Investigations in quantum field theory

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Quantum field theory is one of the most successful tools physicists use to describe the physical world. For example, the Standard Model, which describes in precise detail the behavior of all known particles, is a quantum field theory. Other quantum field theories are used to describe systems of very practical interest, superconductors and other exotic materials which lie at the core of modern and future electronic devices, such as quantum computers. Depending on the specific situation, a quantum field theory may be "weakly coupled" or "strongly coupled". Weakly coupled field theories are very well understood, and allow precise calculations which match in detail experimental results. Strongly coupled field theories are poorly understood, and very hard to use for precise calculations. This fact obstructs our progress in a variety of subjects. The main objective of this proposal is to develop new computational tools and ideas to study strongly coupled quantum field theories. Ultimately, progress in our theoretical understanding of strongly coupled field theories will impact our ability to taylor exotic quantum systems to practical applications, advance out understanding of the fundamental laws of the universe, and lead to deep mathematical advances.