N=4 S-duality Compliant Scattering and within the AdS/CFT Duality

Abstract

It is pointed out the ${\cal N}=4$ supersymmetric gauge theory used in the anti-de Sitter holographic correspondence is required to be modified. The SL(2,Z) completion of the theory is required to map the correlators to string theory amplitudes. This is overlooked in the literature, and requires the (p,q) dyons to be inserted into the gauge theory calculations. In addition, the full four-point and higher-point scattering amplitudes in the spontaneously broken gauge theory are conjectured, in a similar manner as the amplitudes in IIB superstring amplitudes are obtained.