A New Limit of the AdS 5 × S 5 Sigma Model

Using the pure spinor formalism, a quantizable sigma model has been constructed for the superstring in an AdS5 × S 5 background with manifest PSU(2, 2|4) invariance. The PSU(2, 2|4) metric gAB has both vector components gab and spinor components gαβ, and in the limit where the spinor components gαβ are taken to infinity, the AdS5 × S 5 sigma model reduces to the worldsheet action in a flat background. In this paper, we instead consider the limit where the vector components gab are taken to infinity. In this limit, the AdS5 × S 5 sigma model simplifies to a topological Amodel constructed from fermionic N=2 superfields whose bosonic components transform like twistor variables. Just as d=3 Chern-Simons theory can be described by the open string sector of a topological A-model, the open string sector of this topological A-model describes d=4 N=4 super-Yang-Mills. These results might be useful for constructing a worldsheet proof of the Maldacena conjecture analogous to the Gopakumar-Vafa-Ooguri worldsheet proof of Chern-Simons/conifold duality.