Abstract

We present an explicit, exact to all orders in gravitational coupling E 7 ( 7 ) symmetry transformations of on-shell N = 8 supergravity fields in the gauge with 70 scalars in E 7 ( 7 ) SU ( 8 ) coset space, the local SU ( 8 ) symmetry being fixed. The non-linear realization of E 7 ( 7 ) includes a field-dependent SU ( 8 ) transformation preserving the unitary gauge. We find the conserved Noether–Gaillard–Zumino current of E 7 ( 7 ) symmetry, the linear part of it being a chiral SU ( 8 ) symmetry. We comment on the conformal realization of the E 7 ( 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.

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