Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian

TL;DR

This paper analyzes giant magnons in CP3, clarifying their embeddings, calculating dispersion relations using a Hamiltonian approach, and comparing string solutions to algebraic curve predictions in the context of AdS4 x CP3.

Contribution

It provides a detailed study of giant magnon embeddings in CP3, confirms the Hamiltonian for small fluctuations, and compares finite-J solutions with algebraic curve results.

Findings

Confirmed Hamiltonian for small fluctuations

Calculated dispersion relations for various giant magnons

Compared string solutions with algebraic curve predictions

Abstract

This paper studies giant magnons in CP3, which in all known cases are old solutions from S5 placed into two- and three-dimensional subspaces of CP3, namely CP1, RP2 and RP3. We clarify some points about these subspaces, and other potentially interesting three- and four-dimensional subspaces. After confirming that E-(J1-J4)/2 is a Hamiltonian for small fluctuations of the relevant 'vacuum' point particle solution, we use it to calculate the dispersion relation of each of the inequivalent giant magnons. We comment on the embedding of finite-J solutions, and use these to compare string solutions to giant magnons in the algebraic curve.