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Trivializing a family of Sasaki-Einstein spaces

par Evslin, JARAH J ;Kuperstein, Stanislav
Référence The Journal of high energy physics, 2008, 6, 045
Publication Publié, 2008-06

Article révisé par les pairs

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Résumé :

We construct an explicit diffeomorphism between the Sasaki-Einstein spaces Y p,q and the product space S 3 × S 2 in the cases q2. 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 2$"q>2 the fiber is a lens space which is not a Lie group, and this construction fails. We relate the S 2 × 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 × S 2.