Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT

TL;DR

The paper establishes a partial non-renormalisation for the four-point correlator of stress-tensor multiplets in $N=4$ SYM by leveraging Intriligator's insertion formula, superconformal covariance, and harmonic analyticity. It shows that all quantum corrections are controlled by a single universal function $F(s,t)$ of the cross-ratios, with specific linear combinations remaining at their free-field values; contact terms do not modify the structure. At strong coupling, the AdS/CFT prediction derived from tree-level AdS supergravity matches this universal form, providing a nontrivial cross-check of the correspondence. The results illuminate the role of harmonic superspace in constraining correlators and suggest broader implications for the operator product expansion in finite $N=2$ theories and for the holographic description of AdS dynamics.

Abstract

We show that, although the correlator of four stress-tensor multiplets in N=4 SYM is known to have radiative corrections, certain linear combinations of its components are protected from perturbative renormalisation and remain at their free-field values. This result is valid for weak as well as for strong coupling and for any gauge group. Our argument uses Intriligator's insertion formula, and includes a proof that the possible contact term contributions cannot change the form of the amplitudes. Combining this new non-renormalisation theorem with Maldacena's conjecture allows us to make a prediction for the structure of the corresponding correlator in AdS supergravity. This is verified by first considerably simplifying the strong coupling expression obtained by recent supergravity calculations, and then showing that it does indeed exhibit the expected structure.