Finite-size effects from giant magnons

Abstract

In order to analyze finite-size effects for the gauge-fixed string sigma model on AdS 5 × 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.

Review of AdS/CFT Integrability, Chapter III.5: Lüscher Corrections

“…Subsequently, corrections to its energy were found when the excitation was considered on a cylinder of finite size J . The resulting correction was evaluated from the deformed classical solution in [24,25] …”

Wrapping interactions at strong coupling: The giant magnon

“…Finally, finite size corrections were found for the giant magnon dispersion relation at strong coupling from classical string solutions [25,35]. They have the form…”

“…As one increases the coupling, and keeps J fixed the problem becomes more and more severe. Recently there appeared some explicit calculations which showed the limitations of the asymptotic Bethe ansatz both at weak [22] and at strong [23,24,25] coupling. It would be very interesting to understand these phenomenae on some general grounds.…”

“…This particular calculation is interesting since there exists a classical string computation for the same quantity [25] with which one can compare.…”

Spiky strings inAdS4×CP3with Neveu-Schwarz flux

“…Giant magnons can be thought of as a special limit of such spiky strings with shorter wavelength. Recently there has been a lot of work devoted for the understanding of the giant magnon and spiky string solutions in various backgrounds see for example [7]- [27].There has also been numerous papers devoted for understanding the finite size corrections on these solutions [28].…”