Applications of quantum field theory

Abstract

All four known forces in our universe are described by quantum field theory. Yet, despite their absolutely central role in Physics, quantum field theories are very far from being tamed with our current theoretical tools. A mathematically sound analytic description of physical phenomena such as confinement, chiral symmetry breaking or the existence of a mass gap is not available, and to address these fascinating questions, one needs control over QFTs in the strongly coupled regime where standard perturbative techniques fall short. New conceptual approaches and tools are urgently needed. My main research thus far has mainly been precisely focused on developing such tools by means of two complementary approaches. One approach aims at learning about non-perturbative QFT by studying one theory in excruciating detail, namely maximally supersymeetric Yang-Mills theory. The other complementary approach aims at leaning about strongly coupled QFT by chartingthe allowed space of all theories compatible with relativity, quantum mechanics and the assumption of analyticity, closely related tolocality. (AU)