The AdS(4) x CP(3) string and its Bethe equations in the near plane wave limit

TL;DR

This paper analyzes bosonic type IIA strings in an $AdS_4 imes CP_3$ background near the plane wave limit, deriving the Hamiltonian and comparing string energies with Bethe equations, finding perfect agreement.

Contribution

It derives the Hamiltonian up to quartic order and confirms the Bethe equations accurately predict string energies in this setting.

Findings

Hamiltonian derived up to quartic order in fields

String energies match Bethe equation predictions

Unitary transformation removes cubic Hamiltonian terms

Abstract

We perform a detailed study of bosonic type IIA string theory in a large light-cone momentum / near plane wave limit of $AdS_4 \times CP_3$. In order to attain this we derive the Hamiltonian up to cubic and quartic order in number of fields and calculate the energies for string excitations in a $R\times S^2 \times S^2$ subspace. The computation for the string energies is performed for arbitrary length excitations utilizing an unitary transformation which allows us to remove the cubic terms in the Hamiltonian. We then rewrite a recent set of proposed all loop Bethe equations in a light-cone language and compare their predictions with the obtained string energies. We find perfect agreement.