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

TL;DR

This work investigates the bosonic sector of the string in the $AdS_4 \times CP^3$ background in the near-plane-wave limit, using a large $P_+$ expansion to compute string energies in the $SU(2)\times SU(2)$ subsector. A canonical unitary transformation removes cubic interactions, yielding a tractable quartic Hamiltonian, from which energy shifts $\Delta E^{su2\times su2}$ are obtained and expressed in closed form. The authors then recast the all-loop light-cone Bethe equations in a uniform-light-cone basis and perform a nontrivial large $P_+$ expansion, obtaining predictions for the same energy shifts. Remarkably, the Bethe-eigenvalue predictions precisely match the string-theory results for arbitrary numbers of excitations, providing strong evidence for quantum integrability in the $AdS_4/CFT_3$ correspondence. The work lays a foundation for extending the analysis to fermions and massive modes, further elucidating the integrable structure of this duality.

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.