E{7(7)} Symmetry and Finiteness of N=8 Supergravity
Renata Kallosh
TL;DR
This paper demonstrates that E7(7) symmetry constrains N=8 supergravity, predicting its all-loop ultraviolet finiteness by showing candidate counterterms violate deformed symmetry and are thus forbidden.
Contribution
It proves that E7(7) duality symmetry enforces the UV finiteness of N=8 supergravity at all loops by analyzing counterterms and symmetry constraints.
Findings
Candidate counterterms violate deformed E7(7) current conservation.
E7(7) symmetry predicts all-loop UV finiteness.
Uniqueness of the unitarity constraint supports the conclusion.
Abstract
We study N=8 supergravity deformed by the presence of the candidate counterterms. We show that even though they are invariant under undeformed E{7(7)}, all of the candidate counterterms violate the deformed E{7(7)} current conservation. The same conclusion follows from the uniqueness of the Lorentz and SU(8) covariant, E{7(7)} invariant unitarity constraint expressing the 56-dimensional E{7(7)} doublet via 28 independent vectors. Therefore E{7(7)} duality predicts the all-loop UV finiteness of perturbative N=8 supergravity.
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