This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. It is intended to be the first in an occasional series of volumes of CMI lectures. Although not explicitly linked, the topics in this inaugural volume have a common flavour and a common appeal to all who are interested in recent developments in geometry. They are intended to be accessible to all who work in this general area, regardless of their own particular research interests.

Twenty-five years ago, Michael Green, John Schwarz, and Edward Witten wrote two volumes on string theory. Published during a period of rapid progress in this subject, these volumes were highly influential for a generation of students and researchers. Despite the immense progress that has been made in the field since then, the systematic exposition of the foundations of superstring theory presented in these volumes is just as relevant today as when first published. A self-contained introduction to superstrings, Volume 1 begins with an elementary treatment of the bosonic string, before describing the incorporation of additional degrees of freedom: fermionic degrees of freedom leading to supersymmetry and internal quantum numbers leading to gauge interactions. A detailed discussion of the evaluation of tree-approximation scattering amplitudes is also given. Featuring a new Preface setting the work in context in light of recent advances, this book is invaluable for graduate students and researchers in general relativity and elementary particle theory.

Twenty-five years ago, Michael Green, John Schwarz, and Edward Witten wrote two volumes on string theory. Published during a period of rapid progress in this subject, these volumes were highly influential for a generation of students and researchers. Despite the immense progress that has been made in the field since then, the systematic exposition of the foundations of superstring theory presented in these volumes is just as relevant today as when first published. Volume 2 is concerned with the evaluation of one-loop amplitudes, the study of anomalies and phenomenology. It examines the low energy effective field theory analysis of anomalies, the emergence of the gauge groups E8 x E8 and SO(32) and the four-dimensional physics that arises by compactification of six extra dimensions. Featuring a new Preface setting the work in context in light of recent advances, this book is invaluable for graduate students and researchers in high energy physics and astrophysics, as well as mathematicians.

http://www.worldscientific.com/worldscibooks/10.1142/0131

http://www.worldscientific.com/worldscibooks/10.1142/0131