The IQFT research team have been working on many ideas in quantum field theory. Particular emphasis has been placed on studying aspects of the maximally supersymmetric gauge theory in four dimensions: N=4 super Yang-Mills theory. This theory is a close cousin to quantum chromodynamics (QCD) which is the theory describing the strong nuclear interactions and an important ingredient in understanding proton-proton collisions at the LHC. By studying simpler models such as N=4 super Yang-Mills theory we gain greater theoretical control while retaining central features that we wish to study - namely that the results of different calculations are significantly simpler that the textbook approaches would suggest. Understanding and exploiting these features is a key line of investigation.
In the area of scattering amplitudes, new results have been obtained by extending and improving the analytic bootstrap programme. This is a framework for calculating scattering amplitudes based on understanding their general analytic structure. At least in the case of the simpler model of N=4 SYM these methods are vastly more powerful than textbook Feynman diagram calculations. Even more importantly they have lead us to discover new mathematical structures which control the analytic behaviour in suprprising ways. For example, the set of possible singularities of the amplitudes seems to be controlled in certain instances by a mathematical structure known as a cluster algebra. My team has explored and greatly extended the relationship between cluster algebras and scattering amplitudes in N=4 SYM, an insight we hope will lead to general lessons for quantum field theory.
We have also been studying a particular kind of high energy limit known as multi-Regge kinematics. In this regime we have made enormous progress in understanding the mathematical structure of scattering processes - leading us to a very general but compact formula for the scattering of any number of particles of any type at any interaction strength in N=4 super Yang-Mills theory. Such a powerful formula will, we hope, lead us to expressions in such high energy regimes for other models and perhaps even make contact directly with QCD.
Another theme is the study of correlation functions in conformal field theory. A surprising discovery in this area is that our bootstrap methods are also applicable to the study of quantum gravity within the framework of the AdS/CFT correspondence. This correspondence states that quantum field thories without gravity are equivlent to theories which do include gravitational interactions in a type of (negatively) curved space known as anti-de-Sitter space. In the case of N=4 super Yang-Mills theory the gravitational theory is actually a string theory. By using general mathematical properties of N=4 super Yang-Mills theory we have found that we are able to study the regime of strong coupling with a large number of colours (or particle species), instead of the three species which describe QCD in our world. The analytic bootstrap ideas are surprisingly powerful in this regime and have led us to explicit expressions to the quantum corrections to gravitational scatting in anti-de-Sitter space. Such expressions are not currently tractable by more direct textbook methods. By further exploring this line of research we may be able to obtain greater theoretical control over aspects of quantum gravity and string theory than currently available.
