Trivializing a Family of Sasaki-Einstein Spaces
arXiv:0803.3241 · doi:10.1088/1126-6708/2008/06/045
Abstract
We construct an explicit diffeomorphism between the Sasaki-Einstein spaces Y^{p,q} and the product space S^3 \times S^2 in the cases q \le 2. When q=1 we express the Kähler quotient coordinates as an SU(2) bundle over S^2 which we trivialize. When q=2 the quotient coordinates yield a non-trivial SO(3) bundle over S^2 with characteristic class p, which is rotated to a bundle with characteristic class 1 and re-expressed as Y^{2,1}, reducing the problem to the case q=1. When q>2 the fiber is a lens space which is not a Lie group, and this construction fails. We relate the S^2 \times S^3 coordinates to those for which the Sasaki-Einstein metric is known. We check that the RR flux on the S^3 is normalized in accordance with Gauss' law and use this normalization to determine the homology classes represented by the calibrated cycles. As a by-product of our discussion we find a diffeomorphism between T^{p,q} and Y^{p,q} spaces, which means that T^{p,q} manifolds are also topologically S^3 \times S^2.
25 pages, 3 figures
References in corpus (21)
- Supergravity and a Confining Gauge Theory: Duality Cascades and SB-Resolution of Naked Singularities
- Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
- Gravity Duals of Supersymmetric SU(N) x SU(N+M) Gauge Theories
- Gauge Theories from Toric Geometry and Brane Tilings
- An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
- Dynamics of Supersymmetric Gauge Theory
- New Einstein-Sasaki Spaces in Five and Higher Dimensions
- Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
- Gravity Duals of Fractional Branes and Logarithmic RG Flow
- Toric Sasaki-Einstein metrics on S^2 x S^3
- From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr
- New checks and subtleties for AdS/CFT and a-maximization
- The dual superconformal theory for Lpqr manifolds
- Fractional Branes and Dynamical Supersymmetry Breaking
- Supersymmetry Breaking from a Calabi-Yau Singularity
- Supersymmetry breaking at the end of a cascade of Seiberg dualities
- Cascading RG Flows from New Sasaki-Einstein Manifolds
- Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
- Trivializing and Orbifolding the Conifold's Base
- Cascading Quivers from Decaying D-branes
- On the pp-wave limit and the BMN structure of new Sasaki-Einstein spaces