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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
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.
