Topological A-Model for $Ad{S}_5\times S^5$ Superstring and the Maldacena Conjecture

Abstract

A topological A-model constructed from $C{P}^{3|4}$ supertwistor variables is proposed for the $Ad{S}_5\times S^5$ superstring. At zero $AdS$ radius, free N=4 d=4 super-Yang-Mills amplitudes are reproduced by topological amplitudes of the corresponding gauged linear sigma model where the closed superstring vertex operator for a trace of $k$ super-Yang-Mills fields is described by a boundary state with $k$ edges. After turning on a Fayet-Iliopoulis term in the sigma model with coefficient $R^2=\sqrt{g_{YM}^{2}N}$, the topological amplitudes are claimed to reproduce the 't Hooft expansion of perturbative super-Yang-Mills amplitudes. Finally, this topological A-model is related to the usual $Ad{S}_5\times S^5$ superstring in the pure spinor formalism.

Clarified the definition of "vortex charge" which counts the number of edges and corrected typos and a factor of $2\pi$ in the action