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Sasakian Geometry$
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Charles Boyer and Krzysztof Galicki

Print publication date: 2007

Print ISBN-13: 9780198564959

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780198564959.001.0001

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Sasakian Structures, Killing Spinors, and Supersymmetry

Sasakian Structures, Killing Spinors, and Supersymmetry

Chapter:
(p.529) Chapter 14 Sasakian Structures, Killing Spinors, and Supersymmetry
Source:
Sasakian Geometry
Author(s):

Charles P. Boyer

Krzysztof Galicki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198564959.003.0015

This chapter gives a very brief overview of the rich theory of Killing spinors describing Bär's correspondence which connects Sasaki-Einstein geometry to Berger's holonomy theorem. It is then shown how weak holonomy G2 and nearly Kähler structures relate to 3-Sasakian 7-manifolds and Sasaki-Einstein 5-manifolds. The chapter ends with a brief discussion of how Sasakian geometry naturally appears in various supersymmetric physical theories such as supergravity theory, superstring theory, and M-theory. In particular, Sasaki-Einstein 5-manifolds play a crucial role in the AdS/CFT duality conjecture.

Keywords:   AdS/CFT conjecture, Bär's correspondence, Dirac operator, Killing spinors, M-theory, nearly Kähler manifolds, weak holonomy G2 manifolds, supersymmetry, supergravity

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