The progress in physics of elementary particles has been to a large extent driven by the data obtained at the Large Hadron Collider (LHC) in Geneva, Switzerland. The data collected there describe the probability of a multitude of different outcomes for a single initial process - high-energy scattering of two protons. These protons start their life as nuclei of two hydrogen atoms. They are composed of quarks and gluons, which are bound together into protons by the strong interaction force - one of the four known fundamental forces of nature. The behavior of quarks, gluons and the corresponding strong force is known to be governed by the theory of quantum chromodynamics (QCD). Although it is a well-established theory, practical calculations in it are very complicated and require major efforts from particle theorists. This becomes an issue because the outcomes observed at the LHC are largely dominated by QCD scattering processes due to the strong interaction between the protons' constituents. Consequently, our ability to search for new fundamental physical phenomena, such as other kinds of particles and interactions, relies on our capability to make accurate predictions in QCD.
In this project the fellow has been exploring the intricate analytic structure of QCD so as to establish new methods to tackle the complexity that accompanies calculations involving the strong interaction. The theory of QCD belongs to a large class of more abstract theories, which also include the theory of the weak interaction and Maxwell's electrodynamics. Such theories are defined by supplementing the usual ``kinematic'' degrees of freedom, due to the physical spacetime, with additional ``color'' degrees of freedom, which are mathematically isolated from spacetime. Interestingly, these two, otherwise separate, kinds of degrees of freedom have recently been found to share certain algebraic properties. This color-kinematics duality of QCD and similar theories has been the main inspiration for this project.
In addition, the color-kinematics duality provides a link from QCD-like theories to gravitational theories. Gravity is the only of the four fundamental interactions, which is described not by a QCD-like theory but by Einstein's general relativity. However, we now know it to possess a double-copy structure, which is closely related to the color-kinematics duality of QCD-like theories. Using this connection, the fellow has found a novel avenue of research regarding to the computation of gravitational-wave emission from binary black-hole mergers. Such gravitational waves have only been experimentally measured in 2015 for the first time and are destined to become an invaluable source of data about the Universe. Due to the phenomenological importance of being able to compute classical observables in general relativity, the fellow has spent half of his time applying his knowledge of quantum particle theories to the classical gravitational interaction between black holes.
Following these two main avenues of research, in this project the fellow has helped establish new methods of computation in QCD and general relativity, finding new analytic results in both classes of theories and strengthening the link between them.
