Finite-Size Corrections of the $\mathbb{CP}^3$ Giant Magnons: the L\"{u}scher terms

TL;DR

This paper calculates finite-size quantum corrections to giant magnons in $ ext{CP}^3$ using Lüscher techniques, validating the $AdS_4/CFT_3$ integrability correspondence through agreement with string and algebraic curve results.

Contribution

It provides the first quantum finite-size correction computations for giant magnons in $ ext{CP}^3$ using the Lüscher approach, confirming the integrability-based $AdS_4/CFT_3$ duality.

Findings

Agreement between Lüscher corrections and string/algebraic curve results

Validation of the integrability-based $AdS_4/CFT_3$ correspondence

First quantum finite-size corrections for $ ext{CP}^3$ giant magnons

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 L\"{u}scher 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.