A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy

Chuang, W

doi:10.2172/827006

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2010

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“…Examples of complete metrics on non-compact manifolds in higher dimensions with G 2 and spin (7) holonomy were constructed in the later 1980s [16][17][18][19]. Inspired by the AdS/CFT correspondence and applications in M-theory compactification, large classes of explicit metrics on G 2 and spin (7) holonomy spaces have been constructed and their applications in string and M-theory have been discussed [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Constructing Calabi–Yau metrics from hyperkähler spaces

Lü¹,

Pang²,

Wang³

2010

Class. Quantum Grav.

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Recently, a metric construction for the Calabi-Yau 3-folds from a four-dimensional hyperkähler space by adding a complex line bundle was proposed. We extend the construction by adding a U (1) factor to the holomorphic (3, 0)-form, and obtain the explicit formalism for a generic hyperkähler base. We find that a discrete choice arises: the U (1) factor can either depend solely on the fibre coordinates or vanish. In each case, the metric is determined by one differential equation for the modified Kähler potential. As explicit examples, we obtain the generalized resolutions (up to orbifold singularity) of the cone of the Einstein-Sasaki spaces Y p,q . We also obtain a large class of new singular CY3 metrics with SU (2) × U (1) or SU (2) × U (1) 2 isometries.

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