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

TL;DR

This paper formulates the type IIA superstring on AdS_4 x CP^3 as a coset sigma-model, demonstrating its classical integrability and matching its plane-wave limit to known superstring results.

Contribution

It constructs a coset sigma-model for the AdS_4 x CP^3 superstring with kappa-symmetry, providing a new framework for analyzing its integrability and physical spectrum.

Findings

The sigma-model is invariant under a local fermionic symmetry.

It reduces fermionic degrees of freedom from 24 to 16.

In the plane-wave limit, the quadratic action matches the superstring.

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.