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We show how modern methods can be applied to quantum gravity at low energy. We test how quantum corrections challenge the classical framework behind the equivalence principle (EP), for instance through introduction of nonlocality from quantum physics, embodied in the uncertainty principle. When the energy is small, we now have the tools to address this conflict explicitly. Despite the violation of some classical concepts, the EP continues to provide the core of the quantum gravity framework through the symmetry - general coordinate invariance - that is used to organize the effective field theory (EFT). [ABSTRACT FROM AUTHOR]

Gravity amplitudes are, via the Kawai–Lewellen–Tye relations intimately linked to products of Yang–Mills amplitudes. Explicitly, this shows up in computations of $\mathcal{N}=8$ supergravity where the perturbative expansion and ultraviolet behavior of this theory is akin to $\mathcal{N}=4$ super-Yang–Mills at least through three loops. Full persistence to all loop orders would be truly remarkable and imply finiteness of $\mathcal{N}=8$ supergravity in four dimensions. [ABSTRACT FROM AUTHOR]