Bøger af L. Baulieu

Fractal Structure in 4d Gravity.- A One Dimensional Ideal Gas of Spinons, or Some Exact Results on the XXX Spin Chain with Long Range Interaction.- Kodaira-Spencer Theory of Gravity.- 3d Gravity and Gauge Theories.- On the W-Gravity Spectrum and its G-Structure.- Light-Cone Quantization of Matrix Models at c>1.- Multicritical Points of 2-Matrix Models.- The Super Self-Dual Matreoshka.- The Phenomenology of Strings and Clusters in the 3-d Ising Model.- Conformai Field Theory Techniques in Large N Yang-Mills Theory.- to Differential W-Geometry.- Topological Strings and QCD in Two Dimensions.- Continuum QCD2 in Terms of Discrete Random Surfaces with Local Weights.- Strings and Causality.- Loop Equation and Area Law in Turbulence.- The Two-Dimensional String as a Topological Field Theory.- Linear Systems for 2d Poincaré Supergravities.- Quantization of Mirror Symmetry.- Integrable Qft2 Encoded on Products of Dynkin Diagrams.- Remarks on Topological String Theories.- Hamiltonian Reduction of the BRST Complex and N=2 SUSY.- Lattice Models and N=2 Supersymmetry.- Canonical Construction of Liouville Field Operators with Arbitrary Spin.- Bethe Ansatz for the Bloch Particle in Magnetic Field.

As recent developments have shown, supersymmetric quantum field theory and string theory are intimately related, with advances in one area often shedding light on the other. The organising ideas of most of these advances are the notion of duality and the physics of higher dimensional objects or p-branes. The topics covered in the present volume include duality in field theory, in particular in supersymmetric field theory and supergravity, and in string theory. The Seiberg-Witten theory and its recent developments are also covered in detail. A large fraction of the volume is devoted to the current state of the art in M-theory, in particular its underlying superalgebra as well as its connection with superstring and N = 2 strings. The physics of D-branes and its essential role in the beautiful computation of the black hole entropy is also carefully covered. Finally, the last two sets of lectures are devoted to the exciting matrix approach to non-perturbative string theory.

The Cargese Summer School "e;Low Dimensional Applications of Quantum Field Theory"e; was held in July 1995. The School was dedicated to the memory of Claude Itzykson. This session focused on the recent progress in quantum field theory in two dimen- sions with a particular emphasis on integrable models and applications of quantum field theory to condensed matter physics. A large fraction of the school was also devoted to a detailed review of the exciting developments in four dimensional super- symmetric Yang-Mills theory. The diversity of the topics presented constitute, in our opinion, one of the most attractive features of these proceedings. Some contributions constitute a very thor- ough introduction to their subject matter and should be helpful to advanced students in the field while others present entirely new research, not previously published, and should be of considerable interest to the specialist. There were in depth introductory lectures on the application of conformal field theory techniques to disordered systems, on the quantum Hall effect, on quantum in- tegrable systems, on the thermodynamic Bethe Ansatz and on the new developments in supersymmetric gauges theories. The computation of the three point function of the Liouville model using conformal bootstrap methods was presented in detail.

Recent developments in supersymmetric field theory, string theory, and brane theory have been revolutionary. The main focus of the present volume is developments of M-theory and its applications to superstring theory, quantum gravity, and the theory of elementary particles. Topics included are D-branes, boundary states, and world volume solitons. Anti-De-Sitter quantum field theory is explained, emphasising the way it can enforce the holography principle, together with the relation to black hole physics and the way Branes provide the microscopic interpretation for the entropy of black holes. Developments in D-branes within type-I superstring and related theories are described. There are also possible phenomenological implications of superstring theory that would lie within the range of quantum gravity effects in the future generation of accelerators, around 1 TeV.