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arXiv · 1009.1643

E7(7) constraints on counterterms in N=8 supergravity

Niklas Beisert·Henriette Elvang·Daniel Z. Freedman·Michael Kiermaier·Alejandro Morales·Stephan Stieberger
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Abstract

We prove by explicit computation that 6-point matrix elements of D^4R^4 and D^6R^4 in N=8 supergravity have non-vanishing single-soft scalar limits, and therefore these operators violate the continuous E7(7) symmetry. The soft limits precisely match automorphism constraints. Together with previous results for R^4, this provides a direct proof that no E7(7)-invariant candidate counterterm exists below 7-loop order. At 7-loops, we characterize the infinite tower of independent supersymmetric operators D^4R^6, R^8, phi^2 R^8,... with n>4 fields and prove that they all violate E7(7) symmetry. This means that the 4-graviton amplitude determines whether or not the theory is finite at 7-loop order. We show that the corresponding candidate counterterm D^8R^4 has a non-linear supersymmetrization such that its single- and double-soft scalar limits are compatible with E7(7) up to and including 6-points. At loop orders 7, 8, 9 we provide an exhaustive account of all independent candidate counterterms with up to 16, 14, 12 fields, respectively, together with their potential single-soft scalar limits.

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Niklas Beisert, Henriette Elvang, Daniel Z. Freedman, Michael Kiermaier, Alejandro Morales, Stephan Stieberger. 2010-09-22. E7(7) constraints on counterterms in N=8 supergravity. https://doi.org/10.1016/j.physletb.2010.09.069

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