On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring

TL;DR

This work develops a covariant light-cone description of the Type IIA superstring on $AdS_4\times CP^3$ within the ABJM framework by exploiting the $OSP(2,2|6)$ symmetry and a $\mathbb{Z}_4$ grading to derive the string Lagrangian and a gauge-fixed Hamiltonian invariant under $SU(2|2)\times U(1)$. Through a strong coupling (near plane-wave) expansion, the authors obtain the pure bosonic and fermionic Hamiltonian to quartic order, addressing the complications from higher-time-derivative fermionic terms via a fermionic shift and a unitary transformation that removes cubic interactions. They compute energy shifts for fermionic string states and demonstrate precise agreement with the asymptotic light-cone Bethe equations, providing a nontrivial test of the integrable structure in this AdS$_4$/CFT$_3$ setting. Moreover, quantum corrections to the heavy (massive) modes show that these excitations dissolve into a two-particle continuum, clarifying the spectrum and supporting the integrability-based scattering picture for this duality. The results reinforce the role of integrability in ABJM and provide a concrete framework for further one-loop S-matrix analyses and refinements of the interpolating function $h(\lambda)$.

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.

Figures (2)

• Figure 1: Dynkin diagrams for the two choices of gradings, $\eta=\pm 1$
• Figure 2: Self energy graphs.