Exploring Pure Spinor String Theory on AdS(4) x CP**3

In this paper we formulate the pure spinor superstring theory on AdS4 × Bbb CBbb P3. By recasting the pure spinor action as a topological A-model on the fermionic supercoset Osp(6|4)/SO(6) × Sp(4) plus a BRST exact term, we prove the exactness of the σ-model. We then give a gauged linear σ-model which reduces to the superstring in the limit of large volume and we study its branch geometry in different phases. Moreover, we discuss possible D-brane boundary conditions and the principal chiral model for the fermionic supercoset.