John Joseph Murphy Carrasco
A gauge theory called Yang-Mills describes the strongest force we have observed -- the one holding nucleons together in the center of atomic nuclei. Gravity is the weakest force we have observed, even though it seems to couple to all energy we can see. It turns out they're intimately related in many surprising ways.
One of our most exciting discoveries is that the sheer combinatorial explosion of graphs contributing to quantum corrections to the scattering of gluons in gauge theories may be fantastically redundant -- beautifully algorithmic algebraic structures relate all of their contributions to the information associated with a very few. Making this structure manifest (the duality between color and kinematics) allows for efficient calculation, but spectacularly also simple and natural expressions for graviton-scattering predictions in terms of double-copies of gluonic behavior -- even perturbative quantum corrections at the integrand level! How strange and wonderful, for all the information relevant to our description of the (perturbative, at least) evolution of the structure of space and time to be so compactly encoded in the interactions of gluons. Exploring the consequences of this duality, and the symmetries behind it, is very much a subject of rich active research. A completely open question at the moment is its relation to holography -- a robust idea from the early 1990s -- the complementary notion that strongly interacting gravitons in the volume of certain special space-times can be completely described by weakly interacting gluons on its surface.
One of the most surprising and important results we found stood in stark contrast to popular wisdom at the time; quantum field theory may admit perturbatively consistent and probability-conserving quantum descriptions of gravity in four dimensions. Previously physicists believed in the irreconcilability of (point-like) quantum field theory and Einstein's general theory of relativity, even under the protection of maximal supersymmetry. Calculating amplitudes where consensus predicted divergence, and discovering, instead, surprisingly good behavior in the ultraviolet, suggests that these assertions of incompatibility may be overly pessimistic. Rather, we find evidence of cancellations that propagate to all loop orders as can be seen using the unitarity method. We still have no proof of perturbative finiteness -- even if finite, may not prove to be UV-complete non-perturbatively. Even so, through explicit calculation we have exposed mysteries about the quantum behavior of gravity, that almost nobody suspected, which are quite exciting to pursue. I should mention that this has invigorated fields of formal field-theoretic inquiry to explain the observed cancellations -- forming an ongoing dynamic interplay between the amplitudes community, string theorists, and supergravity experts.
This is a research program its early stages, with much important work to be done to eventually get this in the hands of experimentalists. Beyond explicit measurements, this is definitely an intriguing theory in its own right -- a wonderful place for quantum field theorists to explore the consequences of some of their most familiar concepts (renormalization, running, etc.) in a completely classical (stochastic) domain that promises to be very data-rich in the near future.