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

Advances in Theoretical and Mathematical Physics (Impact Factor: 1.35). 01/2004; 8(4). DOI: 10.4310/ATMP.2004.v8.n4.a3


We present a countably infinite number of new explicit co-homo-geneity 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.

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Available from: James Sparks
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    • "The metric (III.1) with A = 0 was studied in [7, 8, 20–22], where it was shown that the metric is obtained as an " off-shell " metric of the BPS limit of the odd-dimensional Kerr-NUT-(A)dS metric and leads to the toric Sasaki-Einstein metrics Y p,q and L a,b,c discovered by [4] [5] [6]. The metric (III.1) "
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    ABSTRACT: We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are K\"ahler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As an example of them, we present an explicit expression of local metrics and see how Sasakian structure is deformed by the presence of torsion. We also demonstrate that our example of the metrics admits the existence of hidden symmetries described by non-trivial odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using these metrics as an {\it ansatz}, we construct exact solutions in five dimensional minimal (un-)gauged supergravity and eleven dimensional supergravity. Finally, we discuss the global structures of the solutions and obtain regular metrics on compact manifolds in five dimensions, which give natural generalizations of Sasaki--Einstein manifolds $Y^{p,q}$ and $L^{a,b,c}$. We also discuss regular metrics on non-compact manifolds in eleven dimensions.
    Full-text · Article · Jul 2012 · Classical and Quantum Gravity
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    • "Prior to AdS/CMT research, the most well known examples in either Type IIB or D = 11 involved sphere reductions to maximally supersymmetric theories on S 5 [1] [2], S 7 [3] and S 4 [4]. A few years ago it was shown that the most general supersymmetric AdS 5 solutions of D = 11 supergravity [5] (of which Sasaki-Einstein Y p,q [6] belong) permits a consistent reduction to minimal N = 2 D = 5 gauged supergravity [7] [8]. Since then there have been subsequent studies on consistent reductions [9] [10], while the extension to examples incorporating massive modes appeared in [11] and [12]. "
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    ABSTRACT: By identifying a bosonic consistent truncation from the \frac14 \frac{1}{4} -BPS wrapped M5-brane geometry of Maldacena, Strominger and Witten in D = 11 supergravity and finding a supersymmetric extension, we recover an N = 2 D = 3 supergravity theory. Reductions of a large class of supersymmetric solutions corresponding to wrapped M2 and M5-branes lead to black strings and warped AdS3 solutions preserving supersymmetry. With a view to AdS/CMT applications, we also construct a numerical hairy BTZ black hole and, as a preliminary step in this direction, determine the conductivity of the dual CFT. KeywordsSupergravity Models–M-Theory–Holography and condensed matter physics (AdS/CMT)
    Preview · Article · Feb 2011 · Journal of High Energy Physics
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    • "Our proof uses the Tian-Yau-Zelditch (TYZ) expansion of the heat kernel [9] [10] [11] [12] which relates the Hilbert series to the curvatures of the 4d base and then we " undo " the Kaluza-Klein reduction to rewrite this in terms of the 5d total space. For several irregular Sasaki-Einstein manifolds where an explicit metric is known [13] we have verified by direct calculation that (1.1) also holds. We therefore conjecture that (1.1) holds not only for L 5 regular Sasaki- Einstein, but for quasi-regular and irregular Sasaki-Einstein manifolds as well. "
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    ABSTRACT: We compute the sub-leading terms in the Tian-Yau-Zelditch asymptotic expansion of the partition function for dual giant gravitons on AdS5 $\times$ L5 and provide a bulk interpretation in terms of curvature invariants. We accomplish this by relating the partition function of dual giant gravitons to the Hilbert series for mesonic operators in the CFT. The coefficients of the subleading terms encode integrated curvature invariants of L5. In the same spirit of Martelli, Sparks and Yau, we are able to compute these integrated curvature invariants without explicit knowledge of the Sasaki-Einstein metric on L5. These curvature invariants contribute to the 1/N^2 corrections of the difference of the 4D anomaly coefficients a and c recently found by Liu and Minasian, which we now have a purely field theoretic method of calculating. Comment: 17 pages
    Preview · Article · Nov 2010 · Journal of High Energy Physics
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