I study Quantum Field Theory and String Theory. Quantum Field Theory is the framework that unifies Quantum Mechanics and Special Relativity. Gauge theories, which are QFTs with a local symmetry, are known to describe three (the electromagnetic, weak and strong forces) of the four fundamental interactions between elementary particles. String Theory is the framework that unifies QFT and General Relativity, and is thus a unified theory of quantum gravity and of the gauge interactions. From another point of view, one can also show that gauge theories in d dimensions are mathematically equivalent to string theories in d+1 dimensions. This holographic correspondence relates the physics of the gauge theories and the physics of Quantum Gravity in a very subtle way.
Quantum field theories are very well understood when the strength of the interactions is weak (see the Nobel Prizes in Physics 1999 and 2004). When the couplings are strong, only a few tools are available to analyse the theories, and, in four dimensions, these tools apply mainly to supersymmetric models. This is a fundamental issue, because there is a great deal of very important non-supersymmetric physics that is entirely in the realm of strong coupling. The most prominent problem is to understand the permanent confinement of quarks into hadrons (like the proton and the neutron). The force that is responsible for this confinement is so strong that the associated energy field actually accounts for more than 90% of the mass of ordinary matter.
My research has mainly focused on the strong coupling properties of gauge theories with various amounts of supersymmetry. I have studied in particular their particle spectra at strong coupling (which differ significantly from the semiclassical spectra), properties of their large N limit, the role of instantons, and the quantum space of parameters of N=1 supersymmetric models. Overall, I have gradually oriented my work towards the study of models with the minimum amount or no supersymmetry at all. One basic motivation was to find how and when the physics of highly supersymmetric theories can be relevant to more realistic models, and I found the study of two dimensional toy models particularly instructive in this respect. Another important contribution was to generalize the double scaling limit approach to non-critical strings from zero or one to four dimensions. This provides the first full non-perturbative definitions of a large set of string theories.
Two of the main limitations of present knowledge are that closed string theories are tractable in general only in weakly curved backgrounds (which corresponds to infinite 't Hooft coupling on the gauge theory side), when a classical treatment based of Einstein's equations and its generalizations make sense; and that a holographic description of cosmological backgrounds is not known. I plan to focus on these two problems in the future. My main objective is to make progresses in understanding the long distance behavior of the Strong Force and the nature of space-like singularities that occur in many cosmological scenarios (like the Big Bang).