Toric Sasaki-Einstein metrics on S2 × S3

By J. Gauntlett, D. Martelli, J. Sparks, D. Waldram. 2004

224 citations recorded by the source corpus.

Abstract We show that by taking a certain scaling limit of a Euclideanised form of the Plebanski–Demianski metrics one obtains a family of local toric Kahler–Einstein metrics. These can be used to construct local Sasaki–Einstein metrics in five dimensions which are generalisations of the Y p , q manifolds. In fact, we find that these metrics are diffeomorphic to those recently found by Cvetic, Lu, Page and Pope. We argue that the corresponding family of smooth Sasaki–Einstein manifolds all have topology S 2 × S 3 . We conclude by setting up the equations describing the warped version of the Calabi–Yau cones, supporting ( 2 , 1 ) three-form flux.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ea8f00df2b0ae7c3417ab15dfaeb3c982ab22452

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Citations in the corpus

The Dual superconformal theory for L**pqr manifolds (2005, methodology): “In this paper we presented the superconformal gauge theory dual to the type IIB background AdS × Lp,q,r constructed in [10, 11 ].”
Gauge theories from toric geometry and brane tilings (2005, background): “First, we recall the metrics [8], and how these are associated to the toric singularities discussed earlier [9].”
Sasaki–Einstein Manifolds and Volume Minimisation (2006, background): “This has subsequently been generalised to a three–parameter cohomogeneity two family L [12, 13, 14].”
Canonical Sasakian Metrics (2006, background): “ﬁrst examples of irregular Sasaki-Einstein manifolds, that is to say, Sasaki-Einstein manifolds that are not quasiregular, came ﬁrst from the physics surrounding the famous CFT/AdS Duality Conjecture [18, 19, 25, 26, 27, 28, 14]. It now appears that there are irregular structures of this type on man”
The Geometric Dual of a–Maximisation for Toric Sasaki–Einstein Manifolds (2005, background): “44) (8)This metric has recently been obtained in [36, 37, 38] as a member of an infinite family of toric Sasaki–Einstein metrics generalising Y .”
Sasaki-Einstein Manifolds (2010, unknown): “Moreover, in [37] (see also [70]) an infinite set of explicit cohomogeneity two Sasaki-Einstein metrics were presented on S2 × S3.”
Supersymmetric AdS3, AdS2 and bubble solutions (2006, background): “The Kähler geometries are toric and hence this construction is analogous to the construction of SE metrics of [12] (see also [13]).”
Dynamical SUSY breaking at meta-stable minima from D-branes at obstructed geometries (2006, background): “In addition to the papers mentioned in the introduction, some of the works that have been crucial for these developments are [11]–[15].”
Supersymmetric AdS5 solutions of type IIB supergravity (2005, methodology): “The Y metrics were generalized to all dimensions in [14–16] and were recently further generalized to the L metrics in [17, 18] (see also [19]).”
Supersymmetric states of N=4 Yang-Mills from giant gravitons (2006, background): “Over the last few years a number of authors have discovered an infinite number of generalizations of the AdS/CFT conjecture [68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78].”
From Sasaki-Einstein spaces to quivers via BPS geodesics: Lp,q|r (2005, background): “For the moment we will assume no non trivial common divisors, that leads [16] to smooth geometries.”
Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds (2006, background): “Examples of irregular Sasaki-Einstein metrics have been only recently known by Gauntlett, Martelli, Sparks and Waldrum [23], [24], [31],”
Ricci-flat Kähler metrics on crepant resolutions of Kähler cones (2008, methodology): “deﬁning X. We then list some examples which are easy to construct using toric geometry. 1. introduction There has been much research recently in constructing examples of SasakiEinstein manifolds (cf. [6, 5, 26, 16, 15, 14]). Recall that a Sasaki-Einstein manifold (S,g) is positive scalar curvature E”