Explicit Action of E7(7) on N=8 Supergravity Fields

TL;DR

This paper derives explicit, all-order E7(7) symmetry transformations for on-shell N=8 supergravity fields, including a conserved current and insights into its algebraic structure, which are relevant for understanding anomalies and UV properties.

Contribution

It provides an explicit, exact realization of E7(7) symmetry transformations in N=8 supergravity, including the conserved current and algebraic structure, fixed in a specific gauge.

Findings

Explicit E7(7) transformations for supergravity fields derived

Conserved Noether-Gaillard-Zumino current identified

Discussion on conformal realization and algebra structure included

Abstract

We present an explicit, exact to all orders in gravitational coupling E7(7) symmetry transformations of on-shell N=8 supergravity fields in the gauge with 70 scalars in E7(7)/SU(8) coset space, the local SU(8) symmetry being fixed. The non-linear realization of E7(7) includes a field-dependent SU(8) transformation preserving the unitary gauge. We find the conserved Noether-Gaillard-Zumino current of E7(7) symmetry, the linear part of it being a chiral SU(8) symmetry. We comment on the conformal realization of the E7(7) algebra which includes a dilatation operator. We hope that these results can be useful for studies of anomalies/absence of anomalies and the UV behavior of N=8 supergravity.