9802813 Fendley Nonperturbative methods are valuable for exploring the large number of interesting systems with strong coupling in condensed matter physics. Experimental advances have allowed extensive scrutiny of systems like the quantum Hall effect, quantum impurities and spin chains where these new techniques are immediately applicable. Many of these systems exhibit fully non-Fermi-liquid behavior, meaning that one usually cannot even formulate a perturbation theory around free electrons. This research program will utilize the Bethe ansatz, conformal field theory, supersymmetry, and other methods of finding exact solutions in these strongly interacting systems. A great deal of progress has been made on developing new methods for exact computations, and a number of deep results of mathematical physics have been derived. More experiments are being done or planned on the Hall devices, and more theoretical work needs to be done. Integrable methods are quite powerful, but are far from computing everything, even in those special cases where they are applicable. There are still many interesting models of condensed matter physics where exact methods should be applicable. This research will develop new tools in order to treat integrable models by exact methods. In addition, the striking progress particle physicists have made in understanding supersymmetric field theories has had only limited application in condensed matter physics. This issue will also be pursued. %%% This grant will support theoretical research on finding exact solutions to a variety of systems characterized by electrons which interact so strongly that conventional methods fail. The techniques to be used are ones which are common throughout theoretical and mathematical physics, but which, sometimes, have had limited application to problems in condensed matter physics. ***
