A New Limit of the AdS_5 x S^5 Sigma Model

Abstract

Using the pure spinor formalism, a quantizable sigma model has been constructed for the superstring in an AdS_5 x S^5 background with manifest PSU(2,2|4) invariance. The PSU(2,2|4) metric g_{AB} has both vector components g_{ab} and spinor components g_{alpha beta}, and in the limit where the spinor components g_{alpha beta} are taken to infinity, the AdS_5 x 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 g_{ab} are taken to infinity. In this limit, the AdS_5 x S^5 sigma model simplifies to a topological A-model 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.

33 pages harvmac, added references and fixed typos

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• $Ad{S}_5\times S^5$ supergravity vertex operators
• Note About Redefinition of BRST Operator for Pure Spinor String in General Background
• Topological String on OSP(1|2)/U(1)
• Integrability of the Gauged Linear Sigma Model for AdS_5xS^5
• Algebra of Lax Connection for T-Dual Models