Ph.D., Princeton University, 1989. Dynamics of strongly-interacting gauge theories (with various amounts of supersymmetry and in various dimensions).
Understanding the strong-coupling dynamics of gauge theories in four dimensions is one of the outstanding problems in theoretical particle physics. The paradigmatic example is to understand quark confinement from QCD, though strong-coupling questions also arise in many classes of models of physics beyond the Standard Model.
Exact analytical control of some non-perturbative quantities in gauge theories is possible if the theory is supersymmetric. Supersymmetric gauge theories are "regular" gauge theories with specially chosen values of the couplings and particle content. Their exact solutions have demonstrated Higgs and confining behavior---phases of gauge theories familiar from our experience with the electroweak and strong forces---as well as many new phases that had not been anticipated.
I am carrying out a systematic exploration of these new phases, with an eye towards qualitative lessons that may carry over to the larger class of non-supersymmetric gauge theories. Some of the more intriguing features of these solutions are the existence of large classes of strong-weak coupling dualities---equivalences between very strongly coupled theories and very weakly coupled ones---and the role that higher-dimensional gauge theories and even gravitational theories (string theory and M theory) play in deriving and organizing the low-energy solutions of many four-dimensional theories.