Article

# Sasaki-Einstein Metrics on S^2 x S^3

04/2004;
Source: arXiv

ABSTRACT We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on S^2 x S^3, in both the quasi-regular and irregular classes. These give rise to new solutions of type IIB supergravity which are expected to be dual to N=1 superconformal field theories in four-dimensions with compact or non-compact R-symmetry and rational or irrational central charges, respectively.

0 0
·
0 Bookmarks
·
50 Views
• Source
##### Article: The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence
[hide abstract]
ABSTRACT: We calculate the volumes of a large class of Einstein manifolds, namely Sasaki-Einstein manifolds which are the bases of Ricci-flat affine cones described by polynomial embedding relations in C^n. These volumes are important because they allow us to extend and test the AdS/CFT correspondence. We use these volumes to extend the central charge calculation of Gubser (1998) to the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999). These volumes also allow one to quantize precisely the D-brane flux of the AdS supergravity solution. We end by demonstrating a relationship between the volumes of these Einstein spaces and the number of holomorphic polynomials (which correspond to chiral primary operators in the field theory dual) on the corresponding affine cone. Comment: 25 pp, LaTeX, 1 figure, v2: refs added
08/2001;
• Source
##### Article: Supersymmetric AdS5 solutions of M-theory
[hide abstract]
ABSTRACT: We analyse the most general supersymmetric solutions of D = 11 supergravity consisting of a warped product of five-dimensional anti-de Sitter space with a six-dimensional Riemannian space M6, with 4-form flux on M6. We show that M6 is partly specified by a one-parameter family of four-dimensional Kähler metrics. We find a large family of new explicit regular solutions where M6 is a compact, complex manifold which is topologically a 2-sphere bundle over a four-dimensional base, where the latter is either (i) Kähler–Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki–Einstein spaces which includes . Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.
Classical and Quantum Gravity 08/2004; 21(18):4335. · 3.56 Impact Factor
• Source
##### Article: Branes at conical singularities and holography
[hide abstract]
ABSTRACT: For supergavrity solutions which are the product of an anti-de Sitter space with an Einstein space X, we study the relation between the amount of supersymmetry preserved and the geometry of X. Depending on the dimension and the amount of supersymmetry, the following geometries for X are possible, in addition to the maximally supersymmetric spherical geometry: Einstein-Sasaki in dimension 2k+1, 3-Sasaki in dimension 4k+3, 7-dimensional manifolds of weak G_2 holonomy and 6-dimensional nearly Kaehler manifolds. Many new examples of such manifolds are presented which are not homogeneous and have escaped earlier classification efforts. String or M theory in these vacua are conjectured to be dual to superconformal field theories. The brane solutions interpolating between these anti-de Sitter near-horizon geometries and the product of Minkowski space with a cone over X lead to an interpretation of the dual superconformal field theory as the world-volume theory for branes at a conical singularity (cone branes). We propose a description of those field theories whose associated cones are obtained by (hyper-)Kaehler quotients.
09/1998;