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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

(p.529) Chapter 14 Sasakian Structures, Killing Spinors, and Supersymmetry
Sasakian Geometry

Charles P. Boyer

Krzysztof Galicki

Oxford University Press

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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