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

TL;DR

This paper demonstrates that certain linear combinations of the stress-tensor four-point function in N=4 SYM are protected from renormalisation, remaining unchanged across coupling regimes, and verifies this via AdS/CFT correspondence.

Contribution

It introduces a partial non-renormalisation theorem for the stress-tensor four-point function in N=4 SYM, valid at all couplings and for any gauge group.

Findings

Protected linear combinations remain at free-field values.

Strong coupling results match protected structures predicted by the theorem.

Contact terms do not alter the amplitude structure.

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.