At the heart of quantum field theory live integrals that resemble mirages. In the familiar four-dimensional world, they are strictly zero — shadows that disappear in the light. But step into a space with a slightly shifted dimension (4 − 2ϵ), and these 'pseudo-vanishing' integrals gain substance and start influencing calculations. Previously, physicists had to deal with them separately, wasting effort on ghosts.
The authors of the new work turned the battle with ghosts into a clever trick. They noticed that if you carefully subtract the infrared and ultraviolet 'filling' from such an integral, the remainder falls apart into simple bricks. The infrared part corresponds to when the loop momentum becomes very soft, like a slowed-down record. The ultraviolet part is when it, on the contrary, goes off the charts. The local subtraction method allows you to decompose a two-loop knot into products of one-loop integrals or single integrals. It's like untangling a complex web by pulling two threads.
The test was performed on the two-loop amplitude for scattering of five gluons with identical helicities. It turned out that all contributions from soft and collinear (nearly parallel) particles exactly cancel against the well-known infrared structure of the theory. The final, regularization-independent answer is generated only by the ultraviolet regions: those where momenta are huge. This is like cleaning a cluttered room: once the dust and debris (infrared and collinear effects) are swept away, only what determines the shape of the furniture (ultraviolet) remains.
Dimensional regularization, which gives rise to pseudo-vanishing integrals, was invented to tame infinities in quantum electrodynamics and has since become a standard tool, although physicists still debate whether spacetime can be considered as continuously changing its number of dimensions.
In Carl Sagan's novel 'Contact', aliens transmit blueprints for a machine that uses extra dimensions — much like physicists 'add' dimensions to simplify calculations and then return to the familiar four.