On the worldsheet theory of the type IIA $ {\text{Ad}}{{\text{S}}_4} \times \mathbb{C}{\mathbb{P}_3} $ superstring

Abstract

We perform a detailed study of the type IIA superstring in AdS(4) x CP(3). After introducing suitable bosonic light-cone and fermionic kappa worldsheet gauges we derive the pure boson and fermion SU(2|2) x U(1) covariant light-cone Hamiltonian up to quartic order in fields. As a first application of our derivation we calculate energy shifts for string configurations in a closed fermionic subsector and successfully match these with a set of light-cone Bethe equations. We then turn to investigate the mismatch between the degrees of freedom of scattering states and oscillatory string modes. Since only light string modes appear as fundamental Bethe roots in the scattering theory, the physical role of the remaining $4_F+4_B$ massive oscillators is rather unclear. By continuing a line of research initiated by Zarembo, we shed light on this question by calculating quantum corrections for the propagators of the bosonic massive fields. We show that, once loop corrections are incorporated, the massive coordinates dissolve in a continuum state of two light particles.