Quantum field theory is the language physicists use to describe elementary particles and their interactions. The authors of the work decided to slightly "tweak" this language: they introduced deformations, that is, small changes to the rules of the game. Because of these, the theory becomes nonlocal: particles begin to sense each other not only at the point of collision but as if from a distance.
Such corrections automatically generate gravity. Terms appear in the equations that depend on the curvature of spacetime, just like in Einstein's theory. For a broad class of theories, called conformal, these terms are universal. They are determined by just one parameter — the central charge, which characterizes the theory. This is like a soap bubble: its shape depends only on the pressure inside, not on the composition of the soap.
The physicists also studied another type of deformation — the so-called trace-trace corrections. Here the key role is played by the quantum anomaly: at the microscopic level, the classical conservation law is violated. It is the anomaly that determines what gravitational response ultimately emerges. Calculations showed that the result is finite. It does not depend on arbitrary choices of mathematical techniques — which is a good sign for the theory.
The work offers a new perspective on the idea of "induced gravity," which was developed by Andrei Sakharov. Gravity is not fundamental but emerges as a collective effect of quantum fields — much as the temperature of a gas is the averaged motion of molecules. And if such deformations were strong in the early universe, they could have left a trace in the cosmic microwave background.
The central charge for a free electromagnetic field is 2, and for an electron field it is 1. Different fields "contribute" different amounts of gravity.
In Alastair Reynolds's novel "Gravity", humans have learned to control gravity by altering the quantum properties of the vacuum — much like in this article.