The areas covered in this volume include: duality in string theory and supersymmetric gauge theories; phenomenological applications of string theory; strings in curved spacetime; quantum gravity; SUSY conformal field theories; QCD strings; aspects of mathematical physics, including: mirror symmetry, W-algebras, representation theory.

This book is aimed at graduate students and researchers in physics and mathematics who seek to understand the basics of supersymmetry from a mathematical point of view. It provides a bridge between the physical and mathematical approaches to the superworld. The physicist who is devoted to learning the basics of supergeometry can find a friendly approach here, since only the concepts that are strictly necessary are introduced. On the other hand, the mathematician who wants to learn from physics will find that all the mathematical assumptions are firmly rooted in physical concepts. This may open up a channel of communication between the two communities working on different aspects of supersymmetry.Starting from special relativity and Minkowski space, the idea of conformal space and superspace is built step by step in a mathematically rigorous way, and always connecting with the ideas and notation used in physics. While the book is mainly devoted to these important physical examples of superspaces, it can also be used as an introduction to the field of supergeometry, where a reader can ease into the subject without being overwhelmed with the technical difficulties.

String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point particles that form the basis for the standard model of particle physics. The phrase is often used as shorthand for Superstring theory, as well as related theories such as M-theory. By replacing the point-like particles with strings, an apparently consistent quantum theory of gravity emerges. Moreover, it may be possible to 'unify' the known natural forces (gravitational, electromagnetic, weak nuclear and strong nuclear) by describing them with the same set of equations. Studies of string theory have revealed that it predicts higher-dimensional objects called branes. String theory strongly suggests the existence of ten or eleven (in M-theory) space-time dimensions, as opposed to the usual four (three spatial and one temporal) used in relativity theory.

This thesis describes the structures of six-dimensional (6d) superconformal field theories and its torus compactifications. The first half summarizes various aspects of 6d field theories, while the latter half investigates torus compactifications of these theories, and relates them to four-dimensional superconformal field theories in the class, called class S. It is known that compactifications of 6d conformal field theories with maximal supersymmetries provide numerous insights into four-dimensional superconformal field theories. This thesis generalizes the story to the theories with smaller supersymmetry, constructing those six-dimensional theories as brane configurations in the M-theory, and highlighting the importance of fractionalization of M5-branes. This result establishes new dualities between the theories with eight supercharges.

The study of W algebras began in 1985 in the context of two-dimensional conf- mal field theories, the aim being to explore higher-spin extensions of the Virasoro algebra. Given the simultaneous growth in the understanding of two-dimensional metric gravity inspired by analyses of string models, it was inevitable that these algebras would be applied to give analogues of putative higher-spin gravity t- ories. This book is an exposition of the past few years of our work on such an application for the algebra: in particular, the BRST quantization of the n- critical 4D string. We calculate the physical spectrum as a problem in BRST cohomology. The corresponding operator cohomology forms a BV algebra, for which we provide a geometrical model. The algebra has one further generator, of spin three, in addition to the (spin two) energy-momentum tensor which generates the Virasoro algebra. C- trary to the Virasoro algebra, it is an algebra defined by nonlinear relations. In deriving our understanding of the resulting gravity theories we have had to - velop a number of results on the representation theory of W algebras, to replace the standard techniques that were so successful in treating linear algebras.

Contents: Lectures:Supermembranes: An Introduction (M J Duff)An Introduction to p-Branes (K S Stelle)Notes on Matrix Strings and Fivebranes (H Verlinde et al.)Intersecting Branes (J P Gauntlett)BPS Bound States, Supermembranes, and T-Duality in M Theory (J G Russo)D=6, N=1 String Vacua and Duality (L E Ibáñez & A M Uranga)Flat Symplectic Bundles of N-Extended Supergravities, Central Charges and Black-Hole Entropy (S Ferrara et al.)Black Hole Thermodynamics and String Theory (S R Das)Seminars:One-Instanton Calculations in N=2 Supersymmetric Gauge Theories (K Ito)Field Theory on Coadjoint Orbit and Self-Dual Chern-Simons Solitons (P Oh)Cohomological Yang-Mills Theory in Eight Dimensions (H Kanno et al.)Charged BTZ Black Hole as a Global Vortex in Anti-de Sitter Space–Time: A Bridge by Duality (Y Kim et al.)Tensionless Gravitational String in D=6, N=1 Heterotic String Vacua (N Kim et al.)Quantum Ergoregion Instability (G Kang) Readership: High energy physicists. Keywords:

This is the proceedings of the third Nagoya workshop on Strong Coupling Gauge Theories (SCGT), after SCGT 88 and SCGT 90. As a tradition of the Nagoya SCGT workshops, the focus is on dynamical symmetry breaking with particular emphasis on the nontrivial fixed points and/or large anomalous dimension, which was actually the basis of walking technicolor, strong ETC technicolor and top quark condensate, etc. Special attention is also paid to the fixed point structure in supersymmetric gauge theories, which has recently been highlighted through duality arguments.