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 theo

Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.

Self-contained and pedagogical introduction to key string theory ideas and techniques needed to understand D-branes.

Detailed, step-by-step introduction to the theoretical foundations of strings and branes, essential reading for graduate students and researchers.

Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.

This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

Boundary conformal field theory is concerned with a class of two-dimensional quantum field theories which display a rich mathematical structure and have many applications ranging from string theory to condensed matter physics. In particular, the framework allows discussion of strings and branes directly at the quantum level. Written by internationally renowned experts, this comprehensive introduction to boundary conformal field theory reaches from theoretical foundations to recent developments, with an emphasis on the algebraic treatment of string backgrounds. Topics covered include basic concepts in conformal field theory with and without boundaries, the mathematical description of strings and D-branes, and the geometry of strongly curved spacetime. The book offers insights into string geometry that go beyond classical notions. Describing the theory from basic concepts, and providing numerous worked examples from conformal field theory and string theory, this reference is of interest to graduate students and researchers in physics and mathematics.