Giant magnons in AdS 4 × CP 3: Embeddings, charges and a Hamiltonian

Abstract

This paper studies giant magnons in CP 3, which in all known cases are old solutions from S 5 placed into two- and three-dimensional subspaces of CP 3, namely CP 1, RP 2 and RP 3. We clarify some points about these subspaces, and other potentially interesting three- and four-dimensional subspaces. After confirming that Δ-(J 1-J 4)/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 com ment on the embedding of finite-J solutions, and use these to compare string solutions to giant magnons in the algebraic curve. © 2009 SISSA.