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We explore and exploit the relation between non-planar correlators in ${\calN}=4$ super-Yang-Mills, and higher-genus closed string amplitudes in type IIBstring theory. By conformal field theory techniques we construct the genus-one,four-point string amplitude in AdS$_5\times S^5$ in the low-energy expansion,dual to an ${\cal N}=4$ super-Yang-Mills correlator in the 't Hooft limit atorder $1/c^2$ in a strong coupling expansion. In the flat space limit, thismaps onto the genus-one, four-point scattering amplitude for type II closedstrings in ten dimensions. Using this approach we reproduce several resultsobtained via string perturbation theory. We also demonstrate a novel mechanismto fix subleading terms in the flat space limit of AdS amplitudes by usingstring/M-theory.

Genus-One String Amplitudes from Conformal Field Theory