Vanishing of Bulk Couplings for Superextremal Correlators

Prove in general that every bulk coupling responsible for a divergent superextremal holographic correlator vanishes, while the corresponding correlator remains finite, under the assumption of holographic renormalisability.

Background

The paper discusses the holographic-consistency conjecture concerning superextremal correlators satisfying conformal-dimension relations of the form Δi−Δj−Δk=2n\Delta_i-\Delta_j-\Delta_k=2n for non-negative integer nn. Such correlators are divergent, but the corresponding boundary divergence cannot be removed by a boundary-local counterterm under the stated assumptions.

The conjecture therefore asserts that the associated bulk coupling must vanish even though the correlator remains finite. The paper notes that this proposal has been verified in several settings, but presents it as a conjecture rather than a general theorem, particularly in the broader higher-point and holographic contexts.

References

Specifically, all (super)extremal correlators satisfying $\Delta_i-\Delta_j-\Delta_k=2n$, with $n$ a non-negative integer, are divergent; the corresponding bulk coupling must therefore vanish, while the correlator remains finite. This conjecture has been extensively verified in several settings, including $\mathcal{N}=2$ supergravity on $AdS_5\times S5$ and massive type-IIA superstring flux compactifications to AdS .

— Conformal Anomalies and Generalised Energy Conservation in De Sitter Spacetime  (2610.08113 - Du, 6 Oct 2026) in Section 1, Generalised energy conservation and holographic consistency