Finite-size Effects from Giant Magnons

TL;DR

This paper constructs finite-size one-magnon solutions in the AdS_5 x S^5 string sigma model, revealing gauge dependence, charge non-conservation, and exponential corrections to the dispersion relation, with implications for the Bethe ansatz.

Contribution

It introduces finite J solutions that extend known infinite J magnons, analyzing their properties and symmetry deviations, and explores their impact on the spectrum's Bethe ansatz.

Findings

Finite J solutions reduce to known magnons as J approaches infinity.

Solutions depend on gauge choice and do not conserve all charges.

Magnon dispersion relation receives exponential finite-size corrections.

Abstract

In order to analyze finite-size effects for the gauge-fixed string sigma model on AdS_5 x 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.