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

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James Sparks, Jul 05, 2015 Available from:- [Show abstract] [Hide abstract]

**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.Classical and Quantum Gravity 07/2012; 30(13). DOI:10.1088/0264-9381/30/13/135008 · 3.10 Impact Factor - [Show abstract] [Hide abstract]

**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)Journal of High Energy Physics 02/2011; 2011(2):1-25. DOI:10.1007/JHEP02(2011)031 · 6.22 Impact Factor - [Show abstract] [Hide abstract]

**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 pagesJournal of High Energy Physics 11/2010; 2013(10). DOI:10.1007/JHEP10(2013)209 · 6.22 Impact Factor