String theory is a leading candidate for the unification of forces and matter. This book explores its predictions of the existence of additional dimensions and presents a unified perspective on the cutting-edge mathematical techniques required by graduate students and researchers in the field.
String theory is a leading candidate for the unification of universal forces and matter, and one of its most striking predictions is the existence of small additional dimensions that have escaped detection so far. This book focuses on the geometry of these dimensions, beginning with the basics of the theory, the mathematical properties of spinors, and differential geometry. It further explores advanced techniques at the core of current research, such as G-structures and generalized complex geometry. Many significant classes of solutions to the theory's equations are studied in detail, from special holonomy and Sasaki–Einstein manifolds to their more recent generalizations involving fluxes for form fields. Various explicit examples are discussed, of interest to graduates and researchers.
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'An excellent introduction to the methods and techniques used to study the geometries that could connect string theory to particle physics.' Prof. Juan Maldacena, Institute for Advanced Study 'This book provides an excellent exposition of the beautiful interplay of geometry and physics arising in string theory and will prove an invaluable introduction to the subject for physicists and mathematicians alike. It presents many of the latest developments and covers topics and details not discussed elsewhere. Written by an expert in the field, this book has a careful pedagogical approach and will be a key text for graduate students and an essential tool for researchers.' Prof. Chris Hull FRS, Imperial College London 'Geometry of String Theory Compactifications would be a most appropriate acquisition for a comprehensive university library, especially one supporting an active group of string theory researchers, whether they be in mathematics or physics departments Recommended.' M. C. Ogilvie, Choice
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A unified perspective on new and advanced mathematical techniques used in string theory research for graduate students and researchers.
Conventions. Preface. Introduction.
1. String theory and supergravity;
2. Spinors;
3. From spinors to forms;
4. Differential geometry;
5. Geometry
of forms;
6. Kähler geometry;
7. Ricci-flatness;
8. Vacua and reductions;
9.
Minkowski compactifications;
10. The vacuum problem in general;
11. AdS
vacua;
12. Frontiers. Bibliography. Index.
Alessandro Tomasiello is Professor of Physics at the University of Milano-Bicocca. He has held various positions in Harvard University, Stanford University, and École Polytechnique, Paris, during early stages in his career, and has been a plenary speaker at the annual Strings conference several times. His research applies modern mathematical techniques to problems of string theory and modern high-energy physics.
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