Finite-size effects from giant magnons

By G. Arutyunov, S. Frolov, M. Zamaklar. 2006

275 citations recorded by the source corpus.

In order to analyze finite-size effects for the gauge-fixed string sigma model on AdS5 × S 5 , we construct one-soliton solutions carrying finite angular momentum J . In the infinite J limit the solutions reduce to the recently constructed one-magnon configuration of Hofman and Maldacena. The solutions do not satisfy the level-matching condition and hence exhibit a dependence on the gauge choice, which however disappears as the size J is taken to infinity. Interestingly, the solutions do not conserve all the global charges of the psu(2, 2|4) algebra of the sigma model, implying that the symmetry algebra of the gauge-fixed string sigma model is different from psu(2, 2|4) for finite J , once one gives up the level-matching condition. The magnon dispersion relation exhibits exponential corrections with respect to the infinite J solution. We also find a generalisation of our one-magnon configuration to a solution carrying two charges on the sphere. We comment on the possible implications of our findings for the existence of the Bethe ansatz describing the spectrum of strings carrying finite charges. © 2007 Elsevier B.V. All rights reserved.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2e474ca0fe58f152dd0a34ccbc5617d248626168

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Citations in the corpus

N = 6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations (2008, result): “The result can be compared with various semi-classical string calculations [27] as has been done for the AdS5/CFT4 in [28] and with perturbative CS computations along the line of [20].”
Worldsheet scattering in AdS(5) x S**5 (2006, methodology): “With this motivation in mind we will use the light-cone gauge3 [29], the fixed-J gauge [27, 34] as well as a one-parameter superposition [ 35 ].4”
Dressing the Giant Magnon (2006, background): “More recent work on giant magnons has considered finite J effects [23], some quantum corrections [24], and giant magnon solutions for β–deformed AdS5 × S(5) [25].”
The off-shell symmetry algebra of the light-cone AdS5 × S5 superstring (2006, background): “Thus, the limit P+ → ∞ defines the theory on a plane and, by this reason, it can be called the “decompactifying limit” [14]-[20].”
Wrapping at four loops in N=4 SYM theory (2007, background): “In [12] it was proposed that the thermodynamic Bethe ansatz captures the wrapping interactions. This work has been extended in [ 13 ,14].”
Dressing and wrapping (2007, background): “A second indication comes from a study of the finite size effects [40] on the dispersion law of classical giant magnons [41].”
Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, background): “Deviations from the asymptotic Bethe ansatz have indeed been observed, mainly at strong coupling [27, 28, 29, 30] but also at weak coupling [32].”
Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “In a more general a-dependent gauge fixing [91, 175, 176], we would have ` = P+ = aE t.”
Foundations of the AdS5 × S5 superstring: I (2009, background): “The uniform light-cone gauge we discuss was introduced in [13, 85, 86], and belongs to the class of gauges used to study the dynamics of spinning strings in AdS5 × S5 [87, 88].”
S-matrix for strings on η-deformed AdS5 × S5 (2013, background): “In the case of the finite angular momentum the corresponding solution would also provide important information about the structure of the finite size corrections [28] in the η-deformed theory.”
Wrapping interactions at strong coupling: The giant magnon (2007, background): “22 08 ∗e-mail: ufrjanik@if.uj.edu.pl †e-mail: tomaszlukowski@gmail.com”
Four loop twist two, BFKL, wrapping and strings (2008, methodology): “In [21] the leading exponential finite size effects at strong coupling for a single giant magnon were computed from the identification with Lüscher-like corrections (see also [22, 23, 24]) and turned out to agree exactly with the expression obtained from classical string solution [25].”
The Zamolodchikov-Faddeev Algebra for AdS5 x S5 Superstring (2006, methodology): “The later was recently computed in [30] by reading off the quartic interaction vertices of the string Lagrangian [43] obtained in the generalized uniform light-cone gauge(7) [44, 24].”
Spiky strings and giant magnons on S5 (2006, unknown): “(1)Conformal gauge was used also in [19, 20]; their solution for a giant magnon with spin is equivalent to the one discussed below.”
On string S-matrix, bound states and TBA (2007, background): “One of the reasons behind this is that the interactions on the world-sheet are not ultra-local, typically the scattered states are solitons of finite size [37, 38].”
Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries (2010, methodology): “This was used in [63] to settle an issue of gauge noninvariance (dependence of the magnon energy on the light-cone gauge fixing parameter, once finite-size effects are considered) which had previously arisen in the AdS5 × S(5) case [64].”