Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation

TL;DR

This paper establishes that the quartic action for scalars in the massless graviton multiplet of type IIB supergravity on AdS_5×S^5, when reduced to five dimensions, precisely matches the corresponding sector of gauged N=8 5d supergravity on AdS_5. Using this equivalence, the authors compute the four-point function of the lowest weight chiral primary operators O_2^I in N=4 SYM_4 in the large-N, strong-coupling regime by evaluating AdS_5 exchange and contact diagrams, expressing the result in terms of D-functions. The analysis demonstrates that these four-point functions are entirely determined by the truncated 5d supergravity and do not receive contributions from higher KK modes. The results provide explicit, conformally covariant expressions for the four-point correlators in terms of boundary data and SO(6) structures, advancing the understanding of OPEs in strongly coupled N=4 SYM_4.

Abstract

We show that the recently found quartic action for the scalars from the massless graviton multiplet of type IIB supergravity compactified on AdS_5\times S^5 background coincides with the relevant part of the action of the gauged N=8 5d supergravity on AdS_5. We then use this action to compute the 4-point function of the lowest weight chiral primary operators $\tr(φ^{(i}φ^{j)})$ in N=4 SYM_4 at large $N$ and at strong `t Hooft coupling.