My research has focused primarily on quantum field theory and particle physics phenomenology. My goal is to address some of the fundamental questions of particle physics: What is the source of electroweak symmetry breaking? Why are there different flavors of quarks and leptons? Why do they have different masses? To answer these questions I have worked on supersymmetry, particle cosmology, and precision electroweak tests of the standard model.
· Extra Dimensions
The realization of the feasibility of millimeter or inverse TeV sized extra dimensions has opened up new classes of theories, especially in the area of electroweak symmetry breaking. Most of my recent work has focused on the possibility of higgsless electroweak symmetry breaking in extra dimensions. My collaborators and I have shown that WW scattering is unitary in a five dimensional theory without a Higgs, provided that the gauge symmetry breaking is achieved through Dirichlet boundary conditions. In a warped anti-de Sitter (AdS) background (like the Randall-Sundrum model) a custodial symmetry can ensure the correct ratio for the W and Z masses. We found that these higgsless models can be consistent with precision constraints on oblique parameters through either brane kinetic terms or requiring the light fermions to be roughly uniformly distributed in the extra dimension. Maintaining the correct Zbbbar coupling while getting the correct top quark mass is a more serious problem. We proposed two solutions based on the idea that the third generation may couple to a different conformal field theory (CFT) or, equivalently through the AdS/CFT correspondence, live in a different warped space from the first two generations and have a separate TeV brane. Separately we analyzed how quark and lepton masses can be produced in a higgsless theory via boundary conditions in the extra dimension. We were also able to use these model building ideas to propose a warped five dimensional lattice construction of a four dimensional chiral gauge theory. This may be a solution of a long-standing problem in lattice gauge theory, and open up new directions of research. Earlier we showed how deconstruction (a.k.a. latticization) of a five dimensional Grand Unified Theory (GUT) allows the GUT gauge symmetry to be broken by an analogue of the Scherk-Schwarz mechanism, and also allows the doublet-triplet splitting problem to be resolved in a simple way.
· Supersymmetry (SUSY)
Recently our understanding of SUSY gauge theories has been revolutionized by the work of Seiberg and Witten. For the last two years I have devoted the majority of my time to studying N=1 SUSY gauge theories with the new non-perturbative tools that have become available. With my collaborator I found a new mechanism for dynamical SUSY breaking that can produce realistic masses for the superpartners (squarks, sleptons, and gauginos) of the observed standard model particles. We also developed a class of models in which new strongly coupled gauge interactions both dynamically break SUSY and form composite quarks, squarks, leptons, and sleptons. Previously realistic models have relied on "messenger" (gravitational or gauge) interactions to communicate the SUSY breaking from a strongly coupled sector to the weakly coupled superpartners. Since, in our models, these particles couple directly to the SUSY breaking dynamics there is no need for intermediate "messengers" at all. In addition to this economy, these models can solve the SUSY flavor problem and also predict a unification of squark and slepton masses independent of gauge coupling unification. I also recently worked on a SUSY model that breaks electroweak symmetry by strong SUSY dynamics, which can be analyzed using Seiberg duality, and solves the mu problem.
Following the work of Maldacena and others on the correspondence between M- theory/supergravity on anti-de Sitter (AdS) backgrounds and conformal N=4 SUSY gauge theories we have tested the correspondence between "orbifolded" AdS theories and conformal gauge theories with fewer SUSY charges, including non-SUSY theories. Using the correspondence between M-theory/supergravity on blackhole AdS backgrounds and non-SUSY QCD, we calculated ratios of glueball masses in three and four dimensions in a strong coupling, large limit of QCD. We found that these ratios are in unexpectedly good agreement with the available lattice data. We also found a method to decouple some of the extra Kaluza-Klein modes that do not correspond to bound states of QCD.
We have also found exact results arising as a consequence of duality. We found a set of SUSY gauge theories that were self-dual, i.e. theories with dual descriptions that had different fundamental fields and a different superpotential, but with the same gauge structure. It had been conjectured that SUSY theories with matter in the adjoint representation of the gauge group and no superpotential were related to string theories. My collaborators and I found an infinite sequence of dual descriptions for such theories. We also found evidence for a new type of non-perturbative phenomena: as the number of matter fields is varied, an interacting conformal theory splits into interacting and free sectors. I also constructed a new dual description for certain chiral SUSY gauge theories. It was previously known that these theories confine with three of four flavors, I demonstrated that with five flavors they possess interacting infrared fixed points. We recently found a class of theories where a-maximization can be used to explicitly show that the IR splits into such a mixed phase. We also produced new D-brane constructions of related SUSY gauge theories with matter in tensor representations and examined how duality is related to D-brane motions in M-theory. We also studied the Seiberg-Witten curve for the deconstructed version of the 6D (0,2) theory on a torus, which clarified the nature of the low-energy effective field theory.