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Explicit action of \(E_{7(7)}\) on \(\mathcal N=8\) supergravity fields plasma from boost invariant expansion. (English) Zbl 1189.83089

Summary: We present an explicit, exact to all orders in gravitational coupling \(E_{7(7)}\) symmetry transformations of on-shell image \(\mathcal N=8\) supergravity fields in the gauge with 70 scalars in the image \(\frac{E_{7(7)}}{SU(8)}\) 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 image \(\mathcal N=8\) supergravity.

MSC:

83E50 Supergravity
17B25 Exceptional (super)algebras
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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