E7(7) symmetry in perturbatively quantised N=8 supergravity
Guillaume Bossard, Christian Hillmann, Hermann Nicolai
TL;DR
This paper demonstrates that the E7(7) symmetry in perturbatively quantised N=8 supergravity remains anomaly-free at all orders, ensuring the symmetry constrains possible divergences and counterterms.
Contribution
It proves the absence of anomalies for the non-linearly realised E7(7) symmetry in N=8 supergravity to all perturbative orders.
Findings
No anomalies for E7(7) symmetry at any order
E7(7) Ward identities are consistently implementable
Counterterms must respect full E7(7) symmetry
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.
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