Graviton exchange and complete four-point functions in the AdS/CFT correspondence

Abstract

The graviton exchange diagram for the correlation function of arbitrary scalar operators is evaluated in anti-de Sitter space, AdSd+1. This enables us to complete the computation of the four-point amplitudes of dilaton and axion fields in IIB supergravity on AdS5×S5. By the AdS/CFT correspondence, we obtain the four-point functions of the marginal operators Tr(F2+…) and Tr(FF̃+…) in N=4, d=4 SU(N) SYM at large N, large gYM2N. The short distance asymptotics of the amplitudes are studied. We find that in the direct channel the leading power singularity agrees with the expected contribution of the stress-energy tensor in a double OPE expansion. Logarithmic singularities occur in the complete four-point functions at subleading orders.