E7(7) symmetry in perturbatively quantised N=8 supergravity

TL;DR

This work demonstrates that perturbatively quantised N=8 supergravity can preserve the full non-linear E_{7(7)} symmetry off-shell within a duality-invariant formulation. By constructing a consistent BRST/BV framework and employing Pauli–Villars regularisation, the authors prove the absence of SU(8) and non-linear E_{7(7)} anomalies to all orders, with any potential divergences constrained to respect the full E_{7(7)} symmetry. A key result is the reduction of the Wess–Zumino consistency problem for the non-linear E_{7(7)} current to the linear SU(8) case, ensuring anomaly vanishing when SU(8) is anomaly-free. The analysis includes explicit one-loop vector contributions, a careful treatment of energy Coulomb divergences in the Coulomb gauge, and a detailed account of the master equations governing both BRST and E_{7(7)} symmetries. Together, these findings support strong non-renormalisation prospects and have implications for the perturbative finiteness of maximal supergravity and the structure of amplitudes in the presence of duality symmetries.

Abstract

We study the perturbative quantisation of N=8 supergravity in a formulation where its E7(7) symmetry is realised off-shell. Relying on the cancellation of SU(8) current anomalies we show that there are no anomalies for the non-linearly realised E7(7) either; this result extends to all orders in perturbation theory. As a consequence, the e7(7) Ward identities can be consistently implemented and imposed at all orders in perturbation theory, and therefore potential divergent counterterms must in particular respect the full non-linear E7(7) symmetry.