Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3

TL;DR

This work advances the finite-size analysis of giant magnons in the SU(2)×SU(2) sector of AdS$_4$×CP$^3$ by employing both the algebraic-curve formalism and Luscher's μ-term. It derives leading finite-size energy corrections for a single magnon, a two-magnon SU(2) configuration, and general multi-magnon states, providing explicit expressions that exhibit exponential suppression and, in some cases, additional $1/g$ prefactors. The results from the two methods are shown to be consistent, notably for the two-magnon equal-momenta case, and the analysis clarifies framework-dependent features such as frame choices in the S-matrix. A key finding is the explicit $Q$-dependence of the leading finite-size corrections, which can vanish when $Q=0$, and the confirmation that the multi-magnon corrections factorize into magnon-magnon scattering data with exponential tails. Together, these results reinforce the integrable structure linking the algebraic curve and S-matrix descriptions in the ABJM-related AdS$_4$/CFT$_3$ setting and provide tools for analyzing wrapping effects in this theory.

Abstract

We use the algebraic curve and Luscher's mu-term to calculate the leading order finite size corrections to the dispersion relation of giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3. We consider a single magnon as well as one magnon in each SU(2). In addition the algebraic curve computation is generalized to give the leading order correction for an arbitrary multi-magnon state in the SU(2) x SU(2) sector.