Graviton exchange and complete 4-point functions in the AdS/CFT correspondence

TL;DR

This paper computes 4-point correlation functions in AdS/CFT by evaluating graviton exchange diagrams in AdS space, providing insights into the structure of correlators in N=4 SYM at strong coupling.

Contribution

It completes the calculation of 4-point functions of scalar operators in AdS/CFT by including graviton exchange, revealing the singularity structure and stress-energy tensor contributions.

Findings

Leading power singularity matches stress-energy tensor contributions.

Logarithmic singularities appear at subleading orders.

Results support the OPE structure in the dual CFT.

Abstract

The graviton exchange diagram for the correlation function of arbitrary scalar operators is evaluated in anti-de Sitter space, AdS(d+1). This enables us to complete the computation of the 4-point amplitudes of dilaton and axion fields in IIB supergravity on AdS5 X S5. By the AdS/CFT correspondence, we obtain the 4-point functions of the marginal operators Tr (F^2+...) and Tr(F F~ +...) in N=4, d=4 SU(N) SYM at large N, large g^2 N. 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 4-point functions at subleading orders.