Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J

TL;DR

This paper explores dyonic giant magnons in AdS_4 x CP^3, establishing their string and algebraic curve descriptions, and computes finite-J corrections, revealing both known and new results in the spectrum.

Contribution

It introduces the dyonic generalization of the CP^1 string solution and clarifies the nature of the 'big' and 'small' giant magnons within the algebraic curve framework.

Findings

Matching of the dyonic CP^1 solution with the 'small' giant magnon

Identification of the dressing method solution as the 'big' giant magnon

Finite-J corrections align with known results for non-dyonic cases and provide new insights for dyonic magnons.

Abstract

This paper studies giant magnons in AdS_4 x CP^3 using both the string sigma-model and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalisation of the CP^1 string solution, which matches the `small' giant magnon in the algebraic curve, and by pointing out that the solution recently constructed by the dressing method is the `big' giant magnon. We then use the curve to compute finite-J corrections to all cases, which for the non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon we recover the S^5 answer, but for the `small' and `big' giant magnons we obtain new corrections.