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

TL;DR

This paper explores a new limit of the AdS_5 x S^5 sigma model using pure spinor formalism, revealing a topological A-model that connects to N=4 super-Yang-Mills and potentially aids in a worldsheet proof of the Maldacena conjecture.

Contribution

It introduces a novel limit of the AdS_5 x S^5 sigma model where the vector components dominate, leading to a topological A-model linked to super-Yang-Mills theory.

Findings

The model reduces to a topological A-model in the new limit.

The open string sector describes d=4 N=4 super-Yang-Mills.

Potential for a worldsheet proof of the Maldacena conjecture.

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.