Abstract :
General conjectures about the SL(2,cZ) modular transformation properties of N = 4 superYang-Mills correlation functions are presented. It is shown how these modular transformation properties arise from the conjectured duality with IIB string theory on AdS5 × S5. We discuss in detail a prediction of the AdS duality: that N = 4 field theory, in an appropriate limit, must exhibit bonus symmetries, corresponding to the enhanced symmetries of IIB string theory in its supergravity limit.