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Journal Article

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


Beisert,  Niklas
Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Beisert, N., Elvang, H., Freedman, D. Z., Kiermaier, M., Morales, A., & Stieberger, S. (2010). E7(7) constraints on counterterms in N=8 supergravity. Physics Letters B, 694(3), 265-271. doi:10.1016/j.physletb.2010.09.069.

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We prove by explicit computation that the operators D^4R^4 and D^6R^4 in N=8 supergravity have non-vanishing single-soft scalar limits at the 6-point level, and therefore they 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 finiteness 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.