantum strings and the AdS4/CFT3 interpolating function

Emergent classical strings from matrix model

Giant magnons and singular curves

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