S-duality and Topological Strings
  In this paper we show how S-duality of type IIB superstrings leads to an S-duality relating A and B model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitudes and D-instantons of the A-model capture perturbative B-model amplitudes.   Moreover this confirms the existence of new branes in the two models.   As an application we explain the recent results concerning A-model topological strings on Calabi-Yau and its equivalence to the statistical mechanical model of melting crystal. 
N. Nekrasov, H. Ooguri and C. Vafa