Geometry and Physics of Branes (Series in High Energy Physics, Cosmology and Gravitation)

This book brings together the contents of the courses given at the doctoral school on 'Geometry and Physics of Branes' which took place in the spring of 2001 at the Centre for Scientific Culture 'Alessandro Volta' located in the beautiful environment of Villa Olmo in Como, Italy. The central topic of the school was the concept of the brane in string theory, from both physical and mathematical viewpoints. Rather than attempting to make a (forcefully superficial) general overview of the mathematics and physics of branes, the philosophy underlying the choice of lectures was to provide an introduction to some lines of research, related to the notion of branes in string theory, which are presently the object of strong interest in the mathematical and physical communities. Branes are solitonic configurations of a string theory that are represented by extended objects in a higher-dimensional space-time. They are essential for a comprehension of the non-perturbative aspects of string theory, in particular, in connection with string dualities. From the mathematical viewpoint, branes are related to several important theories, such as homological mirror symmetry and quantum cohomology. Geometry and Physics of Branes provides an introduction to current research in some of these different areas, both in physics and mathematics. The book opens with a lucid introduction to the basic aspects of branes in string theory. Topics covered in subsequent chapters include tachyon condensation, the geometry surrounding the Gopakumar-Vafa conjecture (a duality between the SU(N) Chern-Simons theory on S3 and a IIA string theory compactified on a Calabi-Yau 3-fold), two-dimensional conformal field theory on open and unoriented surfaces, and the development of a homology theory naturally attached to the deformations of vector bundles that should be relevant to the study of homological mirror symmetry. Pt. 1. An Elementary Introduction To Branes In String Theory -- Pt. 2. Physical Aspects -- Pt. 3. Mathematical Developments. Edited By Ugo Bruzzo, Vittorio Gorini And Ugo Moschella. Includes Bibliographical References And Index. In recent years there has been a remarkable improvement in our understanding of string theory.