We show that for every positive curvature Khler-Einstein manifold in dimension 2n there is a countably infinite class of associated Sasaki-Einstein manifolds X 2n+3 in dimension 2n + 3. When n = 1 we recover a recently discovered family of supersymmetric AdS 5 X 5 solutions of type IIB string theory, while when n = 2 we obtain new supersymmetric AdS 4 X 7 solutions of D = 11 supergravity. Both are expected to provide new supergravity duals of superconformal field theories.
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Gauntlett et al. (2004) studied this question.
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