Bootstrapping One Theory and Bootstrapping All Theories

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Field theory lies at the heart of our understanding of all four known forces in nature: the electromagnetic, weak and strong forces as well as gravity. Moreover, our best candidate for uniting quantum theory and gravity - string theory - is itself best defined through a quantum field theory by means of the so-called gauge/string dualities. (These are remarkable correspondences stating the precise equivalence between certain quantum field theories and string theories in curved space-times with one extra spatial dimension.) Despite their absolutely central role in physics, gauge theories are very far from being tamed with our current theoretical tools. A mathematically sound analytic description of physical phenomena such as confinement, chiral symmetric breaking and the existence of a mass gap is simply not available and the precise field theory mechanism by which gauge/string dualities come about is still elusive. To address these fascinating questions, one needs control over quantum field theories 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 been precisely focused on developing such tools. For the next five years, my trainees and I will investigate dynamical quantities known as Correlation Functions and Scattering Amplitudes at finite coupling in non-perturbative quantum field theories. We shall use N=4 super Yang-Mills theory - a supersymmetric cousin of quantum chromodynamics - as a key subject of our explorations. Holography and Integrability are two modern tools which we shall use intensively. We will look for the most interesting correlators in this theory, precisely those which have thus far evaded all efforts at an analytic description. We will also consider a complementary approach whereby we explore instead the space of all possible quantum field theories compatible with the most sacrosanct principles in physics such as unitarity, relativity and locality. This is the so called S-matrix bootstrap program which we recently revived. We have recently observed that the most exciting physical theories - and in particular those describing real world phenomena - seem to be precisely those living at the boundary of the space of consistent theories, so right at the boundary between the possible and the impossible. We plan to extend the S-matrix bootstrap into a full fledged non-perturbative alternative to conventional methods in quantum field theory which are normally limited to weakly coupled systems.   As far as applications go, it is very hard to estimate the broader impact a theoretical research program in quantum field theory and string theory. Of course, if history serves us well, we can be certain that today's developments in fundamental physics, theoretical as they might sound, will lie at the very heart of tomorrow's technology