Introduction to conformal field theory. With applications to string theory
Conformal Field Theory (CFT) has found applications in string theory, statistical physics, condensed matter, and has been an inspiration for developments in pure mathemathics as well. Of course, the main feature of CFT is its invariance under the conformal group. By now it seems impossible to encompass the whole of the theory within a single volume. Therefore, this book is intentionally limited in scope. It is based on a graduate course at the LMU in Munich in 2007/2008 with special emphasis on computational issues, important for applications in string theory. After an introduction in Chapter 1, the authors discuss the conformal group, the concept of primary fields, radial quantization, operator product expansion and the Virasoro algebra in Chapter 2. Then, in Chapter 3, Kac-Moody algebras and non-linear extensions of the Virsoro algebra are studied, while, in Chapter 4 CFTs on the torus as well as orbifold CFTs and the parafermionic CFT are considered. In Chapter 5, supersymmetric CFTs are introduced, known for their applications in string theory. Also discussed are the spectral flow operator, the chiral ring and the so-called Gepner models, important beyond the perturbative level in string theory. In Chapter 6, the authors look at CFTs with boundaries which, in string theory, correspond to open strings with endpoints on D-branes. Not surprisingly, the orientifold of the bosonic string has 26 dimensions with gauge group SO(8192). This book will be useful to graduate students interested in new mathematical developments in CFT techniques relevant for string theory.
scientific article; zbMATH DE number 5546042