Geometry of String Theory Compactifications

A unified perspective on new and advanced mathematical techniques used in string theory research for graduate students and researchers.

Alessandro Tomasiello (Author)

9781108473736, Cambridge University Press

Hardback, published 13 January 2022

500 pages
26.2 x 18.3 x 4 cm, 1.45 kg

'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

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.

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.

Subject Areas: Mathematical physics [PHU], Particle & high-energy physics [PHP]