Chiral Gauge Theories and Fermion–Higgs Systems

The amount of work on lattice theory relating to chiral gauge theory has dramatically increased this year with some forty papers in the subject, represented by about twenty contributions to this conference. In contrast, only a handful of papers have been written in the broader field of fermion–Higgs systems without an eye toward chiral gauge theory. Therefore, with one exception, I have decided to limit my review to the topic of chiral gauge theories, and within that I will primarily emphasize the conceptual developments rather than numerical simulations. The exception is some work in the pure Higgs sector concerning the regularization dependence of the upper bound for the Higgs mass[1] to which I would like to draw your attention. Last March, a very pleasant workshop was held in Rome, on the topic of non-perturbative approaches to chiral gauge theories. In that workshop, virtually all proposals around at the time were presented, following which some quite intense discussions took place in the proverbial smoke-filled back room in an attempt to understand the problems of some of the proposals and the connections between them. Some valuable insights were gained in these discussions and in my talk I will attempt to portray the underlying theme that we arrived at during that meeting. The topics discussed in the Rome workshop are the following: