Abstract
This book provides a detailed description of the duality between two integrable systems: the 1+1-dimensional Sine-Gordon model and the 1+1-dimensional Thirring model. While of great importance per se, this duality is only part of the target of the book. In order to reach an understanding of the subtleties involved in the duality, one has to take a journey through the properties of quantum integrable systems, building from the ground up the theory of exact S-matrices and familiarising oneself with the mathematical concept of a quantum group. The book therefore becomes an opportunity for a focussed study of integrability in its wider breadth of interest, always maintaining a clear ultimate purpose in mind: understanding the duality between bosons and fermions in 1+1 dimensions. This should make going through the book from the point of view of the reader/early-career researcher a live enterprise, as opposed to a more passive learning exercise.
Starting with a description of the classical and the quantum Sine-Gordon model, in particular the quantum spectrum, S-matrices and underlying quantum-group symmetry, and the renormalisation properties, the book then proceeds to discuss the Thirring model. The book then develops the theory and at the same time provides a significant number of examples, and concludes by presenting the duality with the Thirring model as originally stated by S. Coleman and refined in subsequent literature, and it focusses on a variety of tests of the duality.
Developed from a lecture series, this graduate level textbook includes the basic elements without relying on pre-requisites beyond standard graduate-level quantum field theory knowledge. The open-ended literature reviews included throughout the book constitute ideas for end-of-year projects, while the more standard exercises are accompanied by solutions.