Finite-Size Corrections of the $\mathbb{CP}^3$ Giant Magnons: the Lüscher terms

TL;DR

This work computes classical and first quantum finite-size corrections to CP^3 giant magnons using generalized Lüscher formulas and the proposed exact $S$-matrix for ABJM. It analyzes two subspaces, $\mathbb{R}\times S^2\times S^2$ and $\mathbb{CP}^1$, obtaining leading $\mu$- and $F$-term corrections and comparing them with string theory and algebraic-curve results. The leading results for the big GM agree with GHOS (string) and IS (algebraic curve), while subtleties in contour choices and momentum parametrizations lead to nuanced differences in some subleading terms, informing the consistency of the $AdS_4/CFT_3$ integrability framework. The work also derives next-to-leading $\mu$-term corrections incorporating the strong-coupling expansion of $h(\lambda)$ and discusses their relation to the ${\cal N}=4$ SYM case and to algebraic-curve methods. Overall, the results provide a nontrivial validation of the ABJM integrability program and guide future investigations into wrapping, bound-state dynamics, and dyonic magnons in $\mathbb{CP}^3$.

Abstract

We compute classical and first quantum finite-size corrections to the recently found giant magnon solutions in two different subspaces of $\mathbb{CP}^3$. We use the Lüscher approach on the recently proposed exact S-matrix for $\mathcal{N}=6$ superconformal Chern-Simons theory. We compare our results with the string and algebraic curve computations and find agreement, thus providing a non-trivial test for the new $AdS_4/CFT_3$ correspondence within an integrability framework.