Superstrings on AdS_4 x CP^3 as a Coset Sigma-model

TL;DR

The paper develops a coset sigma-model for type IIA strings on AdS_4 × CP^3 using the supercoset OSP(2,2|6)/({SO(3,1)}×{U(3)}), augmented by a Wess-Zumino term. It shows that a local κ-symmetry reduces the 24 real fermions to 16 physical ones for generic bosonic configurations, and establishes the classical integrability of the model via a Lax connection, paralleling the AdS_5 × S^5 construction. In the plane-wave limit, the quadratic action coincides with the Green–Schwarz pp-wave result, providing nontrivial consistency with the known IIA string theory on AdS_4 × CP^3. The analysis of κ-symmetry rank reveals a distinction between generic AdS_4 × CP^3 embeddings and singular AdS-only backgrounds, highlighting subtleties in quantization within the coset framework. Overall, the work offers a robust, integrable, partially κ-fixed description of the AdS_4 × CP^3 string with potential for semiclassical and S-matrix studies.

Abstract

According to the recent proposal by Aharony, Bergman, Jafferis and Maldacena the N=6 supersymmetric Chern-Simons theory in three dimensions has a 't Hooft limit whose holographic dual is described by type IIA superstings on AdS_4 x CP^3 background. We argue that the Green-Schwarz action for type IIA string theory on AdS_4 x CP^3 with kappa-symmetry partially fixed can be understood as a coset sigma-model on the same space supplied with a proper Wess-Zumino term. We construct the corresponding sigma-model Lagrangian and show that it is invariant under a local fermionic symmetry which for generic bosonic string configurations allows one to remove 8 out of 24 fermionic degrees of freedom. The remaining 16 fermions together with their bosonic partners should describe the physical content of AdS_4 x CP^3 superstring. As further evidence, we demonstrate that in the plane-wave limit the quadratic action arising from our model reproduces the one emerging from the type IIA superstring. The coset sigma-model is classically integrable which opens up the possibility to investigate its dynamics in a way very similar to the case of AdS_5 x S^5 superstrings.