Superstrings on AdS 4 × ℂpdbl; 3 as a coset sigma-model

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 × ℂPdbl; 3 background. We argue that the Green-Schwarz action for type IIA string theory on AdS 4 × ℂPdbl; 3 with κ-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 × ℂPdbl; 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 × S 5 superstrings. © 2008 SISSA.