Of strings and gravitons
In high-energy physics, the bridge between experiment and theory is provided by the scattering cross-section. This represents the probability for particles found in an initial state to scatter to some final state. The probability itself is given by the square of the scattering amplitude. The study of the mathematical properties of scattering amplitudes allows us to extract information about the structure of the underlying theory like symmetries at work. The GEOSCATAMP (The geometry of scattering amplitudes) project focused on gauge and gravity theories. Gauge and gravity scattering amplitudes are intimately related. At weak coupling, gravity amplitudes approximate the square of gauge theory amplitudes. This intriguing connection has only recently begun to be understood; it is the result of a conjectured duality between the colour and kinematical dependence of gauge theory amplitudes. The GEOSCATAMP team investigated the mathematical structures underlying this surprising connection between the scattering amplitudes of field theories. They found that the kinematic algebra used to describe these can be extended to any sector of the theories based on the appearance of so-called scattering equations. The new mathematical framework also revealed a close relation between well-known gravity theory predictions, like the Schwarzschild black hole, and gauge theory solutions, like the Coulomb-like potential. On the other hand, scattering equations for the amplitudes of quantum field theories suggested a connection with string theory. Before the end of the project, researchers constructed world-sheet models for several quantum field theories based on formulas of amplitudes satisfying the scattering equations. In the world-sheet models, interactions were not point-like, as in ordinary quantum field theories, but encoded in a 2D surface called the world-sheet. The study of scattering processes had always provided valuable insights in all branches of physics: from why the sky is blue, based on the light-scattering properties of crystals, to the structure of atoms and beyond. GEOSCATAMP work will extend the theoretical description of high-energy particles to gravity.
Keywords
Scattering amplitudes, gauge, gravity, colour-kinematics duality, GEOSCATAMP, quantum field theories
