Duality Constraints on Counterterms in Supergravities

Abstract

AbstractThe UV finiteness found in calculations of the 4‐point amplitude in supergravity at loop order has not been explained, which motivates our study of the relevant superspace invariants and on‐shell superamplitudes for both and . The local 4‐point superinvariants for are expected to have nonlinear completions whose 6‐point amplitudes have non‐vanishing SSL's (soft scalar limits), violating the behavior required of Goldstone bosons. For , we find at that local 6‐point superinvariant and superamplitudes, which might cancel these SSL's, do not exist. This rules out the candidate 4‐point counterterm and thus gives a plausible explanation of the observed finiteness. However, at we construct a local 6‐point superinvariant with non‐vanishing SSL's, so the SSL argument does not explain the observed UV finiteness. For supergravity there are no 6‐point invariants at either or 4, so the SSL argument predicts UV finiteness.