Sasaki-Einstein Metrics on S^2\times S^3

Abstract

We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on S 2 × S 3 of both quasi-regular and irregular type. 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.

AdS3solutions of IIB supergravity from D3-branes

“…A couple of new, infinite class of Sasaki-Einstein manifolds were discovered recently [10,15]. They all turned out to be toric, and the dual conformal field theories given as quiver gauge theories have been identified.…”

“…Several important class of new solutions have been found using this method. Supersymmetric black ring solutions and Sasaki-Einstein manifolds Y p,q [9,10] are among them. A valuable insight into the gauge/gravity duality has been obtained from the analysis of IIB string solutions containing two factors of threespheres with unbroken supersymmetry [11].…”

New N $$ \mathcal{N} $$ =1 supersymmetric AdS 5 backgrounds in type IIA supergravity

“…We review only the essentials that are needed for our purpose and refer the reader to the original articles [6,7] for further explanations. The local form of the metric ia…”

“…The discovery of a countably infinite family of Sasaki-Einstein manifolds known as Y p,q in [6,7] provided a dramatic expansion in concrete examples of the correspondence. Up to that point, the only explicitly known metrics for X 5 were the round metric on S 5 and the homogenous space T 1,1 -with corresponding field theories being N = 4 SYM and the N = 1 two-node quiver of Klebanov and Witten [3].…”

Dimers and orientifolds

“…In general, gauge theories living on D3-branes at toric singularities 3 have a generic U(1) 3 global symmetry, associated to the toric action on the geometry. 4 This includes the U(1)R 3 In the absence of fractional branes this symmetry is not broken by quantum effects. In the presence of fractional branes, the symmetry is still present but may be broken by quantum effects.…”