Topology, $C^*$-Algebras, and String Duality
About this Title
Jonathan Rosenberg, University of Maryland, College Park, MD
Publication: CBMS Regional Conference Series in Mathematics
Publication Year 2009: Volume 111
ISBNs: 978-0-8218-4922-4 (print); 978-1-4704-1569-3 (online)
MathSciNet review: MR2560910
MSC: Primary 46L85; Secondary 19L50, 46L05, 46L80, 53C08, 58B34, 81T30
String theory is the leading candidate for a physical theory that combines all the fundamental forces of nature, as well as the principles of relativity and quantum mechanics, into a mathematically elegant whole. The mathematical tools used by string theorists are highly sophisticated, and cover many areas of mathematics. As with the birth of quantum theory in the early 20th century, the mathematics has benefited at least as much as the physics from the collaboration. In this book, based on CBMS lectures given at Texas Christian University, Rosenberg describes some of the most recent interplay between string dualities and topology and operator algebras.
The book is an interdisciplinary approach to duality symmetries in string theory. It can be read by either mathematicians or theoretical physicists, and involves a more-or-less equal mixture of algebraic topology, operator algebras, and physics. There is also a bit of algebraic geometry, especially in the last chapter. The reader is assumed to be somewhat familiar with at least one of these four subjects, but not necessarily with all or even most of them. The main objective of the book is to show how several seemingly disparate subjects are closely linked with one another, and to give readers an overview of some areas of current research, even if this means that not everything is covered systematically.
Graduate students and research mathematicians interested in mathematical physics, particularly string theory; topology; C*-algebras.
Table of Contents
- Chapter 1. Introduction and motivation
- Chapter 2. $K$-theory and its relevance to physics
- Chapter 3. A few basics of $C$*-algebras and crossed products
- Chapter 4. Continuous-trace algebras and twisted $K$-theory
- Chapter 5. More on crossed products and their $K$-theory
- Chapter 6. The topology of T-duality and the Bunke-Schick construction
- Chapter 7. T-duality via crossed products
- Chapter 8. Higher-dimensional T-duality via topological methods
- Chapter 9. Higher-dimensional T-duality via $C$*-algebraic methods
- Chapter 10. Advanced topics and open problems