Comments on 4-point functions in the CFT/AdS correspondence
Daniel Z. Freedman, Samir D. Mathur, Alec Matusis, Leonardo Rastelli
TL;DR
The paper investigates four-point functions in the dilaton-axion sector within the $AdS_5\times S^5$/CFT$_4$ framework, focusing on how supergravity graphs relate to boundary OPE structures. By analyzing s-, t-, u-channel and quartic AdS diagrams, it derives relations that express certain exchange graphs in terms of quartic integrals and computes leading logarithmic singularities, revealing nontrivial OPE-like content. The results show that logarithmic terms can appear in individual supergravity graphs and may or may not cancel when all diagrams (including gravitons) are summed, raising questions about the convergence and completeness of OPE expansions built solely from chiral primaries. The discussion argues that duality between bulk graphs and boundary OPEs is subtle and likely requires a larger operator spectrum than chiral primaries alone to achieve a convergent OPE in this AdS/CFT context.
Abstract
We study the four--point function of chiral primaries corresponding to the dilaton--axion sector in supergravity in the $AdS_5$/CFT$_4$ correspondence. We find relations between some of the supergravity graphs and compute their leading singularities. We discuss the issue of logarithmic singularities and their significance for the OPE structure of the CFT.