The Effective Action of N=8 Supergravity

TL;DR

The paper derives a simple, on-shell, gauge-invariant 1-loop effective action for $\mathcal{N}=8$ supergravity that is manifestly $\mathcal{N}=8$ supersymmetric at the linear level. It shows that 1-loop contributions exclude bubble and triangle diagrams, implying the absence of conformal and axial anomalies at this order, and it reveals a dual conformal symmetry in momentum space via a box-type invariant. By comparing with the $\mathcal{N}=4$ SYM warm-up and discussing the no-triangle hypothesis, the work connects these 1-loop structures to ongoing questions about UV behavior and potential all-loop finiteness of $\mathcal{N}=8$ supergravity. The results challenge the conventional emphasis on local counterterms, suggesting that non-local, box-type invariants and dual conformal symmetry may play a central role in the perturbative structure of the theory.

Abstract

We present a simple form of the on-shell gauge-invariant 1-loop effective action of N=8 supergravity which is manifestly N=8 supersymmetric at the linear level. By generalizing the dimensional arguments in superspace to non-local invariants, we show that the 1-loop effective action does not contain any contributions from bubble and triangle diagrams. The absence of bubbles implies the absence of conformal and axial anomalies. We also show that the 1-loop effective action of N=8 supergravity features a "dual" conformal symmetry in the momentum space.