## 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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### References:

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