Quantum Field Theory
Quantum mechanics, as developed by Bohr, Heisenberg and Schrödinger in the early 20th century, describes the peculiar nature of subatomic particles like electrons and protons. It is however insufficient to describe one of the most remarkable features of the microscopic world, namely the creation and annihilation of particles, which requires the formalism of Quantum Field Theory (QFT). All experiments conducted at particle accelerators at CERN and elsewhere are described remarkably well by a QFT, namely the Standard Model of Particle Physics. In special cases where both calculations and experiments can be performed to high accuracy, they agree to over 10 digits of precision, so a deviation of less than one in a billion. More broadly, QFT is used to study varied forms of matter including crystals, metals, superconductors and many more. It is the bedrock of many branches of modern theoretical physics.
Three highly constrained classes of QFTs are Conformal Field Theories (CFT), Supersymmetric Field Theories (SQFT) and integrable QFTs. These types of theories have further symmetries beyond those we typically encounter in nature. CFTs are theories with no dependence on size. This is very counter intuitive, as atoms behave very differently from tennis balls or stars. Yet one can construct systems in the lab that exhibit such behaviour, which in turn are modeled by CFTs. Numerous members of the group are at the forefront of global efforts to find new CFTs including using the novel self-consistency conditions known as the bootstrap equations. Others focus on properties of extended operators, all sharing the goal of charting the space of theories and their dynamics.
Supersymmetry relates different particle types: bosons (like photons and the Higgs boson) and fermions (like the electron and quarks). Treating these disparate particles as pairs simplifies calculations and often allows exact results to be obtained. Gravitational theories can also be supersymmetric and supersymmetry lies at the heart of string theory and M-theory. King's has long played a central role in the development of supersymmetry with a current focus on applications to the counting of degrees of freedom of black holes and constructing and classifying new gravity solutions and interacting field theories. These studies reveal rich connections to abstract algebra, complex geometries and number theory. It is not known whether nature exhibits supersymmetry at high energy, but this is a real possibility that makes this research even more relevant.
Conservation of energy and momentum are powerful principles of classical and quantum mechanics. Integrable systems have an infinite number of further conserved quantities and consequently very ordered dynamics. Rather counterintuitively, such systems may still be immensely rich and complex. Such models are studied for their own right — to find more theories that are rich, yet under good control. They are also used as models for calculations that cannot be done in non-integrable systems. Lastly, they arise naturally in special examples of string theory, supersymmetric theories and the AdS/CFT correspondence. In all these disciplines, the integrable examples are the closest to being completely solved and give a window into phenomena and regimes that cannot be probed by other methods.