Trivializing a Family of Sasaki-Einstein Spaces

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dc.creatorEvslin, Jarah
dc.creatorKuperstein, Stanislav
dc.date2008-03-21
dc.date.accessioned2026-07-07T12:30:01Z
dc.date.available2026-07-07T12:30:01Z
dc.descriptionWe 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.
dc.description25 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0803.3241
dc.identifierhttp://arxiv.org/abs/0803.3241
dc.identifierJHEP 0806:045,2008
dc.identifierdoi:10.1088/1126-6708/2008/06/045
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216024
dc.subjectHigh Energy Physics - Theory
dc.titleTrivializing a Family of Sasaki-Einstein Spaces
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