The all-plus helicity amplitudes turn out to be very closely related to the infinite sequence of one-loop maximally helicity-violating amplitudes in supergravity. The two sequences are related by a curious “dimension shifting formula.” In Ref. , a known dimension shifting formula  between identical helicity QCD and super-Yang–Mills amplitudes was used to obtain the four-, five-, and six-point amplitudes from the identical helicity gravity amplitudes using the KLT relations in the unitarity cuts. Armed with these explicit results, the soft and collinear properties were then used to obtain an ansatz valid for an arbitrary number of external legs . This provides a rather non-trivial illustration of how the KLT relations can be used to identify properties of gravity amplitudes using known properties of gauge theory amplitudes.
Interestingly, the all-plus helicity amplitudes are also connected to self-dual gravity [108, 52, 109] and self-dual Yang–Mills [143, 53, 94, 93, 4, 30, 33], i.e. gravity and gauge theory restricted to self-dual configurations of the respective field strengths, and , with . This connection is simple to see at the linearized (free field theory) level since a superposition of plane waves of identical helicity satisfies the self-duality condition. The self-dual currents and amplitudes have been studied at tree and one-loop levels [53, 4, 30, 33]. In particular, Chalmers and Siegel  have presented self-dual actions for gauge theory (and gravity), which reproduce the all-plus helicity scattering amplitudes at both tree and one-loop levels.
The ability to obtain exact expressions for gravity loop amplitudes demonstrates the utility of this approach for investigating quantum properties of gravity theories. The next section describes how this can be used to study high energy divergence properties in quantum gravity.
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