New Developments in Quantum Field Theory

Quantum field theory is one of most central constructions in 20th century th- retical physics, and it continues to develop rapidly in many different directions. The aim of the workshop New Developments in Quantum Field Theory, which was held in Zakopane, Poland, June 14-20, 1997, was to capture a broad selection of the most recent advances in this field. The conference was sponsored by the Scientific and - vironmental Affairs Division of NATO, as part of the Advanced Research Workshop series. This book contains the proceedings of that meeting. Major topics covered at the workshop include quantized theories of gravity, string theory, conformal field theory, cosmology, field theory approaches to critical phenomena and the renormalization group, matrix models, and field theory techniques applied to the theory of turbulence. One common theme at the conference was the use of large-Nmatrix models to obtain exact results in a variety of different disciplines. For example, it has been known for several years that by taking a suitable double-scaling limit, certain string theories (or two-dimensional quantum gravity coupled to matter) can be re-obtained from the large-Nexpansion of matrix models. There continues to be a large activity in this area of research, which was well reflected by talks given at our workshop. Remarkably, large- Nmatrix models have very recently just a few months before our meeting been shown to have yet another deep relation to string theory.

Zusammenfassung
Proceedings of a NATO ARW held in Zakopane, Poland, July 14-20, 1997.

Inhalt
The Structure of 2D Quantum Space-Time.- Scaling Laws in Turbulence.- Field Theory as Free Fall.- Center Dominance, Center Vortices, and Confinement.- Duality and the Renormalization Group.- Unification of the General Non-Linear Sigma Model and the Virasoro Master Equation.- A Matrix Model Solution of the Hirota Equation.- Lattice Approximation of Quantum Electrodynamics.- Three Introductory Talks on Matrix Models of Superstrings.- New Developments in the Continuous Renormalization Group.- Primordial Magnetic Fields and Their Development (Applied Field theory).- Towards Matrix Models of IIB Superstrings.- Quantum Mechanics of the Electric Charge.- Universal Fluctuations in Dirac Spectra.- Determination of Critical Exponents and Equation of State by Field Theory Methods.- Collective Dynamics of a Domain Wall an Outline.- Path Space Formulation of the BFV Theorem.- Surplus Anomaly and Random Geometries.- Topological Contents of 3D Seiberg-Witten Theory.- Free Strings in Non-Critical Dimensions.- Seiberg-Witten Theory, Integrable Systems and D-Branes.- Microscopic Universality in Random Matrix Models of QCD.- New Developments in Non-Hermitian Random Matrix Models.- Potential Topography and Mass Generation.- Past the Highest-Weight, and What You Can Find There.- The Spectral Dimension on Branched Polymer Ensembles.- Solving the Baxter Equation in High Energy QCD.