Nonperturbative techniques in QFT and holography

One of the most striking successes of the theoretical approach to physics has been without doubt the development of the framework of quantum field theory (QFT) during the 20th century. Since its inception, it has been applied to an incredibly vast number of physical situations, ranging from interactions between fundamental particles, strongly correlated electrons, superconductors, Luttinger liquids, cold atoms at unitarity, early universe cosmology and even quantum gravity thanks to the celebrated AdS/CFT correspondence. Most of the calculational techniques in QFT rely on perturbative methods, where observables are computed as successive approximations around a theory that is easy to solve. However, there are several physical phenomena of interest that have so far resisted this approach, most notably confinement of quarks and gluons in QCD and high-temperature superconductivity. The aim of this research plan is to develop new nonperturbative tools to explore the strongly coupled behavior of quantum field theories. The research will employ state-of-the-art techniques, some developed by myself, to address several open questions in the field, most notably the structure of gauge theories at the nonperturbative level and the physics of black holes in the holographic context.